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 * KIND, either express or implied.  See the License for the
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 *
 * @file madlib_keras_automl.sql_in
 *
 * @brief Functions to run automated machine learning (autoML) methods for model architecture search and hyperparameter tuning.
 * @date August 2020
 *
 *
 *//* ----------------------------------------------------------------------- */

m4_include(`SQLCommon.m4')


/**
@addtogroup grp_automl


@brief Functions to run automated machine learning (autoML) methods for
model architecture search and hyperparameter tuning.

<div class="toc"><b>Contents</b><ul>
<li class="level1"><a href="#madlib_keras_automl">AutoML Function</a></li>
<li class="level1"><a href="#hyperband_schedule">Print Hyperband Schedule</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="#literature">Literature</a></li>
<li class="level1"><a href="#related">Related Topics</a></li>
</ul></div>

This module contains automated machine learning (autoML) methods for
model architecture search and hyperparameter tuning.  

The goal of autoML when
training deep nets is to reduce the amount of hand-tuning by data scientists
to produce a model of acceptable accuracy, compared to manual
methods like grid or random search.  The two autoML methods implemented
here are Hyperband and Hyperopt.  If you want to use grid or random search,
please refer to <a href="group__grp__keras__setup__model__selection.html">Define
Model Configurations</a>.

Hyperband is an effective model selection algorithm that utilizes the idea
of successive halving. It accelerates random search through adaptive resource allocation
and early stopping [1].  The implementation here is designed to
keep MPP database cluster resources as busy as possible when executing
the Hyperband schedule.

There is also a utility function for printing out the Hyperband schedule
for a given set of input parameters, to give you
a sense of how long a run might take before starting.

Hyperopt is meta-modeling approach for automated hyperparameter optimization [2].
It intelligently explores the search space while narrowing down to the best
estimated parameters.  Within Hyperopt we support random search and Tree
of Parzen Estimators (TPE) approach.

@note AutoML methods do not currently support multi-input or multi-output neural networks.

@anchor madlib_keras_automl
@par AutoML

<pre class="syntax">
madlib_keras_automl(
    source_table,
    model_output_table,
    model_arch_table,
    model_selection_table,
    model_id_list,
    compile_params_grid,
    fit_params_grid,
    automl_method,
    automl_params,
    random_state,
    object_table,
    use_gpus,
    validation_table,
    metrics_compute_frequency,
    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 image preprocessor. Independent
  and dependent variables are specified in the preprocessor
  step which is why you do not need to explictly state
  them here. Configurations will be evaluated by the autoML methods on the basis of training loss,
  unless a validation table is specified below, in which case validation loss will be used.
  </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.
  Details of output tables are shown below.
  </dd>

  <dt>model_arch_table</dt>
  <dd>VARCHAR. Table containing model architectures and weights.
  For more information on this table
  refer to <a href="group__grp__keras__model__arch.html">Define Model Architectures</a>.
  </dd>

  <dt>model_selection_table</dt>
  <dd>VARCHAR. Model selection table created by this method.  A summary table
  named <model_selection_table>_summary is also created.  Contents of both of these
  tables are described below.
  </dd>

  <dt>model_id_list</dt>
  <dd>INTEGER[]. Array of model IDs from the 'model_arch_table' to be included
  in the run combinations.  For hyperparameter search, this will typically be
  one model ID.  For model architecture search, this will be the different model IDs
  that you want to try.
  </dd>

  <dt>compile_params_grid</dt>
  <dd>VARCHAR. String representation of a Python dictionary
  of compile parameters to be tested. Each entry
  of the dictionary should consist of keys as compile parameter names,
  and values as a Python list of compile parameter values to be passed to Keras.
  Also, optimizer parameters are a nested dictionary to allow different
  optimizer types to have different parameters or ranges of parameters.
  Here is an example:

  <pre class="example">
  $$
    {'loss': ['categorical_crossentropy'],
     'optimizer_params_list': [
        {'optimizer': ['SGD'], 'lr': [0.0001, 0.001, 'log'], 'momentum': [0.95, 0.99, 'log_near_one']},
        {'optimizer': ['Adam'], 'lr': [0.01, 0.1, 'log'], 'decay': [1e-6, 1e-4, 'log']}],
     'metrics': ['accuracy']
    }
  $$
  </pre>

  The following types of sampling are supported:  'linear', 'log' and 'log_near_one'.
  The 'log_near_one' sampling is useful for exponentially weighted average types of parameters like momentum,
  which are very sensitive to changes near 1.  It has the effect of producing more values near 1
  than regular log-based sampling. However, 'log_near_one' is only supported
  for Hyperband, not for Hyperopt.

