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| <div class="title">Keras<div class="ingroups"><a class="el" href="group__grp__early__stage.html">Early Stage Development</a> » <a class="el" href="group__grp__dl.html">Deep Learning</a></div></div> </div> |
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| <div class="contents"> |
| <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="#keras_predict_byom">Predict BYOM</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><dl class="section warning"><dt>Warning</dt><dd><em> This MADlib method is still in early stage development. Interface and implementation are subject to change. </em></dd></dl> |
| <p>This module allows you to use SQL to call deep learning models designed in Keras [1], which is a high-level neural network API written in Python. Keras was developed for fast experimentation. It can run on top of different backends and the one that is currently supported by MADlib is TensorFlow [2]. The implementation in MADlib is distributed and designed to train a single model across multiple segments (workers) in Greenplum database. (PostgreSQL is also supported.) Alternatively, to train multiple models at the same time for model architecture search or hyperparameter tuning, you can use <a href="group__grp__keras__run__model__selection.html">Model Selection</a>.</p> |
| <p>The main use case is image 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.</p> |
| <p>Before using Keras in MADlib you will need to mini-batch your training and evaluation datasets by calling the <a href="group__grp__input__preprocessor__dl.html">Preprocessor for Images</a> which is a utility that prepares image 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 [3].</p> |
| <p>You can also do inference on models that have not been trained in MADlib, but rather imported from an external source. This is in the section called "Predict BYOM" below, where "BYOM" stands for "Bring Your Own Model."</p> |
| <p>Note that the following MADlib functions are targeting a specific Keras version (2.2.4) with a specific TensorFlow kernel version (1.14). Using a newer or older version may or may not work as intended.</p> |
| <dl class="section note"><dt>Note</dt><dd>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).</dd></dl> |
| <p><a class="anchor" id="keras_fit"></a></p><dl class="section user"><dt>Fit</dt><dd>The fit (training) function has the following format:</dd></dl> |
| <pre class="syntax"> |
| madlib_keras_fit( |
| source_table, |
| model, |
| model_arch_table, |
| model_id, |
| compile_params, |
| fit_params, |
| num_iterations, |
| use_gpus, |
| validation_table, |
| metrics_compute_frequency, |
| warm_start, |
| name, |
| description |
| ) |
| </pre><p><b>Arguments</b> </p><dl class="arglist"> |
| <dt>source_table </dt> |
| <dd><p class="startdd">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 as part of the fit function.</p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>model </dt> |
| <dd><p class="startdd">TEXT. Name of the output table containing the model. Details of the output table are shown below. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>model_arch_table </dt> |
| <dd><p class="startdd">TEXT. Name of the table containing the model architecture and (optionally) initial weights to use for training. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>model_id </dt> |
| <dd><p class="startdd">INTEGER. This is the id in 'model_arch_table' containing the model architecture and (optionally) initial weights to use for training. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>compile_params </dt> |
| <dd><p class="startdd">TEXT. Parameters passed to the compile method of the Keras model class [4]. These parameters will be passed through as is so they must conform to the Keras API definition. As an example, you might use something like: <em>loss='categorical_crossentropy', optimizer='adam', metrics=['acc']</em>. The mandatory parameters that must be specified are 'optimizer' and 'loss'. Others are optional and will use the default values as per Keras if not specified here. Also, when specifying 'loss' and 'metrics' do <em>not</em> include the module and submodule prefixes like <em>loss='losses.categorical_crossentropy'</em> or <em>optimizer='keras.optmizers.adam'</em>.</p> |
| <dl class="section note"><dt>Note</dt><dd>The following loss function is not supported: <em>sparse_categorical_crossentropy</em>. The following metrics are not supported: <em>sparse_categorical_accuracy, top_k_categorical_accuracy, sparse_top_k_categorical_accuracy</em> and custom metrics.</dd></dl> |
| <p class="enddd"></p> |
| </dd> |
| <dt>fit_params </dt> |
| <dd><p class="startdd">TEXT. Parameters passed to the fit method of the Keras model class [4]. These will be passed through as is so they must conform to the Keras API definition. As an example, you might use something like: <em>batch_size=128, epochs=4</em>. There are no mandatory parameters so if you specify NULL, it will use all default values as per Keras. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>num_iterations </dt> |
