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 * regarding copyright ownership.  The ASF licenses this file
 * to you under the Apache License, Version 2.0 (the
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 * Unless required by applicable law or agreed to in writing,
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 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
 * KIND, either express or implied.  See the License for the
 * specific language governing permissions and limitations
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 *
 *
 * @file madlib_keras_model_selection.sql_in
 *
 * @brief Explore network architectures and hyperparameters by training many models a time.
 * @date August 2019
 *
 *
 *//* ----------------------------------------------------------------------- */

m4_include(`SQLCommon.m4')

/**
@addtogroup grp_keras_run_model_selection

@brief Explore network architectures and hyperparameters by training many models a time.

<div class="toc"><b>Contents</b><ul>
<li class="level1"><a href="#keras_fit">Fit</a></li>
<li class="level1"><a href="#keras_evaluate">Evaluate</a></li>
<li class="level1"><a href="#keras_predict">Predict</a></li>
<li class="level1"><a href="#example">Examples</a></li>
<li class="level1"><a href="#notes">Notes</a></li>
<li class="level1"><a href="#background">Technical Background</a></li>
<li class="level1"><a href="#literature">Literature</a></li>
<li class="level1"><a href="#related">Related Topics</a></li>
</ul></div>

This module allows you to explore network architectures and
hyperparameters by training many models a time across the
database cluster.  

The aim is to support efficient empirical comparison of multiple
training configurations. This process is called model selection,
and the implementation here is based on a parallel execution strategy
called model hopper parallelism (MOP) [1,2].

Models are designed in Keras [3], which is a high-level neural
network API written in Python.  It can run
on top of different backends and the one that is currently
supported by MADlib is TensorFlow [4].

The main use case is classification
using sequential models, which are made up of a
linear stack of layers.  This includes multilayer perceptrons (MLPs)
and convolutional neural networks (CNNs).  Regression is not
currently supported.

Before using this model selection method, you will need to 
<a href="group__grp__input__preprocessor__dl.html">Prepocess Data</a>
which prepares data for
use by models that support mini-batch as an optimization option.
This is a one-time operation and you would only
need to re-run the preprocessor if your input data has changed.
The advantage of using mini-batching is that it
can perform better than stochastic gradient descent
because it uses more than one training example at a time,
typically resulting faster and smoother convergence [5].

You can set up the models and hyperparameters to try with the
<a href="group__grp__keras__setup__model__selection.html">Define Model
Configurations</a> function to define the unique combinations
of model architectures, compile and fit parameters.

@note 1. If 'madlib_keras_fit_multiple_model()' is running on GPDB 5 and some versions
of GPDB 6, the database will
keep adding to the disk space (in proportion to model size) and will only
release the disk space once the fit multiple query has completed execution.
This is not the case for GPDB 6.5.0+ where disk space is released during the
fit multiple query.

@note 2. CUDA GPU memory cannot be released until the process holding it is terminated.
When a MADlib deep learning function is called with GPUs, Greenplum internally
creates a process (called a slice) which calls TensorFlow to do the computation.
This process holds the GPU memory until one of the following two things happen:
query finishes and user logs out of the Postgres client/session; or,
query finishes and user waits for the timeout set by gp_vmem_idle_resource_timeout.
The default value for this timeout is 18 sec [8].  So the recommendation is:
log out/reconnect to the session after every GPU query; or
wait for gp_vmem_idle_resource_timeout before you run another GPU query (you can
also set it to a lower value).

@note 3. This method does not currently support multi-input or multi-output neural networks.


@anchor keras_fit
@par Fit
The fit (training) function has the following format:

<pre class="syntax">
madlib_keras_fit_multiple_model(
    source_table,
    model_output_table,
    model_selection_table,
    num_iterations,
    use_gpus,
    validation_table,
    metrics_compute_frequency,
    warm_start,
    name,
    description,
    use_caching
    )
</pre>

\b Arguments
<dl class="arglist">
  <dt>source_table</dt>
  <dd>TEXT. Name of the table containing the training data.
  This is the name of the output
  table from the data preprocessor.  Independent
  and dependent variables are specified in the preprocessor
  step which is why you do not need to explictly state
  them here as part of the fit function.</dd>

  <dt>model_output_table</dt>
  <dd>TEXT. Name of the output table containing the
  multiple models created.
  @note pg_temp is not allowed as an output table schema for fit multiple.
  Details of output tables are shown below.
  </dd>

  <dt>model_selection_table</dt>
  <dd>TEXT. Name of the table containing model selection parameters to be tried.
  Here we mean both hyper-parameter tuning and model architecture search.
  </dd>

  <DT>num_iterations</DT>
  <DD>INTEGER.  Number of iterations to train.

    @note
    This parameter is different than the number of passes over the dataset,
    which is commonly referred to as the number of epochs.  Since MADlib operates
    in a distributed system, the number of
    epochs is actually equal to this parameter 'num_iterations' X 'epochs' as
    specified in the Keras fit parameter.
  </DD>

  <DT>use_gpus (optional)</DT>
  <DD>BOOLEAN, default: FALSE (i.e., CPU). Determines whether GPUs
  are to be used for training the neural network.  Set to TRUE to use GPUs.

    @note
    This parameter must not conflict with how the distribution rules are set in
    the preprocessor function.  For example, if you set a distribution rule to use
    certain segments on hosts that do not have GPUs attached, you will get an error
    if you set ‘use_gpus’ to TRUE.  Also, we have seen some memory related issues
    when segments share GPU resources.
    For example, if you have 1 GPU per segment host and your cluster has 4
    segments per segment host, it means that all 4
    segments will share the same
    GPU on each host. The current recommended
    configuration is 1 GPU per segment.
  </DD>

  <dt>validation_table (optional)</dt>
  <dd>TEXT, default: none. Name of the table containing
  the validation dataset.
  Note that the validation dataset must be preprocessed
  in the same way as the training dataset, so this
  is the name of the output
  table from running the data preprocessor on the validation dataset.
  Using a validation dataset can mean a
  longer training time, depending on its size.
  This can be controlled using the 'metrics_compute_frequency'
  parameter described below.</dd>

  <DT>metrics_compute_frequency (optional)</DT>
  <DD>INTEGER, default: once at the end of training
  after 'num_iterations'.  Frequency to compute per-iteration
  metrics for the training dataset and validation dataset
  (if specified).  There can be considerable cost to
  computing metrics every iteration, especially if the
  training dataset is large.  This parameter is a way of
  controlling the frequency of those computations.
  For example, if you specify 5, then metrics will be computed
  every 5 iterations as well as at the end of training
  after 'num_iterations'.  If you use the default,
  metrics will be computed only
  once after 'num_iterations' have completed.
  </DD>

  <DT>warm_start (optional)</DT>
  <DD>BOOLEAN, default: FALSE.
    Initalize weights with the coefficients
    from the last call to the fit
    function. If set to TRUE, weights will be
    initialized from the model table
    generated by the previous training run.

    @note
    The warm start feature works based on the name of the
    model output table from a previous training run.
    When using warm start, do not drop the model output table
    or the model output summary table
    before calling the fit function, since these are needed to obtain the
    weights from the previous run.
    If you are not using warm start, the model output table
    and the model output table summary must be dropped in
    the usual way before calling the training function.
  </DD>

  <DT>name (optional)</DT>
  <DD>TEXT, default: NULL.
    Free text string to identify a name, if desired.
  </DD>

  <DT>description (optional)</DT>
  <DD>TEXT, default: NULL.
    Free text string to provide a description, if desired.
  </DD>

  <DT>use_caching (optional)</DT>
  <DD>BOOLEAN, default: FALSE. Use caching of data in memory on the
  segment in order to speed up processing.

  @note
  When set to TRUE, byte arrays on each segment are maintained
  in cache (SD). This can speed up training significantly, however the
  memory usage per segment increases.  In effect, it
  requires enough available memory on a segment so that all training data
  residing on that segment can be read into memory.
</dl>

<b>Output tables</b>
<br>
    The model output table produced by fit contains the following columns.
    There is one row per model as per the rows in the 'model_selection_table':
    <table class="output">
      <tr>
        <th>mst_key</th>
        <td>INTEGER. ID that defines a unique tuple for model architecture-compile parameters-fit parameters,
        as defined in the 'model_selection_table'.</td>
      </tr>
      <tr>
        <th>model_weights</th>
        <td>BYTEA8. Byte array containing the weights of the neural net.</td>
      </tr>
      <tr>
        <th>model_arch</th>
        <td>TEXT. A JSON representation of the model architecture
        used in training.</td>
      </tr>
    </table>

    An info table named \<model_output_table\>_info is also created, which has the following columns.
    There is one row per model as per the rows in the 'model_selection_table':
    <table class="output">
      <tr>
        <th>mst_key</th>
        <td>INTEGER. ID that defines a unique tuple for model architecture-compile parameters-fit parameters,
        as defined in the 'model_selection_table'.</td>
      </tr>
      <tr>
        <th>model_id</th>
        <td>INTEGER. ID that defines model in the 'model_arch_table'.</td>
      </tr>
      <tr>
        <th>compile_params</th>
        <td>Compile parameters passed to Keras.</td>
    </tr>
    <tr>
        <th>fit_params</th>
        <td>Fit parameters passed to Keras.</td>
    </tr>
    <tr>
        <th>model_type</th>
        <td>General identifier for type of model trained.
        Currently says 'madlib_keras'.</td>
    </tr>
    <tr>
        <th>model_size</th>
        <td>Size of the model in KB.  Models are stored in
        'bytea' data format which is used for binary strings
        in PostgreSQL type databases.</td>
    </tr>
    <tr>
        <th>metrics_elapsed_time</th>
        <td> Array of elapsed time for metric computations as
        per the 'metrics_compute_frequency' parameter.
        Useful for drawing a curve showing loss, accuracy or
        other metrics as a function of time.
        For example, if 'metrics_compute_frequency=5'
        this would be an array of elapsed time for every 5th
        iteration, plus the last iteration.
        Note that this field reports the time for training +
        validation if there is a validation table provided.</td>
    </tr>
    <tr>
        <th>metrics_type</th>
        <td>Metric specified in the 'compile_params'.</td>
    </tr>
    <tr>
        <th>loss_type</th>
        <td>Loss specified in the 'compile_params'.</td>
    </tr>
    <tr>
        <th>training_metrics_final</th>
        <td>Final value of the training
        metric after all iterations have completed.
        The metric reported is the one
        specified in the 'metrics_type' parameter.</td>
    </tr>
    <tr>
        <th>training_loss_final</th>
        <td>Final value of the training loss after all
        iterations have completed.</td>
    </tr>
    <tr>
        <th>training_metrics</th>
        <td>Array of training metrics as
        per the 'metrics_compute_frequency' parameter.
        For example, if 'metrics_compute_frequency=5'
        this would be an array of metrics for every 5th
        iteration, plus the last iteration.</td>
    </tr>
    <tr>
        <th>training_loss</th>
        <td>Array of training losses as
        per the 'metrics_compute_frequency' parameter.
        For example, if 'metrics_compute_frequency=5'
        this would be an array of losses for every 5th
        iteration, plus the last iteration.</td>
    </tr>
    <tr>
        <th>validation_metrics_final</th>
        <td>Final value of the validation
        metric after all iterations have completed.
        The metric reported is the one
        specified in the 'metrics_type' parameter.</td>
    </tr>
    <tr>
        <th>validation_loss_final</th>
        <td>Final value of the validation loss after all
        iterations have completed.</td>
    </tr>
    <tr>
        <th>validation_metrics</th>
        <td>Array of validation metrics as
        per the 'metrics_compute_frequency' parameter.
        For example, if 'metrics_compute_frequency=5'
        this would be an array of metrics for every 5th
        iteration, plus the last iteration.</td>
    </tr>
    <tr>
        <th>validation_loss</th>
        <td>Array of validation losses as
        per the 'metrics_compute_frequency' parameter.
        For example, if 'metrics_compute_frequency=5'
        this would be an array of losses for every 5th
        iteration, plus the last iteration.</td>
    </tr>