  @note
  - Custom loss functions and custom metrics can be used as defined in
  <a href="group__grp__custom__function.html">Define Custom Functions.</a>
  List the custom function name and provide the name of the table where the 
  serialized Python objects reside using the parameter 'object_table' below.
  - The following loss function is
  not supported: <em>sparse_categorical_crossentropy</em>.
  The following metrics are not
  supported: <em>sparse_categorical_accuracy, sparse_top_k_categorical_accuracy</em>.
  - The Keras accuracy parameter <em>top_k_categorical_accuracy</em> returns top 5 accuracy by 
  default.  If you want a different top k value, use the helper function
  <a href="group__grp__custom__function.html#top_k_function">Top k Accuracy Function</a> 
  to create a custom
  Python function to compute the top k accuracy that you want.
  </dd>

  <dt>fit_params_grid</dt>
  <dd>VARCHAR.  String representation of a Python dictionary
  of fit parameters to be tested. Each entry
  of the dictionary should consist of keys as fit parameter names,
  and values as a Python list of fit parameter values
  to be passed to Keras. Here is an example:

  <pre class="example">
  $$
    {'batch_size': [32, 64, 128, 256],
     'epochs': [10, 20, 30]
    }
  $$
  </pre>

  @note
  Callbacks are not currently supported except for TensorBoard
  which you can specify in the usual way,
  e.g., 'callbacks': ['[TensorBoard(log_dir="/tmp/logs/fit")]']
  </dd>

  <dt>automl_method (optional)</dt>
  <dd>VARCHAR, default 'hyperband'. Name of the autoML algorithm to run.
  Can be either 'hyperband' or 'hyperopt' (case insensitive).

  @note
  If you select 'hyperopt', then the Hyperopt package must be installed on the main node
  of the database cluster [3]. Hyperband does not need any separate package installation.

  </dd>

  <dt>automl_params (optional)</dt>
  <dd>VARCHAR, default depends on the method. Parameters for the chosen autoML method in a
  comma-separated string of key-value pairs.  Please refer to references [1] and [2] for
  more details on the definition of these parameters.

  <DL class="arglist">
  <DT><i>Hyperband params:</i></dt><dd></dd>
  <DT>R</dt>
  <DD>Default: 6. Maximum amount of resources (i.e., iterations) to allocate to a single configuration
  in a round of Hyperband.
  </DD>
  <DT>eta</DT>
  <DD>Default: 3. Controls the proportion of configurations discarded in each
  round of successive halving. For example, for eta=3 will keep the best 1/3 the
  configurations for the next round.</DD>
  <DT>skip_last</DT>
  <DD>Default: 0. The number of last rounds to skip. For example, 'skip_last=1'
  will skip the last round (i.e., last entry in each bracket), which is standard random
  search and can be expensive when run for the total R iterations.</DD>
  </DL>

  <DL class="arglist">
  <DT><i>Hyperopt params:</i></dt><dd></dd>
  <DT>num_configs</dt>
  <DD>Default: 20. Number of trials to evaluate.
  </DD>
  <DT>num_iterations</DT>
  <DD>Default: 5. Number of iterations to run for each trial.</DD>
  <DT>algorithm</DT>
  <DD>Default: 'tpe'. Name of the algorithm to explore the search space in Hyperopt ('rand' or 'tpe').</DD>
  </DL>

  <dt>random_state (optional)</dt>
  <dd>INTEGER, default NULL. Pseudo random number generator state used for random
  uniform sampling from lists of possible values. Pass an integer to evaluate a fixed set of configurations.
  </dd>
  @note
    Specifying a random state does not guarantee result reproducibility
    of the best configuration or the best
    train/validation accuracy/loss. It only guarantees that
    the same set of configurations will be chosen for evaluation.
  </dd>

  <dt>object_table (optional)</dt>
  <dd>VARCHAR, default: NULL. Name of the table containing
  Python objects in the case that custom loss functions,
  metrics or top k categorical accuracy are specified in
  the 'compile_params_grid'.
  </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 image preprocessor on the validation dataset.
  Using a validation dataset can mean a
  longer training time depending on its size, and the configurations in autoML will be
  evaluated on the basis of validation
  loss instead of training loss.</dd>

  <DT>metrics_compute_frequency (optional)</DT>
  <DD>INTEGER, default: once at the end of training.
  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.
  If you use the default,
  metrics will be computed only
  once after training has completed.
  </DD>

  <DT>name (optional)</DT>
  <DD>TEXT, default: NULL.
    Free text string to provide 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 images in memory on the
  segment in order to speed up processing.