| <dd><p class="startdd">INTEGER. Number of iterations to train. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>use_gpus (optional) </dt> |
| <dd><p class="startdd">BOOLEAN, default: FALSE (i.e., CPU). Determines whether GPUs are to be used for training the neural network. Set to TRUE to use GPUs.</p> |
| <dl class="section note"><dt>Note</dt><dd>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></dl> |
| </dd> |
| <dt>validation_table (optional) </dt> |
| <dd><p class="startdd">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. This can be controlled using the 'metrics_compute_frequency' paremeter described below.</p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>metrics_compute_frequency (optional) </dt> |
| <dd><p class="startdd">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. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>warm_start (optional) </dt> |
| <dd><p class="startdd">BOOLEAN, default: FALSE. Initalize weights with the coefficients from the last call of the fit function. If set to TRUE, weights will be initialized from the model table generated by the previous training run.</p> |
| <dl class="section note"><dt>Note</dt><dd>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></dl> |
| </dd> |
| <dt>name (optional) </dt> |
| <dd><p class="startdd">TEXT, default: NULL. Free text string to identify a name, if desired. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>description (optional) </dt> |
| <dd>TEXT, default: NULL. Free text string to provide a description, if desired. </dd> |
| </dl> |
| <p><b>Output tables</b> <br /> |
| The model table produced by fit contains the following columns: </p><table class="output"> |
| <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> |
| <p>A summary table named <model>_summary is also created, which has the following columns: </p><table class="output"> |
| <tr> |
| <th>source_table </th><td>Source table used for training. </td></tr> |
| <tr> |
| <th>model </th><td>Model output table produced by training. </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>dependent_varname </th><td>Dependent variable 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_id </th><td>The id of the model in the model architecture table used for training. </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>num_iterations </th><td>Number of iterations of training completed. </td></tr> |
| <tr> |
| <th>validation_table </th><td>Name of the table containing the validation dataset (if specified). </td></tr> |
| <tr> |
| <th>metrics_compute_frequency </th><td>Frequency that per-iteration metrics are computed for the training dataset and validation dataset. </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>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>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>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>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>class_values </th><td>Array of actual class values used. </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> |
| <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 '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> |
| <p><a class="anchor" id="keras_evaluate"></a></p><dl class="section user"><dt>Evaluate</dt><dd>The evaluation function has the following format:</dd></dl> |
| <pre class="syntax"> |
| madlib_keras_evaluate( |
| model_table, |
| test_table, |
| output_table, |
| use_gpus, |
| mst_key |
| ) |
| </pre><p><b>Arguments</b> </p><dl class="arglist"> |
| <dt>model_table </dt> |
| <dd><p class="startdd">TEXT. Name of the table containing the model to use for validation. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>test_table </dt> |
| <dd><p class="startdd">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 image 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.</p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>output_table </dt> |
| <dd>TEXT. Name of table that validation output will be written to. Table contains: <table class="output"> |
| <tr> |
| <th>loss </th><td>Loss value on evaluation dataset. </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><p class="starttd">Type of metric used that was used in the training step. </p> |
| <p class="endtd"></p> |
| </td></tr> |
| </table> |
| </dd> |
| <dt>use_gpus (optional) </dt> |
| <dd><p class="startdd">BOOLEAN, default: FALSE (i.e., CPU). Determines whether GPUs are to be used for training the neural network. Set to TRUE to use GPUs.</p> |
| <dl class="section note"><dt>Note</dt><dd>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></dl> |
| </dd> |
| <dt>mst_key (optional) </dt> |
| <dd>INTEGER, default: NULL. ID that defines a unique tuple for model architecture-compile parameters-fit parameters in a model selection table. Do not use this if training one model at a time using <a class="el" href="madlib__keras_8sql__in.html#a2277a353d16623515fe4488b43fadaaa">madlib_keras_fit()</a>. See the <a href="group__grp__keras__run__model__selection.html">Model Selection</a> section for more details on model selection by training multiple models at a time. </dd> |