    </table>

    A summary table named \<model\>_summary is also created, which has the following columns:
    <table class="output">
    <tr>
        <th>source_table</th>
        <td>Source table used for training.</td>
    </tr>
    <tr>
        <th>validation_table</th>
        <td>Name of the table containing
        the validation dataset (if specified).</td>
    </tr>
    <tr>
        <th>model</th>
        <td>Name of the output table containing
        the model for each model selection tuple.</td>
    </tr>
    <tr>
        <th>model_info</th>
        <td>Name of the output table containing
        the model performance and other info for
        each model selection tuple.</td>
    </tr>
    <tr>
        <th>dependent_varname</th>
        <td>Dependent variable column from the original
        source table in the data preprocessing step.</td>
    </tr>
    <tr>
        <th>independent_varname</th>
        <td>Independent variables column from the original
        source table in the data preprocessing step.</td>
    </tr>
    <tr>
        <th>model_arch_table</th>
        <td>Name of the table containing
        the model architecture and (optionally) the
        initial model weights.</td>
    </tr>
    <tr>
        <th>num_iterations</th>
        <td>Number of iterations of training completed.</td>
    </tr>
    <tr>
        <th>metrics_compute_frequency</th>
        <td>Frequency that per-iteration metrics are computed
        for the training dataset and validation
        datasets.</td>
    </tr>
    <tr>
        <th>warm_start</th>
        <td>Indicates whether warm start used or not.</td>
    </tr>
    <tr>
        <th>name</th>
        <td>Name of the training run (free text).</td>
    </tr>
    <tr>
        <th>description</th>
        <td>Description of the training run (free text).</td>
    </tr>
    <tr>
        <th>start_training_time</th>
        <td>Timestamp for start of training.</td>
    </tr>
    <tr>
        <th>end_training_time</th>
        <td>Timestamp for end of training.</td>
    </tr>
    <tr>
        <th>madlib_version</th>
        <td>Version of MADlib used.</td>
    </tr>
    <tr>
        <th>num_classes</th>
        <td>Count of distinct classes values used.</td>
    </tr>
    <tr>
        <th><dependent_varname>_class_values</th>
        <td>Array of actual class values used for a particular dependent
        variable. A column will be generated for each dependent variable.</td>
    </tr>
    <tr>
        <th>dependent_vartype</th>
        <td>Data type of the dependent variable.</td>
    </tr>
    <tr>
        <th>normalizing_constant</th>
        <td>Normalizing constant used from the
        data preprocessing step.</td>
    </tr>
    <tr>
        <th>metrics_iters</th>
        <td>Array indicating the iterations for which
        metrics are calculated, as derived from the
        parameters 'num_iterations' and 'metrics_compute_frequency'.
        For example, if 'num_iterations=5'
        and 'metrics_compute_frequency=2', then 'metrics_iters' value
        would be {2,4,5} indicating that metrics were computed
        at iterations 2, 4 and 5 (at the end).
        If 'num_iterations=5'
        and 'metrics_compute_frequency=1', then 'metrics_iters' value
        would be {1,2,3,4,5} indicating that metrics were computed
        at every iteration.</td>
    </tr>
   </table>

@anchor keras_evaluate
@par Evaluate
The evaluation function has the following format:

<pre class="syntax">
madlib_keras_evaluate(
    model_table,
    test_table,
    output_table,
    use_gpus,
    mst_key
    )
</pre>

\b Arguments
<dl class="arglist">

<DT>model_table</DT>
  <DD>TEXT. Name of the table containing the model
  to use for validation.
  </DD>

  <DT>test_table</DT>
  <dd>TEXT. Name of the table containing the evaluation dataset.
  Note that test/validation data must be preprocessed in the same
  way as the training dataset, so
  this is the name of the output
  table from the data preprocessor.  Independent
  and dependent variables are specified in the preprocessor
  step which is why you do not need to explictly state
  them here as part of the fit function.</dd>

  <DT>output_table</DT>
  <DD>TEXT. Name of table that validation output will be
  written to. Table contains:</DD>
    <table class="output">
      <tr>
        <th>loss</th>
        <td>Loss value on evaluation dataset, where 'loss_type'
        below identifies the type of loss.</td>
      </tr>
      <tr>
        <th>metric</th>
        <td>Metric value on evaluation dataset, where 'metrics_type'
        below identifies the type of metric.</td>
      </tr>
      <tr>
        <th>metrics_type</th>
        <td>Type of metric used that was used in the training step.
        (It means you cannot have a different metric in evaluate compared
        to training.)</td>
      </tr>
      <tr>
        <th>loss_type</th>
        <td>Type of loss function that was used in the training step.
        (It means you cannot have a different loss in evaluate compared
        to training.)</td>
      </tr>

  <DT>use_gpus (optional)</DT>
  <DD>BOOLEAN, default: FALSE (i.e., CPU). Determines whether GPUs
  are to be used for training the neural network.  Set to TRUE to use GPUs.

    @note
    This parameter must not conflict with how the distribution rules are set in
    the preprocessor function.  For example, if you set a distribution rule to use
    certain segments on hosts that do not have GPUs attached, you will get an error
    if you set ‘use_gpus’ to TRUE.  Also, we have seen some memory related issues
    when segments share GPU resources.
    For example, if you have 1 GPU per segment host and your cluster has 4
    segments per segment host, it means that all 4
    segments will share the same
    GPU on each host. The current recommended
    configuration is 1 GPU per segment.
  </DD>

  <DT>mst_key (optional)</DT>
  <DD>INTEGER, default: NULL. ID that defines a unique tuple for
  model architecture-compile parameters-fit parameters as defined in the model
  selection table.
  </DD>
</DL>

@anchor keras_predict
@par Predict
The prediction function has the following format:
<pre class="syntax">
madlib_keras_predict(
    model_table,
    test_table,
    id_col,
    independent_varname,
    output_table,
    pred_type,
    use_gpus,    
    mst_key
    )
</pre>

\b Arguments
<dl class="arglist">

<DT>model_table</DT>
  <DD>TEXT. Name of the table containing the model
  to use for prediction.
  </DD>

  <DT>test_table</DT>
  <DD>TEXT. Name of the table containing the dataset to
  predict on.  Note that test data is not preprocessed (unlike
  fit and evaluate) so put one test image per row for prediction.
  Also see the comment below for the 'independent_varname' parameter
  regarding normalization.

  </DD>

  <DT>id_col</DT>
  <DD>TEXT. Name of the id column in the test data table.
  </DD>

  <DT>independent_varname</DT>
  <DD>TEXT. Column with independent variables in the test table.
  If a 'normalizing_const' is specified when preprocessing the
  training dataset, this same normalization will be applied to
  the independent variables used in predict.
  </DD>

  <DT>output_table</DT>
  <DD>TEXT. Name of the table that prediction output will be
  written to. Table contains:</DD>
    <table class="output">
      <tr>
        <th>id</th>
        <td>Gives the 'id' for each prediction, corresponding to each row from
        the test_table.</td>
      </tr>
      <tr>
        <th>class_name</th>
        <td>
        The estimated variable.
        </td>
      </tr>
      <tr>
        <th>class_value</th>
        <td>
        The estimated class for classification.
        </td>
      </tr>
      <tr>
        <th>prob</th>
        <td>
        Probability of a given class.
        </td>
      </tr>
      <tr>
        <th>rank</th>
        <td>
        The rank of a given class based on the ordering of probabilities.
        </td>
      </tr>

  <DT>pred_type (optional)</DT>
  <DD>TEXT or INTEGER or DOUBLE PRECISION default: 'prob'.
  The type and range of output desired. This parameter allows the following options.
  - 'response': the actual prediction
  - 'prob': the probability value for each class
  - 0<value<1: the lower limit for the probability (double precision)
  - 1<=value: the lower limit for the rank of the prediction (integer)
  </DD>

  <DT>use_gpus (optional)</DT>
  <DD>BOOLEAN, default: FALSE (i.e., CPU). Determines
  whether GPUs are to be used for prediction/inference.
  Set to TRUE to use GPUs.

    @note
    The prediction function uses the whole cluster.  If you are using GPUs, it
    requires that GPUs are attached to all hosts, and that there are the same number
    of GPUs on each host (homogeneous cluster).  This is different from the fit()
    and evaluate() functions that support GPUs on only some of the hosts (heterogeneous cluster).
    Therefore, if you have GPUs only on some of the hosts, or an uneven numbers of GPUs per host, then
    set this parameter to FALSE to use CPUs.
  </DD>

  <DT>mst_key (optional)</DT>
  <DD>INTEGER, default: NULL. ID that defines a unique tuple for
  model architecture-compile parameters-fit parameters as defined in the model
  selection table.
  </DD>
</DL>

@anchor example
@par Examples

@note
Deep learning works best on very large datasets,
but that is not convenient for a quick introduction
to the syntax. So in this example we use an MLP on the well
known iris data set from https://archive.ics.uci.edu/ml/datasets/iris.
For more realistic examples with images please refer
to the deep learning notebooks
at https://github.com/apache/madlib-site/tree/asf-site/community-artifacts.