  @note
  When set to TRUE, image byte arrays on each segment are maintained
  in cache (GD). 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 images
  residing on that segment can be read into memory.
</dl>

<b>Output tables</b>
<br>
    The model selection output table <model_selection_table> has only
    one row containing the best model configuration from autoML, based on the
    training/validation loss.  It contains the following columns:
    <table class="output">
      <tr>
        <th>mst_key</th>
        <td>INTEGER. ID that defines a unique tuple for
        model architecture-compile parameters-fit parameters.
        </td>
      </tr>
      <tr>
        <th>model_id</th>
        <td>VARCHAR. Model architecture ID from the 'model_arch_table'.
        </td>
      </tr>
      <tr>
        <th>compile_params</th>
        <td>VARCHAR. Keras compile parameters.
        </td>
      </tr>
      <tr>
        <th>fit_params</th>
        <td>VARCHAR. Keras fit parameters.
        </td>
      </tr>
    </table>

    A summary table named <model_selection_table>_summary is
    also created, which contains the following columns:
    <table class="output">
      <tr>
        <th>model_arch_table</th>
        <td>VARCHAR. Name of the model architecture table containing the
        model architecture IDs.
        </td>
      </tr>
      <tr>
        <th>object_table</th>
        <td>VARCHAR. Name of the object table containing the serialized
        Python objects for custom loss functions, custom metrics
        and top k categorical accuracy.
        If there are none, this field will be blank.
        </td>
      </tr>
    </table>

    The model output table produced by autoML contains columns below.
    There is one row per model configuration generated:
    <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 columns below.
    There is one row per model:
    <table class="output">
      <tr>
        <th>mst_key</th>
        <td>INTEGER. ID that defines a unique tuple for model architecture-compile parameters-fit parameters,
        for each model configuration generated.</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.</td>
    </tr>
    <tr>
        <th>metrics_type</th>
        <td>Metric 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>
    <tr>
        <th>metrics_iters</th>
        <td>Array indicating the iterations for which
        metrics are calculated, as derived from the
        parameters 'metrics_compute_frequency' and iterations decided by the autoML algorithm.
        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.

        Note that 'metrics_iters' values are for the overall iterations.
        For some models, the count might start at a later iteration based on
        the schedule. This representation is selected to simplify representing
        the results in iteration-metric graphs.
        </td>
    </tr>
    <tr>
        <th>s</th>
        <td>Bracket number from Hyperband schedule.
        This column is not present for Hyperopt.</td>
    </tr>
    <tr>
        <th>i</th>
        <td>Latest evaluated round number from Hyperband schedule.
        This column is not present for Hyperopt.</td>
    </tr>
    </table>

    A summary table named \<model_output_table\>_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 image preprocessing step.</td>
    </tr>
    <tr>
        <th>independent_varname</th>
        <td>Independent variables column from the original
        source table in the image 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>model selection table</th>
        <td>Name of the mst table containing
        the best configuration.</td>
    </tr>
    <tr>
        <th>automl_method</th>
        <td>Name of the autoML method used.</td>
    </tr>
    <tr>
        <th>automl_params</th>
        <td>AutoML parameter values.</td>
    </tr>
    <tr>
        <th>random_state</th>
        <td>Chosen random seed.</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>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
        image preprocessing step.</td>
    </tr>
   </table>

@anchor hyperband_schedule
@par Print Hyperband Schedule

This utility prints out the
schedule for a set of input parameters.  It does not run the Hyperband method, rather it
just prints out the schedule so you can see what the brackets look like.
Refer to [1] for information on Hyperband schedules.
<pre class="syntax">
hyperband_schedule(
    schedule_table,
    R,
    eta,
    skip_last
    )
</pre>

\b Arguments
<dl class="arglist">
  <dt>schedule_table</dt>
  <dd>VARCHAR. Name of output table containing hyperband schedule.
  </dd>

  <dt>R</dt>
  <dd>INTEGER. Maximum number of resources (i.e., iterations) to allocate to a single configuration
  in a round of Hyperband.
  </dd>

  <dt>eta</dt>
  <dd>INTEGER. Controls the proportion of configurations discarded in each
  round of successive halving. For example, for eta=3 will keep the best 1/3 the
  configurations for the next round.
  </dd>