| </dl> |
| <p><a class="anchor" id="keras_predict"></a></p><dl class="section user"><dt>Predict</dt><dd>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></dd></dl> |
| <p><b>Arguments</b> </p><dl class="arglist"> |
| <dt>model_table </dt> |
| <dd><p class="startdd">TEXT. Name of the table containing the model to use for prediction. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>test_table </dt> |
| <dd><p class="startdd">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.</p> |
| <p></p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>id_col </dt> |
| <dd><p class="startdd">TEXT. Name of the id column in the test data table. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>independent_varname </dt> |
| <dd><p class="startdd">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. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>output_table </dt> |
| <dd>TEXT. Name of the table that prediction output will be written to. Table contains: <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>estimated_COL_NAME </th><td>(For pred_type='response') The estimated class for classification, where COL_NAME is the name of the column to be predicted from test data. </td></tr> |
| <tr> |
| <th>prob_CLASS </th><td><p class="starttd">(For pred_type='prob' for classification) The probability of a given class. There will be one column for each class in the training data. </p> |
| <p class="endtd"></p> |
| </td></tr> |
| </table> |
| </dd> |
| <dt>pred_type (optional) </dt> |
| <dd><p class="startdd">TEXT, default: 'response'. The type of output desired, where 'response' gives the actual prediction and 'prob' gives the probability value for each class. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>use_gpus (optional) </dt> |
| <dd><p class="startdd">BOOLEAN, default: FALSE (i.e., CPU). Flag to enable GPU support for training neural network. The number of GPUs to use is determined by the parameters passed to the preprocessor.</p> |
| <dl class="section note"><dt>Note</dt><dd>We have seen some memory related issues when segments share GPU resources. For example, if you provide 1 GPU and your database cluster is set up to have 4 segments per segment host, it means that all 4 segments on a segment host will share the same GPU. The current recommended configuration is 1 GPU per segment. </dd></dl> |
| </dd> |
| <dt>mst_key (optional) </dt> |
| <dd>INTEGER, default: NULL. ID that defines a unique tuple for model architecture-compile parameters-fit parameters in a model selection table. Do not use this if training one model at a time using <a class="el" href="madlib__keras_8sql__in.html#a2277a353d16623515fe4488b43fadaaa">madlib_keras_fit()</a>. See the <a href="group__grp__keras__run__model__selection.html">Model Selection</a> section for more details on model selection by training multiple models at a time. </dd> |
| </dl> |
| <p><a class="anchor" id="keras_predict_byom"></a></p><dl class="section user"><dt>Predict BYOM (bring your own model)</dt><dd>The predict BYOM function allows you to do inference on models that have not been trained on MADlib, but rather imported from elsewhere. It has the following format: <pre class="syntax"> |
| madlib_keras_predict_byom( |
| model_arch_table, |
| model_id, |
| test_table, |
| id_col, |
| independent_varname, |
| output_table, |
| pred_type, |
| use_gpus, |
| class_values, |
| normalizing_const |
| ) |
| </pre></dd></dl> |
| <p><b>Arguments</b> </p><dl class="arglist"> |
| <dt>model_arch_table </dt> |
| <dd><p class="startdd">TEXT. Name of the architecture table containing the model to use for prediction. The model weights and architecture can be loaded to this table by using the <a href="group__grp__keras__model__arch.html">load_keras_model</a> function. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>model_id </dt> |
| <dd><p class="startdd">INTEGER. This is the id in 'model_arch_table' containing the model architecture and model weights to use for prediction. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>test_table </dt> |
| <dd><p class="startdd">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. Set the 'normalizing_const' below for the independent variable if necessary. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>id_col </dt> |
| <dd><p class="startdd">TEXT. Name of the id column in the test data table. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>independent_varname </dt> |
| <dd><p class="startdd">TEXT. Column with independent variables in the test table. Set the 'normalizing_const' below if necessary. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>output_table </dt> |
| <dd>TEXT. Name of the table that prediction output will be written to. Table contains: <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>estimated_dependent_var </th><td>(For pred_type='response') Estimated class for classification. If the 'class_values' parameter is passed in as NULL, then we assume that the class labels are [0,1,2...,n-1] where n-1 is the number of classes in the model architecture. </td></tr> |