<h4>Classification</h4>

-#  Create an input data set.
<pre class="example">
DROP TABLE IF EXISTS iris_data;
CREATE TABLE iris_data(
    id serial,
    attributes numeric[],
    class_text varchar
);
INSERT INTO iris_data(id, attributes, class_text) VALUES
(1,ARRAY[5.1,3.5,1.4,0.2],'Iris-setosa'),
(2,ARRAY[4.9,3.0,1.4,0.2],'Iris-setosa'),
(3,ARRAY[4.7,3.2,1.3,0.2],'Iris-setosa'),
(4,ARRAY[4.6,3.1,1.5,0.2],'Iris-setosa'),
(5,ARRAY[5.0,3.6,1.4,0.2],'Iris-setosa'),
(6,ARRAY[5.4,3.9,1.7,0.4],'Iris-setosa'),
(7,ARRAY[4.6,3.4,1.4,0.3],'Iris-setosa'),
(8,ARRAY[5.0,3.4,1.5,0.2],'Iris-setosa'),
(9,ARRAY[4.4,2.9,1.4,0.2],'Iris-setosa'),
(10,ARRAY[4.9,3.1,1.5,0.1],'Iris-setosa'),
(11,ARRAY[5.4,3.7,1.5,0.2],'Iris-setosa'),
(12,ARRAY[4.8,3.4,1.6,0.2],'Iris-setosa'),
(13,ARRAY[4.8,3.0,1.4,0.1],'Iris-setosa'),
(14,ARRAY[4.3,3.0,1.1,0.1],'Iris-setosa'),
(15,ARRAY[5.8,4.0,1.2,0.2],'Iris-setosa'),
(16,ARRAY[5.7,4.4,1.5,0.4],'Iris-setosa'),
(17,ARRAY[5.4,3.9,1.3,0.4],'Iris-setosa'),
(18,ARRAY[5.1,3.5,1.4,0.3],'Iris-setosa'),
(19,ARRAY[5.7,3.8,1.7,0.3],'Iris-setosa'),
(20,ARRAY[5.1,3.8,1.5,0.3],'Iris-setosa'),
(21,ARRAY[5.4,3.4,1.7,0.2],'Iris-setosa'),
(22,ARRAY[5.1,3.7,1.5,0.4],'Iris-setosa'),
(23,ARRAY[4.6,3.6,1.0,0.2],'Iris-setosa'),
(24,ARRAY[5.1,3.3,1.7,0.5],'Iris-setosa'),
(25,ARRAY[4.8,3.4,1.9,0.2],'Iris-setosa'),
(26,ARRAY[5.0,3.0,1.6,0.2],'Iris-setosa'),
(27,ARRAY[5.0,3.4,1.6,0.4],'Iris-setosa'),
(28,ARRAY[5.2,3.5,1.5,0.2],'Iris-setosa'),
(29,ARRAY[5.2,3.4,1.4,0.2],'Iris-setosa'),
(30,ARRAY[4.7,3.2,1.6,0.2],'Iris-setosa'),
(31,ARRAY[4.8,3.1,1.6,0.2],'Iris-setosa'),
(32,ARRAY[5.4,3.4,1.5,0.4],'Iris-setosa'),
(33,ARRAY[5.2,4.1,1.5,0.1],'Iris-setosa'),
(34,ARRAY[5.5,4.2,1.4,0.2],'Iris-setosa'),
(35,ARRAY[4.9,3.1,1.5,0.1],'Iris-setosa'),
(36,ARRAY[5.0,3.2,1.2,0.2],'Iris-setosa'),
(37,ARRAY[5.5,3.5,1.3,0.2],'Iris-setosa'),
(38,ARRAY[4.9,3.1,1.5,0.1],'Iris-setosa'),
(39,ARRAY[4.4,3.0,1.3,0.2],'Iris-setosa'),
(40,ARRAY[5.1,3.4,1.5,0.2],'Iris-setosa'),
(41,ARRAY[5.0,3.5,1.3,0.3],'Iris-setosa'),
(42,ARRAY[4.5,2.3,1.3,0.3],'Iris-setosa'),
(43,ARRAY[4.4,3.2,1.3,0.2],'Iris-setosa'),
(44,ARRAY[5.0,3.5,1.6,0.6],'Iris-setosa'),
(45,ARRAY[5.1,3.8,1.9,0.4],'Iris-setosa'),
(46,ARRAY[4.8,3.0,1.4,0.3],'Iris-setosa'),
(47,ARRAY[5.1,3.8,1.6,0.2],'Iris-setosa'),
(48,ARRAY[4.6,3.2,1.4,0.2],'Iris-setosa'),
(49,ARRAY[5.3,3.7,1.5,0.2],'Iris-setosa'),
(50,ARRAY[5.0,3.3,1.4,0.2],'Iris-setosa'),
(51,ARRAY[7.0,3.2,4.7,1.4],'Iris-versicolor'),
(52,ARRAY[6.4,3.2,4.5,1.5],'Iris-versicolor'),
(53,ARRAY[6.9,3.1,4.9,1.5],'Iris-versicolor'),
(54,ARRAY[5.5,2.3,4.0,1.3],'Iris-versicolor'),
(55,ARRAY[6.5,2.8,4.6,1.5],'Iris-versicolor'),
(56,ARRAY[5.7,2.8,4.5,1.3],'Iris-versicolor'),
(57,ARRAY[6.3,3.3,4.7,1.6],'Iris-versicolor'),
(58,ARRAY[4.9,2.4,3.3,1.0],'Iris-versicolor'),
(59,ARRAY[6.6,2.9,4.6,1.3],'Iris-versicolor'),
(60,ARRAY[5.2,2.7,3.9,1.4],'Iris-versicolor'),
(61,ARRAY[5.0,2.0,3.5,1.0],'Iris-versicolor'),
(62,ARRAY[5.9,3.0,4.2,1.5],'Iris-versicolor'),
(63,ARRAY[6.0,2.2,4.0,1.0],'Iris-versicolor'),
(64,ARRAY[6.1,2.9,4.7,1.4],'Iris-versicolor'),
(65,ARRAY[5.6,2.9,3.6,1.3],'Iris-versicolor'),
(66,ARRAY[6.7,3.1,4.4,1.4],'Iris-versicolor'),
(67,ARRAY[5.6,3.0,4.5,1.5],'Iris-versicolor'),
(68,ARRAY[5.8,2.7,4.1,1.0],'Iris-versicolor'),
(69,ARRAY[6.2,2.2,4.5,1.5],'Iris-versicolor'),
(70,ARRAY[5.6,2.5,3.9,1.1],'Iris-versicolor'),
(71,ARRAY[5.9,3.2,4.8,1.8],'Iris-versicolor'),
(72,ARRAY[6.1,2.8,4.0,1.3],'Iris-versicolor'),
(73,ARRAY[6.3,2.5,4.9,1.5],'Iris-versicolor'),
(74,ARRAY[6.1,2.8,4.7,1.2],'Iris-versicolor'),
(75,ARRAY[6.4,2.9,4.3,1.3],'Iris-versicolor'),
(76,ARRAY[6.6,3.0,4.4,1.4],'Iris-versicolor'),
(77,ARRAY[6.8,2.8,4.8,1.4],'Iris-versicolor'),
(78,ARRAY[6.7,3.0,5.0,1.7],'Iris-versicolor'),
(79,ARRAY[6.0,2.9,4.5,1.5],'Iris-versicolor'),
(80,ARRAY[5.7,2.6,3.5,1.0],'Iris-versicolor'),
(81,ARRAY[5.5,2.4,3.8,1.1],'Iris-versicolor'),
(82,ARRAY[5.5,2.4,3.7,1.0],'Iris-versicolor'),
(83,ARRAY[5.8,2.7,3.9,1.2],'Iris-versicolor'),
(84,ARRAY[6.0,2.7,5.1,1.6],'Iris-versicolor'),
(85,ARRAY[5.4,3.0,4.5,1.5],'Iris-versicolor'),
(86,ARRAY[6.0,3.4,4.5,1.6],'Iris-versicolor'),
(87,ARRAY[6.7,3.1,4.7,1.5],'Iris-versicolor'),
(88,ARRAY[6.3,2.3,4.4,1.3],'Iris-versicolor'),
(89,ARRAY[5.6,3.0,4.1,1.3],'Iris-versicolor'),
(90,ARRAY[5.5,2.5,4.0,1.3],'Iris-versicolor'),
(91,ARRAY[5.5,2.6,4.4,1.2],'Iris-versicolor'),
(92,ARRAY[6.1,3.0,4.6,1.4],'Iris-versicolor'),
(93,ARRAY[5.8,2.6,4.0,1.2],'Iris-versicolor'),
(94,ARRAY[5.0,2.3,3.3,1.0],'Iris-versicolor'),
(95,ARRAY[5.6,2.7,4.2,1.3],'Iris-versicolor'),
(96,ARRAY[5.7,3.0,4.2,1.2],'Iris-versicolor'),
(97,ARRAY[5.7,2.9,4.2,1.3],'Iris-versicolor'),
(98,ARRAY[6.2,2.9,4.3,1.3],'Iris-versicolor'),
(99,ARRAY[5.1,2.5,3.0,1.1],'Iris-versicolor'),
(100,ARRAY[5.7,2.8,4.1,1.3],'Iris-versicolor'),
(101,ARRAY[6.3,3.3,6.0,2.5],'Iris-virginica'),
(102,ARRAY[5.8,2.7,5.1,1.9],'Iris-virginica'),
(103,ARRAY[7.1,3.0,5.9,2.1],'Iris-virginica'),
(104,ARRAY[6.3,2.9,5.6,1.8],'Iris-virginica'),
(105,ARRAY[6.5,3.0,5.8,2.2],'Iris-virginica'),
(106,ARRAY[7.6,3.0,6.6,2.1],'Iris-virginica'),
(107,ARRAY[4.9,2.5,4.5,1.7],'Iris-virginica'),
(108,ARRAY[7.3,2.9,6.3,1.8],'Iris-virginica'),
(109,ARRAY[6.7,2.5,5.8,1.8],'Iris-virginica'),
(110,ARRAY[7.2,3.6,6.1,2.5],'Iris-virginica'),
(111,ARRAY[6.5,3.2,5.1,2.0],'Iris-virginica'),
(112,ARRAY[6.4,2.7,5.3,1.9],'Iris-virginica'),
(113,ARRAY[6.8,3.0,5.5,2.1],'Iris-virginica'),
(114,ARRAY[5.7,2.5,5.0,2.0],'Iris-virginica'),
(115,ARRAY[5.8,2.8,5.1,2.4],'Iris-virginica'),
(116,ARRAY[6.4,3.2,5.3,2.3],'Iris-virginica'),
(117,ARRAY[6.5,3.0,5.5,1.8],'Iris-virginica'),
(118,ARRAY[7.7,3.8,6.7,2.2],'Iris-virginica'),
(119,ARRAY[7.7,2.6,6.9,2.3],'Iris-virginica'),
(120,ARRAY[6.0,2.2,5.0,1.5],'Iris-virginica'),
(121,ARRAY[6.9,3.2,5.7,2.3],'Iris-virginica'),
(122,ARRAY[5.6,2.8,4.9,2.0],'Iris-virginica'),
(123,ARRAY[7.7,2.8,6.7,2.0],'Iris-virginica'),
(124,ARRAY[6.3,2.7,4.9,1.8],'Iris-virginica'),
(125,ARRAY[6.7,3.3,5.7,2.1],'Iris-virginica'),
(126,ARRAY[7.2,3.2,6.0,1.8],'Iris-virginica'),
(127,ARRAY[6.2,2.8,4.8,1.8],'Iris-virginica'),
(128,ARRAY[6.1,3.0,4.9,1.8],'Iris-virginica'),
(129,ARRAY[6.4,2.8,5.6,2.1],'Iris-virginica'),
(130,ARRAY[7.2,3.0,5.8,1.6],'Iris-virginica'),
(131,ARRAY[7.4,2.8,6.1,1.9],'Iris-virginica'),
(132,ARRAY[7.9,3.8,6.4,2.0],'Iris-virginica'),
(133,ARRAY[6.4,2.8,5.6,2.2],'Iris-virginica'),
(134,ARRAY[6.3,2.8,5.1,1.5],'Iris-virginica'),
(135,ARRAY[6.1,2.6,5.6,1.4],'Iris-virginica'),
(136,ARRAY[7.7,3.0,6.1,2.3],'Iris-virginica'),
(137,ARRAY[6.3,3.4,5.6,2.4],'Iris-virginica'),
(138,ARRAY[6.4,3.1,5.5,1.8],'Iris-virginica'),
(139,ARRAY[6.0,3.0,4.8,1.8],'Iris-virginica'),
(140,ARRAY[6.9,3.1,5.4,2.1],'Iris-virginica'),
(141,ARRAY[6.7,3.1,5.6,2.4],'Iris-virginica'),
(142,ARRAY[6.9,3.1,5.1,2.3],'Iris-virginica'),
(143,ARRAY[5.8,2.7,5.1,1.9],'Iris-virginica'),
(144,ARRAY[6.8,3.2,5.9,2.3],'Iris-virginica'),
(145,ARRAY[6.7,3.3,5.7,2.5],'Iris-virginica'),
(146,ARRAY[6.7,3.0,5.2,2.3],'Iris-virginica'),
(147,ARRAY[6.3,2.5,5.0,1.9],'Iris-virginica'),
(148,ARRAY[6.5,3.0,5.2,2.0],'Iris-virginica'),
(149,ARRAY[6.2,3.4,5.4,2.3],'Iris-virginica'),
(150,ARRAY[5.9,3.0,5.1,1.8],'Iris-virginica');
</pre>
Create a test/validation dataset from the training data:
<pre class="example">
DROP TABLE IF EXISTS iris_train, iris_test;
-- Set seed so results are reproducible
SELECT setseed(0);
SELECT madlib.train_test_split('iris_data',     -- Source table
                               'iris',          -- Output table root name
                                0.8,            -- Train proportion
                                NULL,           -- Test proportion (0.2)
                                NULL,           -- Strata definition
                                NULL,           -- Output all columns
                                NULL,           -- Sample without replacement
                                TRUE            -- Separate output tables
                              );
SELECT COUNT(*) FROM iris_train;
</pre>
<pre class="result">
 count
------+
   120
</pre>