  <dt>skip_last</dt>
  <dd>INTEGER. The number of last rounds to skip. For example, 'skip_last=1'
  will skip the last round (i.e., last entry in each bracket), which is standard random
  search and can be expensive when run for the total R iterations.
  </dd>

</dl>

<b>Output table</b>
<br>
    The hyperband schedule output table contains the following columns:
    <table class="output">
      <tr>
        <th>s</th>
        <td>INTEGER. Bracket number.
        </td>
      </tr>
      <tr>
        <th>i</th>
        <td>INTEGER. Round (depth) in bracket.
        </td>
      </tr>
      <tr>
        <th>n_i</th>
        <td>INTEGER. Number of configurations in this round.
        </td>
      </tr>
      <tr>
        <th>r_i</th>
        <td>INTEGER. Resources (iterations) in this round.
        </td>
      </tr>
    </table>
</br>


@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>Setup</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>

<h4>Hyperband</h4>

-# Print Hyperband schedule for example input parameters 'R=9' and 'eta=3':
<pre class="example">
DROP TABLE IF EXISTS hb_schedule;
SELECT madlib.hyperband_schedule ('hb_schedule',
                                   81,
                                   3,
                                   0);
SELECT * FROM hb_schedule ORDER BY s DESC, i;
</pre>
<pre class="result">
 s | i | n_i | r_i
---+---+-----+-----
 4 | 0 |  81 |   1
 4 | 1 |  27 |   3
 4 | 2 |   9 |   9
 4 | 3 |   3 |  27
 4 | 4 |   1 |  81
 3 | 0 |  27 |   3
 3 | 1 |   9 |   9
 3 | 2 |   3 |  27
 3 | 3 |   1 |  81
 2 | 0 |   9 |   9
 2 | 1 |   3 |  27
 2 | 2 |   1 |  81
 1 | 0 |   6 |  27
 1 | 1 |   2 |  81
 0 | 0 |   5 |  81
(15 rows)
</pre>
-# Run Hyperband method with 'R=9' and 'eta=3':
<pre class="example">
DROP TABLE IF EXISTS automl_output, automl_output_info, automl_output_summary, automl_mst_table, automl_mst_table_summary;
SELECT madlib.madlib_keras_automl('iris_train_packed',                -- source table
                                  'automl_output',                    -- model output table
                                  'model_arch_library',               -- model architecture table
                                  'automl_mst_table',                 -- model selection output table
                                  ARRAY[1,2],                         -- model IDs
                                  $${
                                      'loss': ['categorical_crossentropy'],
                                      'optimizer_params_list': [
                                          {'optimizer': ['Adam'],'lr': [0.001, 0.1, 'log']},
                                          {'optimizer': ['RMSprop'],'lr': [0.001, 0.1, 'log']}
                                      ],
                                      'metrics': ['accuracy']
                                  } $$,                               -- compile param grid
                                  $${'batch_size': [4, 8], 'epochs': [1]}$$,  -- fit params grid
                                  'hyperband',                        -- autoML method
                                  'R=9, eta=3, skip_last=0',          -- autoML params
                                  NULL,                               -- random state
                                  NULL,                               -- object table
                                  FALSE,                              -- use GPUs
                                  'iris_test_packed',                 -- validation table
                                  1,                                  -- metrics compute freq
                                  NULL,                               -- name
                                  NULL);                              -- descr
</pre>
-# View the model summary:
<pre class="example">
SELECT * FROM automl_output_summary;
</pre>
<pre class="result">
-[ RECORD 1 ]-------------+---------------------------------------------
source_table              | iris_train_packed
validation_table          | iris_test_packed
model                     | automl_output
model_info                | automl_output_info
dependent_varname         | class_text
independent_varname       | attributes
model_arch_table          | model_arch_library
model_selection_table     | automl_mst_table
automl_method             | hyperband
automl_params             | R=9, eta=3, skip_last=0
random_state              |
object_table              |
use_gpus                  | f
metrics_compute_frequency | 1
name                      |
description               |
start_training_time       | 2021-01-16 01:20:17