| <tr> |
| <th>prob_CLASS </th><td><p class="starttd">(For pred_type='prob' for classification) Probability of a given class. If 'class_values' is passed in as NULL, we create one column called 'prob' which is an array of probabilities for each class. If 'class_values' is not NULL, then there will be one column for each class. </p> |
| <p class="endtd"></p> |
| </td></tr> |
| </table> |
| </dd> |
| <dt>pred_type (optional) </dt> |
| <dd><p class="startdd">TEXT, default: 'response'. The type of output desired, where 'response' gives the actual prediction and 'prob' gives the probability value for each class. </p> |
| <p class="enddd"></p> |
| </dd> |
| <dt>use_gpus (optional) </dt> |
| <dd><p class="startdd">BOOLEAN, default: FALSE (i.e., CPU). Flag to enable GPU support for training neural network. The number of GPUs to use is determined by the parameters passed to the preprocessor.</p> |
| <dl class="section note"><dt>Note</dt><dd>We have seen some memory related issues when segments share GPU resources. For example, if you provide 1 GPU and your database cluster is set up to have 4 segments per segment host, it means that all 4 segments on a segment host will share the same GPU. The current recommended configuration is 1 GPU per segment. </dd></dl> |
| </dd> |
| <dt>class_values (optional) </dt> |
| <dd><p class="startdd">TEXT[], default: NULL. List of class labels that were used while training the model. See the 'output_table' column above for more details.</p> |
| <dl class="section note"><dt>Note</dt><dd>If you specify the class values parameter, it must reflect how the dependent variable was 1-hot encoded for training. If you accidently pick another order that does not match the 1-hot encoding, the predictions would be wrong. </dd></dl> |
| </dd> |
| <dt>normalizing_const (optional) </dt> |
| <dd>DOUBLE PRECISION, default: 1.0. The normalizing constant to divide each value in the 'independent_varname' array by. For example, you would use 255 for this value if the image data is in the form 0-255. </dd> |
| </dl> |
| <p><a class="anchor" id="example"></a></p><dl class="section user"><dt>Examples</dt><dd></dd></dl> |
| <dl class="section note"><dt>Note</dt><dd>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 <a href="https://archive.ics.uci.edu/ml/datasets/iris">https://archive.ics.uci.edu/ml/datasets/iris</a>. For more realistic examples with images please refer to the deep learning notebooks at <a href="https://github.com/apache/madlib-site/tree/asf-site/community-artifacts">https://github.com/apache/madlib-site/tree/asf-site/community-artifacts</a>.</dd></dl> |
| <h4>Classification</h4> |
| <ol type="1"> |
| <li>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></li> |
| <li>Call the preprocessor for deep learning. For the training dataset: <pre class="example"> |
| \x off |
| 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></li> |
| <li>Define and load model architecture. Use Keras to define the model architecture: <pre class="example"> |
| import keras |
| from keras.models import Sequential |
| from keras.layers import Dense |
| model_simple = Sequential() |
| model_simple.add(Dense(10, activation='relu', input_shape=(4,))) |
| model_simple.add(Dense(10, activation='relu')) |
| model_simple.add(Dense(3, activation='softmax')) |
| model_simple.summary() |
| <pre class="fragment">_________________________________________________________________ |
| 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 |
| </pre> |
| </pre> Export the model to JSON: <pre class="example"> |
| model_simple.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> 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 |
| 'A simple model' -- Descr |
| ); |
| </pre></li> |
| <li>Train model and view summary table: <pre class="example"> |
| DROP TABLE IF EXISTS iris_model, iris_model_summary; |
| SELECT madlib.madlib_keras_fit('iris_train_packed', -- source table |
| 'iris_model', -- model output table |
| 'model_arch_library', -- model arch table |
| 1, -- model arch id |
| $$ loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'] $$, -- compile_params |
| $$ batch_size=5, epochs=3 $$, -- fit_params |
| 10 -- num_iterations |
| ); |
| SELECT * FROM iris_model_summary; |
| </pre> <pre class="result"> |
| -[ RECORD 1 ]-------------+-------------------------------------------------------------------------- |
| source_table | iris_train_packed |
| model | iris_model |
| dependent_varname | class_text |
| independent_varname | attributes |
| model_arch_table | model_arch_library |
| model_id | 1 |
| compile_params | loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'] |
| fit_params | batch_size=5, epochs=3 |
| num_iterations | 10 |
| validation_table | |
| metrics_compute_frequency | 10 |
| name | |
| description | |
| model_type | madlib_keras |
| model_size | 0.7900390625 |