-# Call the preprocessor for deep learning.  For the training dataset:
<pre class="example">
\\x on
DROP TABLE IF EXISTS iris_train_packed, iris_train_packed_summary;
SELECT madlib.training_preprocessor_dl('iris_train',         -- Source table
                                       'iris_train_packed',  -- Output table
                                       'class_text',         -- Dependent variable
                                       'attributes'          -- Independent variable
                                        );
SELECT * FROM iris_train_packed_summary;
</pre>
<pre class="result">
-[ RECORD 1 ]-------+---------------------------------------------
source_table        | iris_train
output_table        | iris_train_packed
dependent_varname   | class_text
independent_varname | attributes
dependent_vartype   | character varying
class_values        | {Iris-setosa,Iris-versicolor,Iris-virginica}
buffer_size         | 60
normalizing_const   | 1.0
num_classes         | 3
</pre>
For the validation dataset:
<pre class="example">
DROP TABLE IF EXISTS iris_test_packed, iris_test_packed_summary;
SELECT madlib.validation_preprocessor_dl('iris_test',          -- Source table
                                         'iris_test_packed',   -- Output table
                                         'class_text',         -- Dependent variable
                                         'attributes',         -- Independent variable
                                         'iris_train_packed'   -- From training preprocessor step
                                          );
SELECT * FROM iris_test_packed_summary;
</pre>
<pre class="result">
-[ RECORD 1 ]-------+---------------------------------------------
source_table        | iris_test
output_table        | iris_test_packed
dependent_varname   | class_text
independent_varname | attributes
dependent_vartype   | character varying
class_values        | {Iris-setosa,Iris-versicolor,Iris-virginica}
buffer_size         | 15
normalizing_const   | 1.0
num_classes         | 3
</pre>

-# Define and load model architecture.  Use Keras to define
the model architecture with 1 hidden layer:
<pre class="example">
from tensorflow import keras
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense
model1 = Sequential()
model1.add(Dense(10, activation='relu', input_shape=(4,)))
model1.add(Dense(10, activation='relu'))
model1.add(Dense(3, activation='softmax'))
model1.summary()
\verbatim

_________________________________________________________________
Layer (type)                 Output Shape              Param #
=================================================================
dense_1 (Dense)              (None, 10)                50
_________________________________________________________________
dense_2 (Dense)              (None, 10)                110
_________________________________________________________________
dense_3 (Dense)              (None, 3)                 33
=================================================================
Total params: 193
Trainable params: 193
Non-trainable params: 0
\endverbatim
</pre>
Export the model to JSON:
<pre class="example">
model1.to_json()
</pre>
<pre class="result">
'{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_1", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}'
</pre>
Define model architecture with 2 hidden layers:
<pre class="example">
model2 = Sequential()
model2.add(Dense(10, activation='relu', input_shape=(4,)))
model2.add(Dense(10, activation='relu'))
model2.add(Dense(10, activation='relu'))
model2.add(Dense(3, activation='softmax'))
model2.summary()
\verbatim

Layer (type)                 Output Shape              Param #
=================================================================
dense_4 (Dense)              (None, 10)                50
_________________________________________________________________
dense_5 (Dense)              (None, 10)                110
_________________________________________________________________
dense_6 (Dense)              (None, 10)                110
_________________________________________________________________
dense_7 (Dense)              (None, 3)                 33
=================================================================
Total params: 303
Trainable params: 303
Non-trainable params: 0
\endverbatim
</pre>
Export the model to JSON:
<pre class="example">
model2.to_json()
</pre>
<pre class="result">
'{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_4", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_5", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_6", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_7", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}'
</pre>
Load into model architecture table:
<pre class="example">
DROP TABLE IF EXISTS model_arch_library;
SELECT madlib.load_keras_model('model_arch_library',  -- Output table,
$$
{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_1", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}
$$
::json,         -- JSON blob
                               NULL,                  -- Weights
                               'Sophie',              -- Name
                               'MLP with 1 hidden layer'       -- Descr
);
SELECT madlib.load_keras_model('model_arch_library',  -- Output table,
$$
{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_4", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_5", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_6", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_7", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}
$$
::json,         -- JSON blob
                               NULL,                  -- Weights
                               'Maria',               -- Name
                               'MLP with 2 hidden layers'       -- Descr
);
</pre>
-# Generate model configurations using grid search. The output table for grid 
search contains the unique combinations of model architectures, compile and 
fit parameters.
<pre class="example">
DROP TABLE IF EXISTS mst_table, mst_table_summary;
SELECT madlib.generate_model_configs(
                                        'model_arch_library', -- model architecture table
                                        'mst_table',          -- model selection table output
                                         ARRAY[1,2],          -- model ids from model architecture table
                                         $$
                                            {'loss': ['categorical_crossentropy'],
                                             'optimizer_params_list': [ {'optimizer': ['Adam'], 'lr': [0.001, 0.01, 0.1]} ],
                                             'metrics': ['accuracy']}
                                         $$,                  -- compile_param_grid
                                         $$
                                         { 'batch_size': [4, 8],
                                           'epochs': [1]
                                         }
                                         $$,                  -- fit_param_grid
                                         'grid'               -- search_type
                                         );
SELECT * FROM mst_table ORDER BY mst_key;
</pre>
<pre class="result">
 mst_key | model_id |                                 compile_params                                  |      fit_params       
---------+----------+---------------------------------------------------------------------------------+-----------------------
       1 |        1 | optimizer='Adam(lr=0.001)',metrics=['accuracy'],loss='categorical_crossentropy' | epochs=1,batch_size=4
       2 |        1 | optimizer='Adam(lr=0.001)',metrics=['accuracy'],loss='categorical_crossentropy' | epochs=1,batch_size=8
       3 |        1 | optimizer='Adam(lr=0.01)',metrics=['accuracy'],loss='categorical_crossentropy'  | epochs=1,batch_size=4
       4 |        1 | optimizer='Adam(lr=0.01)',metrics=['accuracy'],loss='categorical_crossentropy'  | epochs=1,batch_size=8
       5 |        1 | optimizer='Adam(lr=0.1)',metrics=['accuracy'],loss='categorical_crossentropy'   | epochs=1,batch_size=4
       6 |        1 | optimizer='Adam(lr=0.1)',metrics=['accuracy'],loss='categorical_crossentropy'   | epochs=1,batch_size=8
       7 |        2 | optimizer='Adam(lr=0.001)',metrics=['accuracy'],loss='categorical_crossentropy' | epochs=1,batch_size=4
       8 |        2 | optimizer='Adam(lr=0.001)',metrics=['accuracy'],loss='categorical_crossentropy' | epochs=1,batch_size=8
       9 |        2 | optimizer='Adam(lr=0.01)',metrics=['accuracy'],loss='categorical_crossentropy'  | epochs=1,batch_size=4
      10 |        2 | optimizer='Adam(lr=0.01)',metrics=['accuracy'],loss='categorical_crossentropy'  | epochs=1,batch_size=8
      11 |        2 | optimizer='Adam(lr=0.1)',metrics=['accuracy'],loss='categorical_crossentropy'   | epochs=1,batch_size=4
      12 |        2 | optimizer='Adam(lr=0.1)',metrics=['accuracy'],loss='categorical_crossentropy'   | epochs=1,batch_size=8
(12 rows)
</pre>
This is the name of the model architecture table that corresponds to the model selection table:
<pre class="example">
SELECT * FROM mst_table_summary;
</pre>
<pre class="result">
  model_arch_table  | object_table 
--------------------+--------------
 model_arch_library | 
</pre>