end_training_time         | 2021-01-16 01:21:47
madlib_version            | 1.18.0
num_classes               | 3
class_values              | {Iris-setosa,Iris-versicolor,Iris-virginica}
dependent_vartype         | character varying
normalizing_const         | 1
</pre>
-# View results for a few models:
<pre class="example">
SELECT * FROM automl_output_info ORDER BY validation_metrics_final DESC, validation_loss_final LIMIT 3;
</pre>
<pre class="result">
-[ RECORD 1 ]------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------
mst_key                  | 15
model_id                 | 1
compile_params           | optimizer='Adam(lr=0.005948073640447284)',metrics=['accuracy'],loss='categorical_crossentropy'
fit_params               | epochs=1,batch_size=8
model_type               | madlib_keras
model_size               | 0.7900390625
metrics_elapsed_time     | {41.9598820209503,47.7600600719452,53.5559930801392,59.2904281616211,65.0303740501404,70.910637140274,76.6586999893188,82.3321261405945,88.0252130031586}
metrics_type             | {accuracy}
loss_type                | categorical_crossentropy
training_metrics_final   | 0.975000023841858
training_loss_final      | 0.174209594726562
training_metrics         | {0.683333337306976,0.683333337306976,0.816666662693024,0.791666686534882,0.966666638851166,0.850000023841858,0.966666638851166,0.966666638851166,0.975000023841858}
training_loss            | {0.658287584781647,0.56329345703125,0.489711940288544,0.417204052209854,0.333063006401062,0.325938105583191,0.237209364771843,0.216858893632889,0.174209594726562}
validation_metrics_final | 0.933333337306976
validation_loss_final    | 0.282542854547501
validation_metrics       | {0.600000023841858,0.600000023841858,0.733333349227905,0.733333349227905,0.899999976158142,0.800000011920929,0.933333337306976,0.899999976158142,0.933333337306976}
validation_loss          | {0.844917356967926,0.739157736301422,0.651688754558563,0.567608654499054,0.458681106567383,0.461867392063141,0.344642341136932,0.335768848657608,0.282542854547501}
metrics_iters            | {5,6,7,8,9,10,11,12,13}
s                        | 0
i                        | 0
-[ RECORD 2 ]------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------
mst_key                  | 10
model_id                 | 1
compile_params           | optimizer='RMSprop(lr=0.01152123686692268)',metrics=['accuracy'],loss='categorical_crossentropy'
fit_params               | epochs=1,batch_size=8
model_type               | madlib_keras
model_size               | 0.7900390625
metrics_elapsed_time     | {21.1628739833832,27.9904689788818,34.9025909900665}
metrics_type             | {accuracy}
loss_type                | categorical_crossentropy
training_metrics_final   | 0.933333337306976
training_loss_final      | 0.239687830209732
training_metrics         | {0.699999988079071,0.699999988079071,0.933333337306976}
training_loss            | {0.600760638713837,0.386314034461975,0.239687830209732}
validation_metrics_final | 0.899999976158142
validation_loss_final    | 0.369663149118423
validation_metrics       | {0.533333361148834,0.600000023841858,0.899999976158142}
validation_loss          | {0.723896682262421,0.539595663547516,0.369663149118423}
metrics_iters            | {2,3,4}
s                        | 1
i                        | 0
-[ RECORD 3 ]------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------
mst_key                  | 2
model_id                 | 1
compile_params           | optimizer='RMSprop(lr=0.005464438486993435)',metrics=['accuracy'],loss='categorical_crossentropy'
fit_params               | epochs=1,batch_size=4
model_type               | madlib_keras
model_size               | 0.7900390625
metrics_elapsed_time     | {11.6164019107819,20.9570059776306,27.7901480197906,34.7061359882355}
metrics_type             | {accuracy}
loss_type                | categorical_crossentropy
training_metrics_final   | 0.925000011920929
training_loss_final      | 0.17901936173439
training_metrics         | {0.949999988079071,0.883333325386047,0.958333313465118,0.925000011920929}
training_loss            | {0.547602951526642,0.321837723255157,0.197886273264885,0.17901936173439}
validation_metrics_final | 0.866666674613953
validation_loss_final    | 0.325421392917633
validation_metrics       | {0.866666674613953,0.800000011920929,0.899999976158142,0.866666674613953}
validation_loss          | {0.723824441432953,0.462396681308746,0.326263695955276,0.325421392917633}
metrics_iters            | {1,2,3,4}
s                        | 2
i                        | 1
</pre>