| start_training_time | 2019-06-05 20:55:15.785034 |
| end_training_time | 2019-06-05 20:55:25.373035 |
| metrics_elapsed_time | {9.58799290657043} |
| madlib_version | 1.17.0 |
| num_classes | 3 |
| class_values | {Iris-setosa,Iris-versicolor,Iris-virginica} |
| dependent_vartype | character varying |
| normalizing_const | 1 |
| metrics_type | {accuracy} |
| training_metrics_final | 0.766666650772 |
| training_loss_final | 0.721103310585 |
| training_metrics | {0.766666650772095} |
| training_loss | {0.721103310585022} |
| validation_metrics_final | |
| validation_loss_final | |
| validation_metrics | |
| validation_loss | |
| metrics_iters | {10} |
| </pre></li> |
| <li>Use the test dataset to evaluate the model we built above: <pre class="example"> |
| DROP TABLE IF EXISTS iris_validate; |
| SELECT madlib.madlib_keras_evaluate('iris_model', -- model |
| 'iris_test_packed', -- test table |
| 'iris_validate' -- output table |
| ); |
| SELECT * FROM iris_validate; |
| </pre> <pre class="result"> |
| loss | metric | metrics_type |
| -------------------+-------------------+-------------- |
| 0.719491899013519 | 0.800000011920929 | {accuracy} |
| (1 row) |
| </pre></li> |
| <li>Predict. We will use the validation dataset 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_model', -- model |
| 'iris_test', -- test_table |
| 'id', -- id column |
| 'attributes', -- independent var |
| 'iris_predict' -- output table |
| ); |
| SELECT * FROM iris_predict ORDER BY id; |
| </pre> <pre class="result"> |
| id | estimated_class_text |
| -----+---------------------- |
| 4 | Iris-setosa |
| 6 | Iris-setosa |
| 8 | Iris-setosa |
| 12 | Iris-setosa |
| 13 | Iris-setosa |
| 15 | Iris-setosa |
| 24 | Iris-setosa |
| 30 | Iris-setosa |
| 38 | Iris-setosa |
| 49 | Iris-setosa |
| 60 | Iris-virginica |
| 68 | Iris-versicolor |
| 69 | Iris-versicolor |
| 76 | Iris-versicolor |
| 78 | Iris-versicolor |
| 81 | Iris-versicolor |
| 85 | Iris-virginica |
| 90 | Iris-versicolor |
| 91 | Iris-versicolor |
| 94 | Iris-virginica |
| 104 | Iris-virginica |
| 106 | Iris-versicolor |
| 107 | Iris-virginica |
| 110 | Iris-virginica |
| 119 | Iris-versicolor |
| 127 | Iris-virginica |
| 129 | Iris-virginica |
| 134 | Iris-versicolor |
| 139 | Iris-virginica |
| 144 | Iris-virginica |
| (30 rows) |
| </pre> Count missclassifications: <pre class="example"> |
| SELECT COUNT(*) FROM iris_predict JOIN iris_test USING (id) |
| WHERE iris_predict.estimated_class_text != iris_test.class_text; |
| </pre> <pre class="result"> |
| count |
| -------+ |
| 6 |
| (1 row) |
| </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.estimated_class_text 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 |
| -----------------------+ |
| 80.00 |
| (1 row) |
| </pre></li> |
| <li>Predict BYOM. We will use the validation dataset for prediction as well, which is not usual but serves to show the syntax. See <a href="group__grp__keras__model__arch.html">load_keras_model</a> for details on how to load the model architecture and weights. In this example we will use weights we already have: <pre class="example"> |
| UPDATE model_arch_library |
| SET model_weights = iris_model.model_weights |
| FROM iris_model |
| WHERE model_arch_library.model_id = 1; |
| </pre> Now train using a model from the model architecture table directly without referencing the model table from the MADlib training. Note that if you specify the class values parameter as we do below, it must reflect how the dependent variable was 1-hot encoded for training. In this example the '<a class="el" href="input__data__preprocessor_8sql__in.html#a11a26c03a879a4c7e40e3ba07ca39a22">training_preprocessor_dl()</a>' in Step 2 above encoded in the order {'Iris-setosa', 'Iris-versicolor', 'Iris-virginica'} so this is the order we pass in the parameter. If we accidently pick another order that does not match the 1-hot encoding, the predictions would be wrong. <pre class="example"> |
| DROP TABLE IF EXISTS iris_predict_byom; |
| SELECT madlib.madlib_keras_predict_byom('model_arch_library', -- model arch table |
| 1, -- model arch id |
| 'iris_test', -- test_table |
| 'id', -- id column |
| 'attributes', -- independent var |
| 'iris_predict_byom', -- output table |
| 'response', -- prediction type |
| FALSE, -- use GPUs |
| ARRAY['Iris-setosa', 'Iris-versicolor', 'Iris-virginica'], -- class values |
| 1.0 -- normalizing const |
| ); |
| SELECT * FROM iris_predict_byom ORDER BY id; |
| </pre> The prediction is in the 'estimated_dependent_var' column: <pre class="result"> |
| id | estimated_dependent_var |
| -----+---------------------- |
| 4 | Iris-setosa |
| 6 | Iris-setosa |
| 8 | Iris-setosa |
| 12 | Iris-setosa |
| 13 | Iris-setosa |
| 15 | Iris-setosa |
| 24 | Iris-setosa |
| 30 | Iris-setosa |
| 38 | Iris-setosa |
| 49 | Iris-setosa |
| 60 | Iris-virginica |
| 68 | Iris-versicolor |
| 69 | Iris-versicolor |
| 76 | Iris-versicolor |
| 78 | Iris-versicolor |
| 81 | Iris-versicolor |
| 85 | Iris-virginica |
| 90 | Iris-versicolor |
| 91 | Iris-versicolor |
| 94 | Iris-virginica |