-# Train multiple models.
<pre class="example">
DROP TABLE IF EXISTS iris_multi_model, iris_multi_model_summary, iris_multi_model_info;
SELECT madlib.madlib_keras_fit_multiple_model('iris_train_packed',    -- source_table
                                              'iris_multi_model',     -- model_output_table
                                              'mst_table',            -- model_selection_table
                                              10,                     -- num_iterations
                                              FALSE                   -- use gpus
                                             );
</pre>
View the model summary:
<pre class="example">
SELECT * FROM iris_multi_model_summary;
</pre>
<pre class="result">
source_table              | iris_train_packed
validation_table          | 
model                     | iris_multi_model
model_info                | iris_multi_model_info
dependent_varname         | {class_text}
independent_varname       | {attributes}
model_arch_table          | model_arch_library
model_selection_table     | mst_table
object_table              | 
num_iterations            | 10
metrics_compute_frequency | 10
warm_start                | f
name                      | 
description               | 
start_training_time       | 2021-02-05 00:40:42.695613
end_training_time         | 2021-02-05 00:42:20.796712
madlib_version            | 1.18.0
num_classes               | {1}
class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}
dependent_vartype         | {"character varying"}
normalizing_const         | 1
metrics_iters             | {10}
</pre>
View results for each model:
<pre class="example">
SELECT * FROM iris_multi_model_info ORDER BY training_metrics_final DESC, training_loss_final;
</pre>
<pre class="result">
  mst_key | model_id |                                 compile_params                                  |      fit_params       |  model_type  | model_size | metrics_elapsed_time | metrics_type |        loss_type         | training_metrics_final | training_loss_final |  training_metrics   |    training_loss     | validation_metrics_final | validation_loss_final | validation_metrics | validation_loss 
---------+----------+---------------------------------------------------------------------------------+-----------------------+--------------+------------+----------------------+--------------+--------------------------+------------------------+---------------------+---------------------+----------------------+--------------------------+-----------------------+--------------------+-----------------
       2 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['accuracy']   | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {96.2744579315186}   | {accuracy}   | categorical_crossentropy |      0.966666638851166 |  0.0771341994404793 | {0.966666638851166} | {0.0771341994404793} |                          |                       |                    | 
       3 |        1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['accuracy'] | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {95.0798950195312}   | {accuracy}   | categorical_crossentropy |      0.958333313465118 |    0.14112713932991 | {0.958333313465118} | {0.14112713932991}   |                          |                       |                    | 
      10 |        2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['accuracy'] | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {95.7743279933929}   | {accuracy}   | categorical_crossentropy |      0.949999988079071 |   0.126085489988327 | {0.949999988079071} | {0.126085489988327}  |                          |                       |                    | 
       5 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['accuracy'] | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {97.8191220760345}   | {accuracy}   | categorical_crossentropy |      0.866666674613953 |   0.459462374448776 | {0.866666674613953} | {0.459462374448776}  |                          |                       |                    | 
       4 |        1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['accuracy'] | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {96.7445840835571}   | {accuracy}   | categorical_crossentropy |      0.858333349227905 |   0.279698997735977 | {0.858333349227905} | {0.279698997735977}  |                          |                       |                    | 
       9 |        2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['accuracy'] | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {95.3640351295471}   | {accuracy}   | categorical_crossentropy |      0.824999988079071 |   0.325970768928528 | {0.824999988079071} | {0.325970768928528}  |                          |                       |                    | 
       7 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['accuracy']   | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {94.8350050449371}   | {accuracy}   | categorical_crossentropy |      0.800000011920929 |   0.458843886852264 | {0.800000011920929} | {0.458843886852264}  |                          |                       |                    | 
      12 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['accuracy'] | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {96.0411529541016}   | {accuracy}   | categorical_crossentropy |      0.783333361148834 |   0.766786217689514 | {0.783333361148834} | {0.766786217689514}  |                          |                       |                    | 
      11 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['accuracy'] | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {98.098680973053}    | {accuracy}   | categorical_crossentropy |      0.683333337306976 |   0.607033967971802 | {0.683333337306976} | {0.607033967971802}  |                          |                       |                    | 
       6 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['accuracy'] | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {96.5071561336517}   | {accuracy}   | categorical_crossentropy |      0.683333337306976 |   0.704851150512695 | {0.683333337306976} | {0.704851150512695}  |                          |                       |                    | 
       8 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['accuracy']   | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {97.4749901294708}   | {accuracy}   | categorical_crossentropy |      0.641666650772095 |   0.473412454128265 | {0.641666650772095} | {0.473412454128265}  |                          |                       |                    | 
       1 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['accuracy']   | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {96.9749960899353}   | {accuracy}   | categorical_crossentropy |      0.358333319425583 |    1.09744954109192 | {0.358333319425583} | {1.09744954109192}   |                          |                       |                    | 
(12 rows)
</pre>

-# Evaluate.  Now run evaluate using models we built above:
<pre class="example">
DROP TABLE IF EXISTS iris_validate;
SELECT madlib.madlib_keras_evaluate('iris_multi_model',  -- model
                                    'iris_test_packed',  -- test table
                                    'iris_validate',     -- output table
                                     NULL,               -- use gpus
                                     3                   -- mst_key to use
                                   );
SELECT * FROM iris_validate;
</pre>
<pre class="result">
        loss        | metric | metrics_type |        loss_type         
--------------------+--------+--------------+--------------------------
 0.0789926201105118 |      1 | {accuracy}   | categorical_crossentropy
</pre>

-# Predict.  Now predict using one of the models we built. We will use the validation data set
for prediction as well, which is not usual but serves to show the syntax.
The prediction is in the estimated_class_text column:
<pre class="example">
DROP TABLE IF EXISTS iris_predict;
SELECT madlib.madlib_keras_predict('iris_multi_model', -- model
                                   'iris_test',        -- test_table
                                   'id',               -- id column
                                   'attributes',       -- independent var
                                   'iris_predict',     -- output table
                                    'response',        -- prediction type
                                    FALSE,             -- use gpus
                                    3                  -- mst_key to use
                                   );
SELECT * FROM iris_predict ORDER BY id;
</pre>
<pre class="result">
 id  | class_name |   class_value   |    prob    
-----+------------+-----------------+------------
   8 | class_text | Iris-setosa     |  0.9979984
  15 | class_text | Iris-setosa     | 0.99929357
  20 | class_text | Iris-setosa     |  0.9985701
  21 | class_text | Iris-setosa     |  0.9984106
  22 | class_text | Iris-setosa     |  0.9983991
  27 | class_text | Iris-setosa     | 0.99763095
  28 | class_text | Iris-setosa     |   0.998376
  33 | class_text | Iris-setosa     | 0.99901116
  37 | class_text | Iris-setosa     | 0.99871385
  38 | class_text | Iris-setosa     | 0.99740535
  46 | class_text | Iris-setosa     |  0.9968368
  51 | class_text | Iris-versicolor | 0.93798196
  57 | class_text | Iris-versicolor | 0.73391247
  58 | class_text | Iris-versicolor |  0.9449931
  59 | class_text | Iris-versicolor |  0.8938894
  64 | class_text | Iris-versicolor |  0.6563309
  65 | class_text | Iris-versicolor | 0.95828146
  72 | class_text | Iris-versicolor |    0.94206
  75 | class_text | Iris-versicolor | 0.93305194
  87 | class_text | Iris-versicolor |  0.8458596
  95 | class_text | Iris-versicolor | 0.76850986
  97 | class_text | Iris-versicolor |  0.8467575
  98 | class_text | Iris-versicolor |  0.9081358
 120 | class_text | Iris-virginica  | 0.86913925
 121 | class_text | Iris-virginica  | 0.96328884
 122 | class_text | Iris-virginica  |  0.9474733
 123 | class_text | Iris-virginica  | 0.97997576
 140 | class_text | Iris-virginica  |  0.8721462
 144 | class_text | Iris-virginica  |  0.9745266
 147 | class_text | Iris-virginica  |  0.8978669
(30 rows)
</pre>
Count missclassifications:
<pre class="example">
SELECT COUNT(*) FROM iris_predict JOIN iris_test USING (id) 
WHERE iris_predict.class_value != iris_test.class_text;
</pre>
<pre class="result">
 count 
-------+
     0
</pre>
Accuracy:
<pre class="example">
SELECT round(count(*)*100/(150*0.2),2) as test_accuracy_percent from
    (select iris_test.class_text as actual, iris_predict.class_value as estimated
     from iris_predict inner join iris_test
     on iris_test.id=iris_predict.id) q
WHERE q.actual=q.estimated;
</pre>
<pre class="result">
 test_accuracy_percent 
-----------------------+
                100.00
</pre>