<h4>Hyperopt</h4>

-# Run Hyperopt for a set number of trials, i.e., model configurations:
<pre class="example">
DROP TABLE IF EXISTS automl_output, automl_output_info, automl_output_summary, automl_mst_table, automl_mst_table_summary;
SELECT madlib.madlib_keras_automl('iris_train_packed',                -- source table
                                  'automl_output',                    -- model output table
                                  'model_arch_library',               -- model architecture table
                                  'automl_mst_table',                 -- model selection output table
                                  ARRAY[1,2],                         -- model IDs
                                  $${
                                      'loss': ['categorical_crossentropy'],
                                      'optimizer_params_list': [
                                          {'optimizer': ['Adam'],'lr': [0.001, 0.1, 'log']},
                                          {'optimizer': ['RMSprop'],'lr': [0.001, 0.1, 'log']}
                                      ],
                                      'metrics': ['accuracy']
                                  } $$,                               -- compile param grid
                                  $${'batch_size': [4, 8], 'epochs': [1]}$$,  -- fit params grid
                                  'hyperopt',                         -- autoML method
                                  'num_configs=20, num_iterations=10, algorithm=tpe',  -- autoML params
                                  NULL,                               -- random state
                                  NULL,                               -- object table
                                  FALSE,                              -- use GPUs
                                  'iris_test_packed',                 -- validation table
                                  1,                                  -- metrics compute freq
                                  NULL,                               -- name
                                  NULL);                              -- descr
</pre>
-# View the model summary:
<pre class="example">
SELECT * FROM automl_output_summary;
</pre>
<pre class="result">
-[ RECORD 1 ]-------------+-------------------------------------------------
source_table              | iris_train_packed
validation_table          | iris_test_packed
model                     | automl_output
model_info                | automl_output_info
dependent_varname         | class_text
independent_varname       | attributes
model_arch_table          | model_arch_library
model_selection_table     | automl_mst_table
automl_method             | hyperopt
automl_params             | num_configs=20, num_iterations=10, algorithm=tpe
random_state              |
object_table              |
use_gpus                  | f
metrics_compute_frequency | 1
name                      |
description               |
start_training_time       | 2020-10-23 00:24:43
end_training_time         | 2020-10-23 00:28:41
madlib_version            | 1.18.0
num_classes               | 3
class_values              | {Iris-setosa,Iris-versicolor,Iris-virginica}
dependent_vartype         | character varying
normalizing_const         | 1
</pre>
-# View results for a few models:
<pre class="example">
SELECT * FROM automl_output_info ORDER BY validation_metrics_final DESC, validation_loss_final LIMIT 3;
</pre>
<pre class="result">
-[ RECORD 1]----------------------------------------------------------------------------------------------------------
mst_key                  | 4
model_id                 | 1
compile_params           | optimizer='Adam(lr=0.021044174547856155)',metrics=['accuracy'],loss='categorical_crossentropy'
fit_params               | epochs=1,batch_size=8
model_type               | madlib_keras
model_size               | 0.7900390625
metrics_elapsed_time     | {24.9291331768036,27.1591901779175,29.3875880241394,31.4712460041046,33.6599950790405,35.9415881633759,38.0477111339569,40.2351109981537,42.3932039737701,44.4729251861572}
metrics_type             | {accuracy}
loss_type                | categorical_crossentropy
training_metrics_final   | 0.958333313465118
training_loss_final      | 0.116280987858772
training_metrics         | {0.658333361148834,0.658333361148834,0.733333349227905,0.816666662693024,0.949999988079071,0.949999988079071,0.949999988079071,0.875,0.958333313465118,0.958333313465118}
training_loss            | {0.681611657142639,0.50702965259552,0.41643014550209,0.349031865596771,0.2586330473423,0.234042942523956,0.204623967409134,0.337687611579895,0.116805233061314,0.116280987858772}
validation_metrics_final | 1
validation_loss_final    | 0.067971371114254
validation_metrics       | {0.699999988079071,0.699999988079071,0.733333349227905,0.766666650772095,0.899999976158142,0.899999976158142,0.899999976158142,0.899999976158142,1,1}
validation_loss          | {0.523795306682587,0.386897593736649,0.323715627193451,0.29447802901268,0.218715354800224,0.216124311089516,0.186037495732307,0.257792592048645,0.0693960413336754,0.067971371114254}
metrics_iters            | {1,2,3,4,5,6,7,8,9,10}
-[ RECORD 2]----------------------------------------------------------------------------------------------------------