| 104 | Iris-virginica |
| 106 | Iris-versicolor |
| 107 | Iris-virginica |
| 110 | Iris-virginica |
| 119 | Iris-versicolor |
| 127 | Iris-virginica |
| 129 | Iris-virginica |
| 134 | Iris-versicolor |
| 139 | Iris-virginica |
| 144 | Iris-virginica |
| (30 rows) |
| </pre> Count missclassifications: <pre class="example"> |
| SELECT COUNT(*) FROM iris_predict_byom JOIN iris_test USING (id) |
| WHERE iris_predict_byom.estimated_dependent_var != iris_test.class_text; |
| </pre> <pre class="result"> |
| count |
| -------+ |
| 6 |
| (1 row) |
| </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_byom.estimated_dependent_var as estimated |
| from iris_predict_byom inner join iris_test |
| on iris_test.id=iris_predict_byom.id) q |
| WHERE q.actual=q.estimated; |
| </pre> <pre class="result"> |
| test_accuracy_percent |
| -----------------------+ |
| 80.00 |
| (1 row) |
| </pre></li> |
| </ol> |
| <h4>Classification with Other Parameters</h4> |
| <ol type="1"> |
| <li>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. <pre class="example"> |
| DROP TABLE IF EXISTS iris_model, iris_model_summary; |
| SELECT madlib.madlib_keras_fit('iris_train_packed', -- source table |
| 'iris_model', -- model output table |
| 'model_arch_library', -- model arch table |
| 1, -- model arch id |
| $$ loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'] $$, -- compile_params |
| $$ batch_size=5, epochs=3 $$, -- fit_params |
| 10, -- num_iterations |
| FALSE, -- use GPUs |
| 'iris_test_packed', -- validation dataset |
| 3, -- metrics compute frequency |
| FALSE, -- warm start |
| 'Sophie L.', -- name |
| 'Simple MLP for iris dataset' -- description |
| ); |
| SELECT * FROM iris_model_summary; |
| </pre> <pre class="result"> |
| -[ RECORD 1 ]-------------+-------------------------------------------------------------------------- |
| source_table | iris_train_packed |
| model | iris_model |
| dependent_varname | class_text |
| independent_varname | attributes |
| model_arch_table | model_arch_library |
| model_id | 1 |
| compile_params | loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'] |
| fit_params | batch_size=5, epochs=3 |
| num_iterations | 10 |
| validation_table | iris_test_packed |
| metrics_compute_frequency | 3 |
| name | Sophie L. |
| description | Simple MLP for iris dataset |
| model_type | madlib_keras |
| model_size | 0.7900390625 |
| start_training_time | 2019-06-05 20:58:23.224629 |
| end_training_time | 2019-06-05 20:58:35.477499 |
| metrics_elapsed_time | {4.69859290122986,8.2062520980835,10.8104848861694,12.2528700828552} |
| madlib_version | 1.17.0 |
| num_classes | 3 |
| class_values | {Iris-setosa,Iris-versicolor,Iris-virginica} |
| dependent_vartype | character varying |
| normalizing_const | 1 |
| metrics_type | {accuracy} |
| training_metrics_final | 0.941666662693 |
| training_loss_final | 0.40586027503 |
| training_metrics | {0.699999988079071,0.800000011920929,0.899999976158142,0.941666662693024} |
| training_loss | {0.825238645076752,0.534248650074005,0.427499741315842,0.405860275030136} |
| validation_metrics_final | 0.866666674614 |
| validation_loss_final | 0.409001916647 |
| validation_metrics | {0.733333349227905,0.733333349227905,0.866666674613953,0.866666674613953} |
| validation_loss | {0.827081918716431,0.536275088787079,0.431326270103455,0.409001916646957} |
| metrics_iters | {3,6,9,10} |
| </pre></li> |
| <li>Predict probabilities for each class: <pre class="example"> |
| DROP TABLE IF EXISTS iris_predict; |
| SELECT madlib.madlib_keras_predict('iris_model', -- model |
| 'iris_test', -- test_table |
| 'id', -- id column |
| 'attributes', -- independent var |
| 'iris_predict', -- output table |
| 'prob' -- response type |
| ); |
| SELECT * FROM iris_predict ORDER BY id; |
| </pre> <pre class="result"> |
| id | prob_Iris-setosa | prob_Iris-versicolor | prob_Iris-virginica |
| -----+------------------+----------------------+--------------------- |
| 4 | 0.9241953 | 0.059390426 | 0.01641435 |
| 6 | 0.9657151 | 0.02809224 | 0.0061926916 |
| 8 | 0.9543316 | 0.03670931 | 0.008959154 |
| 12 | 0.93851465 | 0.048681837 | 0.012803554 |
| 13 | 0.93832576 | 0.04893658 | 0.012737647 |
| 15 | 0.98717564 | 0.01091238 | 0.0019119986 |
| 24 | 0.9240628 | 0.060805064 | 0.015132156 |
| 30 | 0.92063266 | 0.062279057 | 0.017088294 |
| 38 | 0.9353765 | 0.051353406 | 0.013270103 |
| 49 | 0.9709265 | 0.023811856 | 0.005261566 |
| 60 | 0.034395564 | 0.5260507 | 0.43955377 |
| 68 | 0.031360663 | 0.53689945 | 0.43173987 |
| 69 | 0.0098787155 | 0.46121457 | 0.52890676 |
| 76 | 0.031186827 | 0.5644549 | 0.40435827 |
| 78 | 0.00982633 | 0.48929632 | 0.5008774 |
| 81 | 0.03658528 | 0.53248984 | 0.4309249 |
| 85 | 0.015423619 | 0.48452598 | 0.5000504 |
| 90 | 0.026857043 | 0.5155698 | 0.45757324 |
| 91 | 0.013675574 | 0.47155368 | 0.5147708 |
| 94 | 0.073440716 | 0.5418821 | 0.3846772 |
| 104 | 0.0021637122 | 0.3680499 | 0.62978643 |
| 106 | 0.00052832486 | 0.30891812 | 0.6905536 |
| 107 | 0.007315576 | 0.40949163 | 0.5831927 |
| 110 | 0.0022259138 | 0.4058138 | 0.59196025 |