<h4>Classification with Other Parameters</h4>

-# Validation dataset.  Now use a validation dataset
and compute metrics every 3rd iteration using
the 'metrics_compute_frequency' parameter. This can
help reduce run time if you do not need metrics
computed at every iteration.  Also turn on caching.
<pre class="example">
DROP TABLE IF EXISTS iris_multi_model, iris_multi_model_summary, iris_multi_model_info;
SELECT madlib.madlib_keras_fit_multiple_model('iris_train_packed',    -- source_table
                                              'iris_multi_model',     -- model_output_table
                                              'mst_table',            -- model_selection_table
                                               10,                     -- num_iterations
                                               FALSE,                 -- use gpus
                                              'iris_test_packed',     -- validation dataset
                                               3,                     -- metrics compute frequency
                                               FALSE,                 -- warm start
                                              'Sophie L.',            -- name
                                              'Model selection for iris dataset',  -- description
                                               TRUE                   -- use caching
                                             );
</pre>
View the model summary:
<pre class="example">
SELECT * FROM iris_multi_model_summary;
</pre>
<pre class="result">
-[ RECORD 1 ]-------------+---------------------------------------------
source_table              | iris_train_packed
validation_table          | iris_test_packed
model                     | iris_multi_model
model_info                | iris_multi_model_info
dependent_varname         | {class_text}
independent_varname       | {attributes}
model_arch_table          | model_arch_library
model_selection_table     | mst_table
object_table              | 
num_iterations            | 10
metrics_compute_frequency | 3
warm_start                | f
name                      | Sophie L.
description               | Model selection for iris dataset
start_training_time       | 2021-02-05 01:03:11.337798
end_training_time         | 2021-02-05 01:05:14.988912
madlib_version            | 1.18.0
num_classes               | {1}
class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}
dependent_vartype         | {"character varying"}
normalizing_const         | 1
metrics_iters             | {3,6,9,10}
</pre>
View results for each model:
<pre class="example">
SELECT * FROM iris_multi_model_info ORDER BY training_metrics_final DESC, training_loss_final;
</pre>
<pre class="result">
 ---------+----------+---------------------------------------------------------------------------------+-----------------------+--------------+------------+-----------------------------------------------------------------------+--------------+--------------------------+------------------------+---------------------+---------------------------------------------------------------------------+---------------------------------------------------------------------------+--------------------------+-----------------------+---------------------------------------------------------------------------+------------------------------------------------------------------------------
      10 |        2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['accuracy'] | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {34.347088098526,69.4049510955811,105.285098075867,121.389348983765}  | {accuracy}   | categorical_crossentropy |      0.975000023841858 |   0.166684880852699 | {0.949999988079071,0.949999988079071,0.908333361148834,0.975000023841858} | {0.615781545639038,0.269571483135223,0.242876216769218,0.166684880852699} |                        1 |     0.107727721333504 | {1,1,0.966666638851166,1}                                                 | {0.620104968547821,0.227639734745026,0.155238434672356,0.107727721333504}
       3 |        1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['accuracy'] | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {33.7874810695648,68.735356092453,104.679323911667,120.741965055466}  | {accuracy}   | categorical_crossentropy |      0.958333313465118 |   0.151768147945404 | {0.958333313465118,0.816666662693024,0.941666662693024,0.958333313465118} | {0.232924744486809,0.356248170137405,0.160927340388298,0.151768147945404} |                        1 |    0.0933234840631485 | {1,0.866666674613953,0.966666638851166,1}                                 | {0.197644680738449,0.244517579674721,0.0969053283333778,0.0933234840631485}
       4 |        1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['accuracy'] | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {35.5827050209045,70.4194140434265,106.230206012726,122.374103069305} | {accuracy}   | categorical_crossentropy |      0.941666662693024 |   0.146068558096886 | {0.824999988079071,0.958333313465118,0.941666662693024,0.941666662693024} | {0.339193284511566,0.171411842107773,0.154963329434395,0.146068558096886} |                        1 |    0.0618178397417068 | {0.933333337306976,1,1,1}                                                 | {0.302341401576996,0.0991373136639595,0.0709080845117569,0.0618178397417068}
       5 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['accuracy'] | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {36.3988909721375,71.1546559333801,107.219161987305,123.366652965546} | {accuracy}   | categorical_crossentropy |      0.908333361148834 |   0.656857788562775 | {0.358333319425583,0.683333337306976,0.766666650772095,0.908333361148834} | {0.996901094913483,0.852809607982635,0.694450318813324,0.656857788562775} |        0.899999976158142 |     0.630161166191101 | {0.233333334326744,0.600000023841858,0.633333325386047,0.899999976158142} | {1.05581676959991,0.876067101955414,0.700714349746704,0.630161166191101}
       2 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['accuracy']   | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {35.0734770298004,69.949450969696,105.773796081543,121.901873111725}  | {accuracy}   | categorical_crossentropy |      0.866666674613953 |    0.26227542757988 | {0.558333337306976,0.683333337306976,0.708333313465118,0.866666674613953} | {0.755041897296906,0.551798105239868,0.504159986972809,0.26227542757988}  |        0.899999976158142 |     0.156955525279045 | {0.633333325386047,0.600000023841858,0.633333325386047,0.899999976158142} | {0.663675665855408,0.674827337265015,0.613502621650696,0.156955525279045}
       6 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['accuracy'] | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {35.3355600833893,70.1827409267426,106.000793933868,122.135368108749} | {accuracy}   | categorical_crossentropy |      0.858333349227905 |   0.403681367635727 | {0.708333313465118,0.850000023841858,0.783333361148834,0.858333349227905} | {0.609176814556122,0.488206028938293,0.425172030925751,0.403681367635727} |        0.899999976158142 |     0.393621385097504 | {0.600000023841858,0.833333313465118,0.800000011920929,0.899999976158142} | {0.624664425849915,0.48302897810936,0.428876429796219,0.393621385097504}
       9 |        2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['accuracy'] | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {34.0762810707092,69.0332140922546,105.02664899826,121.034147024155}  | {accuracy}   | categorical_crossentropy |      0.816666662693024 |    0.40071240067482 | {0.716666638851166,0.975000023841858,0.941666662693024,0.816666662693024} | {0.530809044837952,0.112755678594112,0.178483173251152,0.40071240067482}  |        0.899999976158142 |     0.160617485642433 | {0.666666686534882,1,1,0.899999976158142}                                 | {0.510058879852295,0.0435655005276203,0.0271952152252197,0.160617485642433}
      11 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['accuracy'] | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {36.664577960968,71.4262120723724,107.501835107803,123.646811962128}  | {accuracy}   | categorical_crossentropy |      0.816666662693024 |   0.683901190757751 | {0.358333319425583,0.574999988079071,0.758333325386047,0.816666662693024} | {0.969602465629578,0.828204095363617,0.7138671875,0.683901190757751}      |        0.833333313465118 |     0.720155417919159 | {0.233333334326744,0.466666668653488,0.666666686534882,0.833333313465118} | {1.04192113876343,0.878720223903656,0.755707621574402,0.720155417919159}
       1 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['accuracy']   | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {35.8240220546722,70.6528959274292,106.680663108826,122.609847068787} | {accuracy}   | categorical_crossentropy |      0.683333337306976 |   0.479730814695358 | {0.675000011920929,0.683333337306976,0.683333337306976,0.683333337306976} | {0.507641136646271,0.467351347208023,0.507468938827515,0.479730814695358} |        0.600000023841858 |     0.503782331943512 | {0.600000023841858,0.600000023841858,0.600000023841858,0.600000023841858} | {0.504352450370789,0.448328793048859,0.561446607112885,0.503782331943512}
       7 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['accuracy']   | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {33.5537171363831,68.2605030536652,104.443753004074,120.498863935471} | {accuracy}   | categorical_crossentropy |      0.683333337306976 |   0.940275907516479 | {0.733333349227905,0.641666650772095,0.933333337306976,0.683333337306976} | {0.419289141893387,0.746466338634491,0.25556743144989,0.940275907516479}  |        0.600000023841858 |       1.1002448797226 | {0.633333325386047,0.766666650772095,0.966666638851166,0.600000023841858} | {0.457020550966263,0.510054171085358,0.249405279755592,1.1002448797226}
      12 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['accuracy'] | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {34.8103830814362,69.698233127594,105.547440052032,121.659696102142}  | {accuracy}   | categorical_crossentropy |      0.633333325386047 |   0.711242735385895 | {0.458333343267441,0.5,0.683333337306976,0.633333325386047}               | {1.71241450309753,0.98362809419632,0.776128530502319,0.711242735385895}   |        0.566666662693024 |     0.721668004989624 | {0.433333337306976,0.5,0.600000023841858,0.566666662693024}               | {1.30801546573639,0.950868666172028,0.841940879821777,0.721668004989624}
       8 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['accuracy']   | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {36.0954039096832,70.921669960022,106.977710008621,123.112148046494}  | {accuracy}   | categorical_crossentropy |      0.358333319425583 |    1.10370969772339 | {0.324999988079071,0.358333319425583,0.358333319425583,0.358333319425583} | {1.10047388076782,1.09791541099548,1.09736382961273,1.10370969772339}     |        0.233333334326744 |      1.11518168449402 | {0.366666674613953,0.233333334326744,0.233333334326744,0.233333334326744} | {1.09480428695679,1.1150735616684,1.10827457904816,1.11518168449402}
(12 rows)
</pre>