mst_key                  | 8
model_id                 | 1
compile_params           | optimizer='RMSprop(lr=0.055711748803920255)',metrics=['accuracy'],loss='categorical_crossentropy'
fit_params               | epochs=1,batch_size=4
model_type               | madlib_keras
model_size               | 0.7900390625
metrics_elapsed_time     | {68.9713232517242,71.1428651809692,73.0566282272339,75.2099182605743,77.4740402698517,79.4580070972443,81.5958452224731,83.6865520477295,85.6433861255646,87.8569240570068}
metrics_type             | {accuracy}
loss_type                | categorical_crossentropy
training_metrics_final   | 0.966666638851166
training_loss_final      | 0.106823824346066
training_metrics         | {0.658333361148834,0.699999988079071,0.875,0.691666662693024,0.699999988079071,0.791666686534882,0.774999976158142,0.966666638851166,0.966666638851166,0.966666638851166}
training_loss            | {0.681002557277679,0.431159198284149,0.418115794658661,0.51969450712204,0.605500161647797,0.36535832285881,0.451890885829926,0.126570284366608,0.116986438632011,0.106823824346066}
validation_metrics_final | 1
validation_loss_final    | 0.0758842155337334
validation_metrics       | {0.699999988079071,0.699999988079071,0.966666638851166,0.699999988079071,0.699999988079071,0.800000011920929,0.766666650772095,0.966666638851166,0.966666638851166,1}
validation_loss          | {0.693905889987946,0.364648938179016,0.287941485643387,0.509377717971802,0.622031152248383,0.377092003822327,0.488217085599899,0.10258474200964,0.0973251685500145,0.0758842155337334}
metrics_iters            | {1,2,3,4,5,6,7,8,9,10}
-[ RECORD 3]----------------------------------------------------------------------------------------------------------
mst_key                  | 13
model_id                 | 1
compile_params           | optimizer='RMSprop(lr=0.006381376508189085)',metrics=['accuracy'],loss='categorical_crossentropy'
fit_params               | epochs=1,batch_size=4
model_type               | madlib_keras
model_size               | 0.7900390625
metrics_elapsed_time     | {141.029213190079,143.075024366379,145.330604314804,147.341159343719,149.579845190048,151.819869279861,153.939630270004,156.235336303711,158.536979198456,160.583434343338}
metrics_type             | {accuracy}
loss_type                | categorical_crossentropy
training_metrics_final   | 0.975000023841858
training_loss_final      | 0.0981351062655449
training_metrics         | {0.875,0.933333337306976,0.875,0.975000023841858,0.975000023841858,0.908333361148834,0.949999988079071,0.966666638851166,0.975000023841858,0.975000023841858}
training_loss            | {0.556384921073914,0.32896700501442,0.29009011387825,0.200998887419701,0.149432390928268,0.183790743350983,0.120595499873161,0.12202025949955,0.101290702819824,0.0981351062655449}
validation_metrics_final | 1
validation_loss_final    | 0.0775858238339424
validation_metrics       | {0.899999976158142,0.966666638851166,0.766666650772095,1,1,0.933333337306976,0.966666638851166,0.966666638851166,1,1}
validation_loss          | {0.442976772785187,0.249921068549156,0.268403559923172,0.167330235242844,0.134699374437332,0.140658855438232,0.0964709892868996,0.110730975866318,0.0810751244425774,0.0775858238339424}
metrics_iters            | {1,2,3,4,5,6,7,8,9,10}
</pre>
-# Run inference on one of the models generated by Hyperopt.  In this example we use the
validation set to predict on:
<pre class="example">
DROP TABLE IF EXISTS iris_predict;
SELECT madlib.madlib_keras_predict('automl_output',    -- model
                                   'iris_test',        -- test_table
                                   'id',               -- id column
                                   'attributes',       -- independent var
                                   'iris_predict',     -- output table
                                    'response',        -- prediction type
                                    FALSE,             -- use gpus
                                    4                 -- MST key
                                   );
SELECT * FROM iris_predict ORDER BY id;
</pre>
<pre class="result">
 id  |   class_text    |    prob
-----+-----------------+------------
   5 | Iris-setosa     |  0.9998704
   7 | Iris-setosa     | 0.99953365
  10 | Iris-setosa     |  0.9993413
  16 | Iris-setosa     |  0.9999825
  17 | Iris-setosa     |  0.9999256
  21 | Iris-setosa     |  0.9995347
  23 | Iris-setosa     |  0.9999405
  27 | Iris-setosa     |  0.9989955
  30 | Iris-setosa     |  0.9990559
  31 | Iris-setosa     |  0.9986846
  32 | Iris-setosa     |  0.9992879
  37 | Iris-setosa     | 0.99987197
  39 | Iris-setosa     |  0.9989151
  46 | Iris-setosa     |  0.9981341
  47 | Iris-setosa     |  0.9999044
  53 | Iris-versicolor |  0.9745001
  54 | Iris-versicolor |  0.8989025
  56 | Iris-versicolor | 0.97066855
  63 | Iris-versicolor | 0.96652734
  71 | Iris-versicolor | 0.84569126
  77 | Iris-versicolor |  0.9564522
  83 | Iris-versicolor |  0.9664927
  85 | Iris-versicolor | 0.96553373
  93 | Iris-versicolor | 0.96748537
 103 | Iris-virginica  |  0.9343488
 108 | Iris-virginica  | 0.91668576
 117 | Iris-virginica  |  0.7323582
 124 | Iris-virginica  | 0.72906417
 132 | Iris-virginica  | 0.50430095
 144 | Iris-virginica  |  0.9487652
(30 rows)
</pre>