| 119 | 0.00018505375 | 0.24510723 | 0.7547077 |
| 127 | 0.009542585 | 0.46958733 | 0.52087003 |
| 129 | 0.0019719477 | 0.36288205 | 0.635146 |
| 134 | 0.0056418083 | 0.43401477 | 0.56034344 |
| 139 | 0.01067015 | 0.4755573 | 0.51377255 |
| 144 | 0.0018909549 | 0.37689638 | 0.6212126 |
| (30 rows) |
| </pre></li> |
| <li>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('iris_train_packed', -- source table |
| 'iris_model', -- model output table |
| 'model_arch_library', -- model arch table |
| 1, -- model arch id |
| $$ loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'] $$, -- compile_params |
| $$ batch_size=5, epochs=3 $$, -- fit_params |
| 5, -- 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 |
| ); |
| SELECT * FROM iris_model_summary; |
| </pre> <pre class="result"> |
| -[ RECORD 1 ]-------------+-------------------------------------------------------------------------------------------- |
| source_table | iris_train_packed |
| model | iris_model |
| dependent_varname | class_text |
| independent_varname | attributes |
| model_arch_table | model_arch_library |
| model_id | 1 |
| compile_params | loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'] |
| fit_params | batch_size=5, epochs=3 |
| num_iterations | 5 |
| validation_table | iris_test_packed |
| metrics_compute_frequency | 1 |
| name | Sophie L. |
| description | Simple MLP for iris dataset |
| model_type | madlib_keras |
| model_size | 0.7900390625 |
| start_training_time | 2019-06-05 20:59:43.971792 |
| end_training_time | 2019-06-05 20:59:51.654586 |
| metrics_elapsed_time | {2.89326310157776,4.14273309707642,5.24781513214111,6.34498596191406,7.68279695510864} |
| madlib_version | 1.17.0 |
| num_classes | 3 |
| class_values | {Iris-setosa,Iris-versicolor,Iris-virginica} |
| dependent_vartype | character varying |
| normalizing_const | 1 |
| metrics_type | {accuracy} |
| training_metrics_final | 0.933333337307 |
| training_loss_final | 0.334455043077 |
| training_metrics | {0.933333337306976,0.933333337306976,0.975000023841858,0.975000023841858,0.933333337306976} |
| training_loss | {0.386842548847198,0.370587915182114,0.357161343097687,0.344598710536957,0.334455043077469} |
| validation_metrics_final | 0.866666674614 |
| validation_loss_final | 0.34414178133 |
| validation_metrics | {0.866666674613953,0.866666674613953,0.933333337306976,0.866666674613953,0.866666674613953} |
| validation_loss | {0.391442179679871,0.376414686441422,0.362262904644012,0.351912915706635,0.344141781330109} |
| metrics_iters | {1,2,3,4,5} |
| </pre> Note that the loss and accuracy values pick up from where the previous run left off.</li> |
| </ol> |
| <h4>Transfer Learning</h4> |
| <p>Here we want to start with initial weights from a pre-trained model rather than training from scratch. We also want to use a model architecture with the earlier feature layer(s) frozen to save on training time. The example below is somewhat contrived but gives you the idea of the steps.</p> |
| <ol type="1"> |
| <li>Define and load a model architecture with the 1st hidden layer frozen:</li> |
| </ol> |
| <pre class="example"> |
| model_transfer = Sequential() |
| model_transfer.add(Dense(10, activation='relu', input_shape=(4,), trainable=False)) |
| model_transfer.add(Dense(10, activation='relu')) |
| model_transfer.add(Dense(3, activation='softmax')) |
| model_simple.summary() |
| <pre class="fragment">_________________________________________________________________ |
| 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: 143 |
| Non-trainable params: 50 |
| </pre> |
| </pre><p> Export the model to JSON: </p><pre class="example"> |
| model_simple.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_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": false, "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_3", "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_4", "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><p> Load into model architecture table: </p><pre class="example"> |
| SELECT madlib.load_keras_model('model_arch_library', -- Output table, |
| $$ |
| {"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": false, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_4", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"} |
| $$ |
| ::json, -- JSON blob |
| NULL, -- Weights |
| 'Maria', -- Name |
| 'A transfer model' -- Descr |
| ); |
| </pre><p> Fetch the weights from a previous MADlib run. (Normally these would be downloaded from a source that trained the same model architecture on a related dataset.) </p><pre class="example"> |
| UPDATE model_arch_library |
| SET model_weights = iris_model.model_weights |
| FROM iris_model |
| WHERE model_arch_library.model_id = 2; |
| </pre><p> Now train the model using the transfer model and the pre-trained weights: </p><pre class="example"> |
| DROP TABLE IF EXISTS iris_model, iris_model_summary; |
| SELECT madlib.madlib_keras_fit('iris_train_packed', -- source table |
| 'iris_model', -- model output table |