-# Predict probabilities for each class:
<pre class="example">
DROP TABLE IF EXISTS iris_predict;
SELECT madlib.madlib_keras_predict('iris_multi_model', -- model
                                   'iris_test',        -- test_table
                                   'id',               -- id column
                                   'attributes',       -- independent var
                                   'iris_predict',     -- output table
                                    'prob',            -- prediction type
                                    FALSE,             -- use gpus
                                    3                  -- mst_key to use
                                   );
SELECT * FROM iris_predict ORDER BY id, rank;
</pre>
<pre class="result">
-----+------------+-----------------+---------------+------
   8 | class_text | Iris-setosa     |    0.99961567 |    1
   8 | class_text | Iris-versicolor | 0.00038426166 |    2
   8 | class_text | Iris-virginica  | 5.4132368e-08 |    3
  15 | class_text | Iris-setosa     |     0.9999677 |    1
  15 | class_text | Iris-versicolor |  3.235117e-05 |    2
  15 | class_text | Iris-virginica  | 7.5747697e-10 |    3
  20 | class_text | Iris-setosa     |    0.99956757 |    1
  20 | class_text | Iris-versicolor |  0.0004323488 |    2
  20 | class_text | Iris-virginica  | 6.8698306e-08 |    3
  21 | class_text | Iris-setosa     |    0.99978334 |    1
  21 | class_text | Iris-versicolor | 0.00021666527 |    2
  21 | class_text | Iris-virginica  |  1.741537e-08 |    3
  22 | class_text | Iris-setosa     |    0.99955314 |    1
  22 | class_text | Iris-versicolor | 0.00044669537 |    2
  22 | class_text | Iris-virginica  |  8.287442e-08 |    3
  27 | class_text | Iris-setosa     |      0.999393 |    1
  27 | class_text | Iris-versicolor | 0.00060693553 |    2
  27 | class_text | Iris-virginica  | 1.4125514e-07 |    3
  28 | class_text | Iris-setosa     |     0.9997589 |    1
  28 | class_text | Iris-versicolor | 0.00024109415 |    2
  28 | class_text | Iris-virginica  | 2.3418018e-08 |    3
  33 | class_text | Iris-setosa     |    0.99966764 |    1
  33 | class_text | Iris-versicolor | 0.00033237415 |    2
  33 | class_text | Iris-virginica  | 3.2712443e-08 |    3
  37 | class_text | Iris-setosa     |     0.9999347 |    1
  37 | class_text | Iris-versicolor | 6.5290136e-05 |    2
  37 | class_text | Iris-virginica  | 2.6893372e-09 |    3
  38 | class_text | Iris-setosa     |    0.99963343 |    1
  38 | class_text | Iris-versicolor |  0.0003665546 |    2
  38 | class_text | Iris-virginica  | 4.7346873e-08 |    3
  46 | class_text | Iris-setosa     |     0.9995722 |    1
  46 | class_text | Iris-versicolor | 0.00042761036 |    2
  46 | class_text | Iris-virginica  | 8.4179504e-08 |    3
  51 | class_text | Iris-versicolor |     0.9678325 |    1
  51 | class_text | Iris-virginica  |   0.031179406 |    2
  51 | class_text | Iris-setosa     |  0.0009880556 |    3
  57 | class_text | Iris-versicolor |     0.7971095 |    1
  57 | class_text | Iris-virginica  |    0.20281655 |    2
  57 | class_text | Iris-setosa     |  7.402597e-05 |    3
  58 | class_text | Iris-versicolor |    0.93808955 |    1
  58 | class_text | Iris-virginica  |   0.045088027 |    2
  58 | class_text | Iris-setosa     |   0.016822474 |    3
  59 | class_text | Iris-versicolor |    0.95377713 |    1
  59 | class_text | Iris-virginica  |   0.045621604 |    2
  59 | class_text | Iris-setosa     |  0.0006012956 |    3
  64 | class_text | Iris-versicolor |     0.8078371 |    1
  64 | class_text | Iris-virginica  |    0.19210756 |    2
  64 | class_text | Iris-setosa     | 5.5370016e-05 |    3
  65 | class_text | Iris-versicolor |      0.946594 |    1
  65 | class_text | Iris-virginica  |    0.04081257 |    2
  65 | class_text | Iris-setosa     |   0.012593448 |    3
  72 | class_text | Iris-versicolor |     0.9616088 |    1
  72 | class_text | Iris-virginica  |      0.033955 |    2
  72 | class_text | Iris-setosa     |   0.004436169 |    3
  75 | class_text | Iris-versicolor |    0.96245867 |    1
  75 | class_text | Iris-virginica  |    0.03556654 |    2
  75 | class_text | Iris-setosa     |  0.0019747794 |    3
  87 | class_text | Iris-versicolor |     0.9264334 |    1
  87 | class_text | Iris-virginica  |    0.07328824 |    2
  87 | class_text | Iris-setosa     | 0.00027841402 |    3
  95 | class_text | Iris-versicolor |    0.85156035 |    1
  95 | class_text | Iris-virginica  |    0.14813933 |    2
  95 | class_text | Iris-setosa     | 0.00030031145 |    3
  97 | class_text | Iris-versicolor |    0.87470025 |    1
  97 | class_text | Iris-virginica  |     0.1248041 |    2
  97 | class_text | Iris-setosa     |  0.0004957556 |    3
  98 | class_text | Iris-versicolor |     0.9439469 |    1
  98 | class_text | Iris-virginica  |    0.05491364 |    2
  98 | class_text | Iris-setosa     |   0.001139452 |    3
 120 | class_text | Iris-virginica  |    0.58107394 |    1
 120 | class_text | Iris-versicolor |    0.41892523 |    2
 120 | class_text | Iris-setosa     | 8.7891783e-07 |    3
 121 | class_text | Iris-virginica  |    0.90112364 |    1
 121 | class_text | Iris-versicolor |   0.098876335 |    2
 121 | class_text | Iris-setosa     | 5.8106266e-09 |    3
 122 | class_text | Iris-virginica  |     0.8664512 |    1
 122 | class_text | Iris-versicolor |    0.13354866 |    2
 122 | class_text | Iris-setosa     |  8.255242e-08 |    3
 123 | class_text | Iris-virginica  |    0.90162355 |    1
 123 | class_text | Iris-versicolor |    0.09837647 |    2
 123 | class_text | Iris-setosa     |  2.745874e-10 |    3
 140 | class_text | Iris-virginica  |     0.7306292 |    1
 140 | class_text | Iris-versicolor |     0.2693706 |    2
 140 | class_text | Iris-setosa     | 1.9480031e-07 |    3
 144 | class_text | Iris-virginica  |    0.92295665 |    1
 144 | class_text | Iris-versicolor |    0.07704339 |    2
 144 | class_text | Iris-setosa     | 1.6369142e-09 |    3
 147 | class_text | Iris-virginica  |    0.69545543 |    1
 147 | class_text | Iris-versicolor |    0.30454406 |    2
 147 | class_text | Iris-setosa     | 4.5714978e-07 |    3
(90 rows)
</pre>

-# Warm start.  Next, use the warm_start parameter
to continue learning, using the coefficients from
the run above. Note that we don't drop the
model table or model summary table:
<pre class="example">
SELECT madlib.madlib_keras_fit_multiple_model('iris_train_packed',    -- source_table
                                              'iris_multi_model',     -- model_output_table
                                              'mst_table',            -- model_selection_table
                                               3,                     -- num_iterations
                                               FALSE,                 -- use gpus
                                              'iris_test_packed',     -- validation dataset
                                               1,                     -- metrics compute frequency
                                               TRUE,                  -- warm start
                                              'Sophie L.',            -- name
                                              'Simple MLP for iris dataset',  -- description
                                               TRUE                   -- use caching
                                             );
SELECT * FROM iris_multi_model_summary;
</pre>
<pre class="result">
-[ RECORD 1 ]-------------+---------------------------------------------
source_table              | iris_train_packed
validation_table          | iris_test_packed
model                     | iris_multi_model
model_info                | iris_multi_model_info
dependent_varname         | {class_text}
independent_varname       | {attributes}
model_arch_table          | model_arch_library
model_selection_table     | mst_table
object_table              | 
num_iterations            | 3
metrics_compute_frequency | 1
warm_start                | t
name                      | Sophie L.
description               | Simple MLP for iris dataset
start_training_time       | 2021-02-05 01:17:19.432839
end_training_time         | 2021-02-05 01:18:09.062384
madlib_version            | 1.18.0
num_classes               | {1}
class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}
dependent_vartype         | {"character varying"}
normalizing_const         | 1
metrics_iters             | {1,2,3}
</pre>
View results for each model:
<pre class="example">
SELECT * FROM iris_multi_model_info ORDER BY training_metrics_final DESC, training_loss_final;
</pre>
<pre class="result">
  mst_key | model_id |                                 compile_params                                  |      fit_params       |  model_type  | model_size |                 metrics_elapsed_time                 | metrics_type |        loss_type         | training_metrics_final | training_loss_final |                    training_metrics                     |                      training_loss                      | validation_metrics_final | validation_loss_final |                   validation_metrics                    |                      validation_loss                      
---------+----------+---------------------------------------------------------------------------------+-----------------------+--------------+------------+------------------------------------------------------+--------------+--------------------------+------------------------+---------------------+---------------------------------------------------------+---------------------------------------------------------+--------------------------+-----------------------+---------------------------------------------------------+-----------------------------------------------------------
      10 |        2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['accuracy'] | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {15.5192940235138,31.2597029209137,47.3274641036987} | {accuracy}   | categorical_crossentropy |      0.966666638851166 |   0.122704714536667 | {0.925000011920929,0.808333337306976,0.966666638851166} | {0.172832280397415,0.354962348937988,0.122704714536667} |                        1 |    0.0603121444582939 | {1,0.866666674613953,1}                                 | {0.100369863212109,0.210344776511192,0.0603121444582939}
       4 |        1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['accuracy'] | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {16.485249042511,32.207494020462,48.3005399703979}   | {accuracy}   | categorical_crossentropy |      0.958333313465118 |   0.104984156787395 | {0.949999988079071,0.866666674613953,0.958333313465118} | {0.126872479915619,0.29683381319046,0.104984156787395}  |                        1 |    0.0291607566177845 | {1,0.933333337306976,1}                                 | {0.0433581434190273,0.127146035432816,0.0291607566177845}
       3 |        1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['accuracy'] | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {14.8933939933777,30.7211890220642,46.7588970661163} | {accuracy}   | categorical_crossentropy |      0.958333313465118 |   0.107885278761387 | {0.941666662693024,0.966666638851166,0.958333313465118} | {0.155905768275261,0.129546254873276,0.107885278761387} |                        1 |    0.0387893654406071 | {1,1,1}                                                 | {0.087645135819912,0.0574964620172977,0.0387893654406071}
       7 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['accuracy']   | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {14.657429933548,30.4864449501038,46.5082159042358}  | {accuracy}   | categorical_crossentropy |      0.958333313465118 |   0.215500101447105 | {0.891666650772095,0.649999976158142,0.958333313465118} | {0.2352494597435,0.490339070558548,0.215500101447105}   |                        1 |     0.194652214646339 | {0.899999976158142,0.766666650772095,1}                 | {0.235657200217247,0.335934072732925,0.194652214646339}
       6 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['accuracy'] | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {16.2535049915314,31.9760749340057,48.0661840438843} | {accuracy}   | categorical_crossentropy |      0.941666662693024 |   0.354692339897156 | {0.975000023841858,0.908333361148834,0.941666662693024} | {0.38957467675209,0.367432981729507,0.354692339897156}  |                        1 |     0.321579396724701 | {1,0.966666638851166,1}                                 | {0.348732680082321,0.345716863870621,0.321579396724701}
       2 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['accuracy']   | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {16.0124208927155,31.7479128837585,47.8348250389099} | {accuracy}   | categorical_crossentropy |      0.933333337306976 |   0.238343968987465 | {0.975000023841858,0.975000023841858,0.933333337306976} | {0.17331151664257,0.0775784701108932,0.238343968987465} |        0.966666638851166 |     0.182112962007523 | {0.966666638851166,1,0.966666638851166}                 | {0.114220358431339,0.0159573350101709,0.182112962007523}
       9 |        2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['accuracy'] | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {15.1569800376892,30.9868409633636,47.0489699840546} | {accuracy}   | categorical_crossentropy |      0.908333361148834 |   0.254226505756378 | {0.858333349227905,0.833333313465118,0.908333361148834} | {0.450037389993668,0.500195503234863,0.254226505756378} |        0.966666638851166 |    0.0769383609294891 | {0.899999976158142,0.899999976158142,0.966666638851166} | {0.163723081350327,0.211927503347397,0.0769383609294891}
      11 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['accuracy'] | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {17.7095139026642,33.4267060756683,49.6263670921326} | {accuracy}   | categorical_crossentropy |      0.899999976158142 |   0.602623522281647 | {0.824999988079071,0.899999976158142,0.899999976158142} | {0.65915185213089,0.633350729942322,0.602623522281647}  |        0.899999976158142 |     0.626452326774597 | {0.833333313465118,0.899999976158142,0.899999976158142} | {0.695301294326782,0.661069989204407,0.626452326774597}
       5 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['accuracy'] | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {17.4354989528656,33.1478018760681,49.3430600166321} | {accuracy}   | categorical_crossentropy |      0.741666674613953 |   0.532543838024139 | {0.916666686534882,0.875,0.741666674613953}             | {0.610130310058594,0.571656167507172,0.532543838024139} |        0.633333325386047 |     0.540634453296661 | {0.966666638851166,0.899999976158142,0.633333325386047} | {0.601030588150024,0.567581355571747,0.540634453296661}
      12 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['accuracy'] | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {15.7747659683228,31.5215599536896,47.6013031005859} | {accuracy}   | categorical_crossentropy |      0.675000011920929 |   0.581513583660126 | {0.683333337306976,0.683333337306976,0.675000011920929} | {0.660648465156555,0.623969316482544,0.581513583660126} |        0.600000023841858 |     0.594986796379089 | {0.600000023841858,0.600000023841858,0.600000023841858} | {0.694275736808777,0.665920257568359,0.594986796379089}
       1 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['accuracy']   | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {16.8983609676361,32.4361009597778,48.5357549190521} | {accuracy}   | categorical_crossentropy |      0.608333349227905 |   0.687089145183563 | {0.583333313465118,0.699999988079071,0.608333349227905} | {0.816642761230469,0.455933183431625,0.687089145183563} |        0.533333361148834 |     0.692391216754913 | {0.533333361148834,0.600000023841858,0.533333361148834} | {0.85290253162384,0.465981602668762,0.692391216754913}
       8 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['accuracy']   | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {17.1899569034576,32.8988509178162,49.0880739688873} | {accuracy}   | categorical_crossentropy |      0.358333319425583 |    1.11154329776764 | {0.358333319425583,0.324999988079071,0.358333319425583} | {1.09858739376068,1.09980893135071,1.11154329776764}    |        0.233333334326744 |      1.16109442710876 | {0.233333334326744,0.366666674613953,0.233333334326744} | {1.12281405925751,1.10376691818237,1.16109442710876}
(12 rows)
</pre>
Note that the loss and accuracy values pick up from where the previous run left off.