@anchor notes
@par Notes

1. Hyperopt must be installed on the main node of the database cluster
if you want to use the Hyperopt method of autoML.
You can pip install it in the usual way [3].  Hyperband does not require
any separate package installation.

2. In practice you may need to do more than one run of an autoML method to arrive
at a model with adequate accuracy.  One approach is to set the search space to
be quite broad initially, then observe which hyperparameter ranges and model architectures
seem to be doing the best.  Subesquent runs can then zoom in on those good ones
in order to fine tune the model.

@anchor literature
@par Literature

[1] Li <em>et al.</em>, "Hyperband: A Novel Bandit-Based Approach to
Hyperparameter Optimization", Journal of Machine Learning Research 18 (2018) 1-52.

[2] J. Bergstra, D. Yamins, D. D. Cox, "Making a Science of Model Search:
Hyperparameter Optimization in Hundreds of Dimensions for Vision Architectures,"
<em>Proceedings of the 30th International Conference on Machine Learning</em>, Atlanta, Georgia,
USA, 2013. JMLR: W&CP volume 28.

[3] Python catalog for Hyperopt https://pypi.org/project/hyperopt/

@anchor related
@par Related Topics

madlib_keras_automl.sql_in

*/

CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.hyperband_schedule(
      schedule_table        VARCHAR,
      r                     INTEGER,
      eta                   INTEGER DEFAULT 3,
      skip_last             INTEGER DEFAULT 0
) RETURNS VOID AS $$
    PythonFunctionBodyOnly(`deep_learning', `madlib_keras_automl_hyperband')
    with AOControl(False):
        with MinWarning('warning'):
            schedule_loader = madlib_keras_automl_hyperband.HyperbandSchedule(schedule_table, r, eta, skip_last)
            schedule_loader.load()
$$ LANGUAGE plpythonu VOLATILE
              m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `MODIFIES SQL DATA', `');

CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.madlib_keras_automl(
    source_table                   VARCHAR,
    model_output_table             VARCHAR,
    model_arch_table               VARCHAR,
    model_selection_table          VARCHAR,
    model_id_list                  INTEGER[],
    compile_params_grid            VARCHAR,
    fit_params_grid                VARCHAR,
    automl_method                  VARCHAR DEFAULT 'hyperband',
    automl_params                  VARCHAR DEFAULT NULL,
    random_state                   INTEGER DEFAULT NULL,
    object_table                   VARCHAR DEFAULT NULL,
    use_gpus                       BOOLEAN DEFAULT FALSE,
    validation_table               VARCHAR DEFAULT NULL,
    metrics_compute_frequency      INTEGER DEFAULT NULL,
    name                           VARCHAR DEFAULT NULL,
    description                    VARCHAR DEFAULT NULL,
    use_caching                    BOOLEAN DEFAULT FALSE
) RETURNS VOID AS $$
if automl_method is None or automl_method.lower() == 'hyperband':
    PythonFunctionBodyOnly(`deep_learning', `madlib_keras_automl_hyperband')
    with AOControl(False):
        with MinWarning('warning'):
            schedule_loader = madlib_keras_automl_hyperband.AutoMLHyperband(**globals())
elif automl_method.lower() == 'hyperopt':
    PythonFunctionBodyOnly(`deep_learning', `madlib_keras_automl_hyperopt')
    with AOControl(False):
        with MinWarning('warning'):
            schedule_loader = madlib_keras_automl_hyperopt.AutoMLHyperopt(**globals())
else:
    plpy.error("madlib_keras_automl: The chosen automl method must be 'hyperband' or 'hyperopt'")
$$ LANGUAGE plpythonu VOLATILE
    m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `MODIFIES SQL DATA', `');