| 'model_arch_library', -- model arch table |
| 2, -- model arch id |
| $$ loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'] $$, -- compile_params |
| $$ batch_size=5, epochs=3 $$, -- fit_params |
| 10 -- num_iterations |
| ); |
| SELECT * FROM iris_model_summary; |
| </pre> <pre class="result"> |
| -[ RECORD 1 ]-------------+-------------------------------------------------------------------------- |
| source_table | iris_train_packed |
| model | iris_model |
| dependent_varname | class_text |
| independent_varname | attributes |
| model_arch_table | model_arch_library |
| model_id | 2 |
| compile_params | loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'] |
| fit_params | batch_size=5, epochs=3 |
| num_iterations | 10 |
| validation_table | |
| metrics_compute_frequency | 10 |
| name | |
| description | |
| model_type | madlib_keras |
| model_size | 0.7900390625 |
| start_training_time | 2019-06-05 21:01:03.998422 |
| end_training_time | 2019-06-05 21:01:13.525838 |
| metrics_elapsed_time | {9.52741599082947} |
| madlib_version | 1.17.0 |
| num_classes | 3 |
| class_values | {Iris-setosa,Iris-versicolor,Iris-virginica} |
| dependent_vartype | character varying |
| normalizing_const | 1 |
| metrics_type | {accuracy} |
| training_metrics_final | 0.975000023842 |
| training_loss_final | 0.245171800256 |
| training_metrics | {0.975000023841858} |
| training_loss | {0.245171800255775} |
| validation_metrics_final | |
| validation_loss_final | |
| validation_metrics | |
| validation_loss | |
| metrics_iters | {10} |
| </pre><p><a class="anchor" id="notes"></a></p><dl class="section user"><dt>Notes</dt><dd></dd></dl> |
| <ol type="1"> |
| <li>Refer to the deep learning section of the Apache MADlib wiki [5] for important information including supported libraries and versions.</li> |
| <li>Classification is currently supported, not regression.</li> |
| <li>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.</li> |
| </ol> |
| <p><a class="anchor" id="background"></a></p><dl class="section user"><dt>Technical Background</dt><dd></dd></dl> |
| <p>For an introduction to deep learning foundations, including MLP and CNN, refer to [6].</p> |
| <p>This module trains a single large model across the database cluster using the bulk synchronous parallel (BSP) approach, with model averaging [7].</p> |
| <p>On the effect of database cluster size: as the database cluster size increases, the per iteration loss will be higher since the model only sees 1/n of the data, where n is the number of segments. However, each iteration runs faster than single node because it is only traversing 1/n of the data. For highly non-convex solution spaces, convergence behavior may diminish as cluster size increases. Ensure that each segment has sufficient volume of data and examples of each class value.</p> |
| <p>Alternatively, to train multiple models at the same time for model architecture search or hyperparameter tuning, you can use <a href="group__grp__keras__run__model__selection.html">Model Selection</a>, which does not do model averaging and hence may have better covergence efficiency.</p> |
| <p><a class="anchor" id="literature"></a></p><dl class="section user"><dt>Literature</dt><dd></dd></dl> |
| <p><a class="anchor" id="mlp-lit-1"></a>[1] <a href="https://keras.io/">https://keras.io/</a></p> |
| <p>[2] <a href="https://www.tensorflow.org/">https://www.tensorflow.org/</a></p> |
| <p>[3] "Neural Networks for Machine Learning", Lectures 6a and 6b on mini-batch gradient descent, Geoffrey Hinton with Nitish Srivastava and Kevin Swersky, <a href="http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf">http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf</a></p> |
| <p>[4] <a href="https://keras.io/models/model/">https://keras.io/models/model/</a></p> |
| <p>[5] Deep learning section of Apache MADlib wiki, <a href="https://cwiki.apache.org/confluence/display/MADLIB/Deep+Learning">https://cwiki.apache.org/confluence/display/MADLIB/Deep+Learning</a></p> |
| <p>[6] Deep Learning, Ian Goodfellow, Yoshua Bengio and Aaron Courville, MIT Press, 2016.</p> |
| <p>[7] "Resource-Efficient and Reproducible Model Selection on Deep Learning Systems," Supun Nakandala, Yuhao Zhang, and Arun Kumar, Technical Report, Computer Science and Engineering, University of California, San Diego <a href="https://adalabucsd.github.io/papers/TR_2019_Cerebro.pdf">https://adalabucsd.github.io/papers/TR_2019_Cerebro.pdf</a>.</p> |
| <p>[8] Greenplum Database server configuration parameters <a href="https://gpdb.docs.pivotal.io/latest/ref_guide/config_params/guc-list.html">https://gpdb.docs.pivotal.io/latest/ref_guide/config_params/guc-list.html</a></p> |
| <p><a class="anchor" id="related"></a></p><dl class="section user"><dt>Related Topics</dt><dd></dd></dl> |
| <p>File <a class="el" href="madlib__keras_8sql__in.html" title="SQL functions for distributed deep learning with keras. ">madlib_keras.sql_in</a> documenting the training, evaluate and predict functions. </p> |
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