@anchor notes
@par Notes

1. Refer to the deep learning section of the Apache MADlib
wiki [6] for important information including supported libraries
and versions.

2. Classification is currently supported, not regression.

3. Reminder about the distinction between warm start and transfer learning.  Warm start uses model
state (weights) from the model output table from a previous training run -
set the 'warm_start' parameter to TRUE in the fit function.
Transfer learning uses initial model state (weights) stored in the 'model_arch_table' - in this case set the
'warm_start' parameter to FALSE in the fit function.

4. Here are some more details on how warm start works.  These details are mostly applicable when implementing autoML algorithms on top of MADlib's model selection.  In short, the 'model_selection_table' dictates which models get trained and output to the 'model_output_table' and associated summary and info tables.  When 'warm_start' is TRUE, models are built for each 'mst_key' in the 'model_selection_table'.  If there are prior runs for an 'mst_key' then the weights from that run will be used.  If there are no prior runs for an 'mst_key' then random initialization will be used.  For example, let's say we start with 'mst_keys' of 1, 2, 3, and 4 in the 'model_selection_table'. We run fit once to get model and info tables for 1, 2, 3, and 4.  Then we modify the 'model_selection_table' as part of an autoML scheme, in which we remove the 'mst_key' for 1 and add a new 'mst_key' for 5.  Next we run fit with warm start.  The result will be models created for 'mst_keys' of 2, 3, 4, and 5.  Warm start will be used for 2, 3, and 4 (using prior run) and random initialization will be used for 5 (no prior run).  The 'mst_key' of 1 will be dropped.

5. The 'num_iterations' parameter and the Keras fit parameter 'epochs' can substantially affect accuracy and run-time.
In general, increasing the number of 'epochs' for a fixed 'num_iterations' will speed up training, but may result
in lower accuracy.  It's best to do some experimentation to find out what works for your models and dataset.

@anchor background
@par Technical Background

For an introduction to deep learning foundations, including MLP and CNN,
refer to [7].

This module trains many models a time across the database cluster in order
to explore network architectures and hyperparameters.  It uses model hopper
parallelism (MOP) and has high convergence efficiency since it does not do
model averaging [2].

On the effect of database cluster size: as the database cluster size increases,
it will be faster to train a set of models, as long as you have at
least as many model selection tuples as segments. This is because model state is "hopped" from
segment to segment and training takes place in parallel [1,2]. If you have fewer model
selection tuples to train than segments, then some
segments may not be busy 100% of the time so speedup will not necessarily increase
on a larger cluster. Inference (prediction) is an embarrassingly parallel operation so
inference runtimes will be proportionally faster as the number of segments increases.

@anchor literature
@literature

@anchor mlp-lit-1
[1] "Cerebro: Efficient and Reproducible Model Selection on Deep Learning Systems,"
Supun Nakandala, Yuhao Zhang, and Arun Kumar, ACM SIGMOD 2019 DEEM Workshop,
https://adalabucsd.github.io/papers/2019_Cerebro_DEEM.pdf

[2] "Cerebro: A Data System for Optimized Deep Learning Model Selection,"
Supun Nakandala, Yuhao Zhang, and Arun Kumar, Proceedings of the VLDB Endowment (2020), Vol. 13, No. 11
https://adalabucsd.github.io/papers/2020_Cerebro_VLDB.pdf

[3] https://keras.io/

[4] https://www.tensorflow.org/

[5] "Neural Networks for Machine Learning", Lectures 6a and 6b on mini-batch gradient descent,
Geoffrey Hinton with Nitish Srivastava and Kevin Swersky,
http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf

[6] Deep learning section of Apache MADlib wiki https://cwiki.apache.org/confluence/display/MADLIB/Deep+Learning

[7] Deep Learning, Ian Goodfellow, Yoshua Bengio and Aaron Courville, MIT Press, 2016.

[8] Greenplum Database server configuration parameters https://gpdb.docs.pivotal.io/latest/ref_guide/config_params/guc-list.html

@anchor related
@par Related Topics

File madlib_keras_fit_multiple_model.sql_in documents training, evaluate and predict functions.

*/

CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.madlib_keras_fit_multiple_model(
    source_table                VARCHAR,
    model_output_table          VARCHAR,
    model_selection_table       VARCHAR,
    num_iterations              INTEGER,
    use_gpus                    BOOLEAN,
    validation_table            VARCHAR,
    metrics_compute_frequency   INTEGER,
    warm_start                  BOOLEAN,
    name                        VARCHAR,
    description                 VARCHAR,
    use_caching                 BOOLEAN DEFAULT FALSE
) RETURNS VOID AS $$
    PythonFunctionBodyOnly(`deep_learning', `madlib_keras_fit_multiple_model')
    from utilities.control import SetGUC
    with AOControl(False):
        with SetGUC("plan_cache_mode", "force_generic_plan"):
            with MinWarning("warning"):
                fit_obj = madlib_keras_fit_multiple_model.FitMultipleModel(**globals())
                fit_obj.fit_multiple_model()
$$ LANGUAGE plpythonu VOLATILE
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `MODIFIES SQL DATA', `');

CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.madlib_keras_fit_multiple_model(
    source_table            VARCHAR,
    model_output_table      VARCHAR,
    model_selection_table   VARCHAR,
    num_iterations          INTEGER,
    use_gpus                BOOLEAN,
    validation_table        VARCHAR,
    metrics_compute_frequency  INTEGER,
    warm_start              BOOLEAN,
    name                    VARCHAR
) RETURNS VOID AS $$
    SELECT MADLIB_SCHEMA.madlib_keras_fit_multiple_model($1, $2, $3, $4, $5, $6, $7, $8, $9, NULL);
$$ LANGUAGE sql VOLATILE
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `MODIFIES SQL DATA');

CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.madlib_keras_fit_multiple_model(
    source_table            VARCHAR,
    model_output_table      VARCHAR,
    model_selection_table   VARCHAR,
    num_iterations          INTEGER,
    use_gpus                BOOLEAN,
    validation_table        VARCHAR,
    metrics_compute_frequency  INTEGER,
    warm_start              BOOLEAN
) RETURNS VOID AS $$
    SELECT MADLIB_SCHEMA.madlib_keras_fit_multiple_model($1, $2, $3, $4, $5, $6, $7, $8, NULL, NULL);
$$ LANGUAGE sql VOLATILE
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `MODIFIES SQL DATA');

CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.madlib_keras_fit_multiple_model(
    source_table            VARCHAR,
    model_output_table      VARCHAR,
    model_selection_table   VARCHAR,
    num_iterations          INTEGER,
    use_gpus                BOOLEAN,
    validation_table        VARCHAR,
    metrics_compute_frequency  INTEGER
) RETURNS VOID AS $$
    SELECT MADLIB_SCHEMA.madlib_keras_fit_multiple_model($1, $2, $3, $4, $5, $6, $7, FALSE, NULL, NULL);
$$ LANGUAGE sql VOLATILE
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `MODIFIES SQL DATA');

CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.madlib_keras_fit_multiple_model(
    source_table            VARCHAR,
    model_output_table      VARCHAR,
    model_selection_table   VARCHAR,
    num_iterations          INTEGER,
    use_gpus                BOOLEAN,
    validation_table        VARCHAR
) RETURNS VOID AS $$
    SELECT MADLIB_SCHEMA.madlib_keras_fit_multiple_model($1, $2, $3, $4, $5, $6, NULL, FALSE, NULL, NULL);
$$ LANGUAGE sql VOLATILE
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `MODIFIES SQL DATA');

CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.madlib_keras_fit_multiple_model(
    source_table            VARCHAR,
    model_output_table      VARCHAR,
    model_selection_table   VARCHAR,
    num_iterations          INTEGER,
    use_gpus                BOOLEAN
) RETURNS VOID AS $$
    SELECT MADLIB_SCHEMA.madlib_keras_fit_multiple_model($1, $2, $3, $4, $5, NULL, NULL, FALSE, NULL, NULL);
$$ LANGUAGE sql VOLATILE
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `MODIFIES SQL DATA');

CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.fit_transition_multiple_model(
    dependent_var              BYTEA[],
    independent_var            BYTEA[],
    dependent_var_shape        INTEGER[],
    independent_var_shape      INTEGER[],
    model_architecture         TEXT,
    compile_params             TEXT,
    fit_params                 TEXT,
    dist_key                   INTEGER,
    dist_key_mapping           INTEGER[],
    current_seg_id             INTEGER,
    segments_per_host          INTEGER[],
    images_per_seg             INTEGER[],
    accessible_gpus_for_seg    INTEGER[],
    serialized_weights         BYTEA,
    is_final_training_call     BOOLEAN,
    use_caching                BOOLEAN,
    custom_function_map        BYTEA
) RETURNS BYTEA AS $$
PythonFunctionBodyOnlyNoSchema(`deep_learning', `madlib_keras')
    import traceback
    from sys import exc_info
    import plpy
    try:
        if use_caching:
            return madlib_keras.fit_multiple_transition_caching(**globals())
        else:
            return madlib_keras.fit_transition(state=None, prev_serialized_weights=serialized_weights,
                                               is_multiple_model=True, **globals())
    except Exception as e:
        etype, _, tb = exc_info()
        detail = ''.join(traceback.format_exception(etype, e, tb))
        message = e.message + 'UDFDetail' + detail
        e.args = (message,)
        raise e
$$ LANGUAGE plpythonu
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `NO SQL', `');