2.1.0
User Documentation for Apache MADlib
Train Single Model

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 can run on top of different backends and the one that is currently supported by MADlib is TensorFlow [2]. The implementation in MADlib is 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 the methods in Train Multiple Models.

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

Before using Keras in MADlib you will need to preprocess your training and evaluation datasets by using the method called Preprocess Data which is a utility that prepares data for use by models that support mini-batch as an optimization option. This is a one-time operation and you would only need to re-run the preprocessor if your input data has changed. The advantage of using mini-batching is that it can perform better than stochastic gradient descent because it uses more than one training example at a time, typically resulting faster and smoother convergence [3].

You can also do inference on models that have not been trained in MADlib, but rather imported from an external source. This is described in the section called "Predict BYOM" below, where "BYOM" stands for "Bring Your Own Model."

Note that the following MADlib functions are targeting a specific TensorFlow kernel version (1.14). Using a newer or older version may or may not work as intended.

MADlib's deep learning methods are designed to use the TensorFlow package and its built in Keras functions. To ensure consistency, please use tensorflow.keras objects (models, layers, etc.) instead of importing Keras and using its objects.

Note
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).

Fit
The fit (training) function has the following format:
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,
    object_table
    )

Arguments

source_table

TEXT. Name of the table containing the training data. This is the name of the output table from the data preprocessor. Independent and dependent variables are specified in the preprocessor step which is why you do not need to explictly state them here as part of the fit function.

model

TEXT. Name of the output table containing the model. Details of the output table are shown below.

model_arch_table

TEXT. Name of the table containing the model architecture and (optionally) initial weights to use for training.

model_id

INTEGER. This is the id in 'model_arch_table' containing the model architecture and (optionally) initial weights to use for training.

compile_params

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: loss='categorical_crossentropy', optimizer='adam', metrics=['acc']. 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 not include the module and submodule prefixes like loss='losses.categorical_crossentropy' or optimizer='keras.optmizers.adam'.

Note
  • Custom loss functions and custom metrics can be used as defined in Define Custom Functions. 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: sparse_categorical_crossentropy. The following metrics are not supported: sparse_categorical_accuracy, sparse_top_k_categorical_accuracy.
  • The Keras accuracy parameter top_k_categorical_accuracy returns top 5 accuracy by default. If you want a different top k value, use the helper function Top k Accuracy Function to create a custom Python function to compute the top k accuracy that you want.

fit_params

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: batch_size=128, epochs=4. There are no mandatory parameters so if you specify NULL, it will use all default values as per Keras.

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")]
num_iterations

INTEGER. Number of iterations to train.

use_gpus (optional)

BOOLEAN, default: FALSE (i.e., CPU). Determines whether GPUs are to be used for training the neural network. Set to TRUE to use GPUs.

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

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

metrics_compute_frequency (optional)

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.

warm_start (optional)

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.

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

TEXT, default: NULL. Free text string to identify a name, if desired.

description (optional)

TEXT, default: NULL. Free text string to provide a description, if desired.

object_table (optional)
TEXT, default: NULL. Name of the table that contains the custom functions. Note that this table must be created using the Define Custom Functions method. Do not qualify with a schema name, since schema will be automatically pulled from the function definition.

Output tables
The model table produced by fit contains the following columns:

model_weights BYTEA8. Byte array containing the weights of the neural net.
model_arch TEXT. A JSON representation of the model architecture used in training.

A summary table named <model>_summary is also created, which has the following columns:

source_table Source table used for training.
model Model output table produced by training.
dependent_varname Dependent variable column from the original source table in the data preprocessing step.
independent_varname Independent variables column from the original source table in the data preprocessing step.
model_arch_table Name of the table containing the model architecture and (optionally) the initial model weights.
model_id The id of the model in the model architecture table used for training.
compile_params Compile parameters passed to Keras.
fit_params Fit parameters passed to Keras.
num_iterations Number of iterations of training completed.
validation_table Name of the table containing the validation dataset (if specified).
metrics_compute_frequency Frequency that per-iteration metrics are computed for the training dataset and validation dataset.
name Name of the training run (free text).
description Description of the training run (free text).
model_type General identifier for type of model trained. Currently says 'madlib_keras'.
model_size Size of the model in KB. Models are stored in 'bytea' data format which is used for binary strings in PostgreSQL type databases.
start_training_time Timestamp for start of training.
end_training_time Timestamp for end of training.
metrics_elapsed_time Array of elapsed time for metric computations as per the 'metrics_compute_frequency' parameter. Useful for drawing a curve showing loss, accuracy or other metrics as a function of time. For example, if 'metrics_compute_frequency=5' this would be an array of elapsed time for every 5th iteration, plus the last iteration. Note that this field reports the time for training + validation, if there is a validation table provided.
madlib_version Version of MADlib used.
num_classes Count of distinct classes values used for each dependent variable.
dependent_vartype Data type for each dependent variable.
normalizing_constant Normalizing constant used from the data preprocessing step.
metrics_type Metric specified in the 'compile_params'.
loss_type Loss specified in the 'compile_params'.
training_metrics_final Final value of the training metric after all iterations have completed. The metric reported is the one specified in the 'metrics_type' parameter.
training_loss_final Final value of the training loss after all iterations have completed.
training_metrics 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.
training_loss 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.
validation_metrics_final Final value of the validation metric after all iterations have completed. The metric reported is the one specified in the 'metrics_type' parameter.
validation_loss_final Final value of the validation loss after all iterations have completed.
validation_metrics 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.
validation_loss 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.
metrics_iters 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.
<dependent_varname>_class_values Array of class values used for a particular dependent variable. A column will be generated for each dependent variable.

Evaluate
The evaluation function has the following format:
madlib_keras_evaluate(
    model_table,
    test_table,
    output_table,
    use_gpus
    )

Arguments

model_table

TEXT. Name of the table containing the model to use for validation.

test_table

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

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

Type of loss function that was used in the training step. (It means you cannot have a different loss in evaluate compared to training.)

use_gpus (optional)

BOOLEAN, default: FALSE (i.e., CPU). Determines whether GPUs are to be used for training the neural network. Set to TRUE to use GPUs.

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

Predict
The prediction function has the following format:
madlib_keras_predict(
    model_table,
    test_table,
    id_col,
    independent_varname,
    output_table,
    pred_type,
    use_gpus
    )

Arguments

model_table

TEXT. Name of the table containing the model to use for prediction.

test_table

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.

id_col

TEXT. Name of the id column in the test data table.

independent_varname

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. In the case that there are multiple independent variables, representing a multi-input neural network, put the columns as a comma separated list, e.g., 'indep_var1, indep_var2, indep_var3' in the same way as was done in the preprocessor step for the training data.

output_table
TEXT. Name of the table that prediction output will be written to. Table contains:
id Gives the 'id' for each prediction, corresponding to each row from the test_table.
class_name Name of variable being predicted.
class_value Estimated class value.
prob Probability of a given class value.
rank

The rank of a given class based on the ordering of probabilities.

pred_type (optional)

TEXT or INTEGER or DOUBLE PRECISION default: 'prob'. The type and range of output desired. This parameter allows the following options.

  • 'response': the actual prediction
  • 'prob': the probability value for each class
  • 0<value<1: the lower limit for the probability (double precision)
  • 1<=value: the lower limit for the rank of the prediction (integer)

use_gpus (optional)

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.

Note
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.

Predict BYOM (bring your own model)
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:
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,
    dependent_count
    )

Arguments

model_arch_table

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 Define Model Architectures function.

model_id

INTEGER. This is the id in 'model_arch_table' containing the model architecture and model weights to use for prediction.

test_table

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.

id_col

TEXT. Name of the id column in the test data table.

independent_varname

TEXT. Column with independent variables in the test table. Set the 'normalizing_const' below if necessary.

output_table
TEXT. Name of the table that prediction output will be written to. Table contains:
id Gives the 'id' for each prediction, corresponding to each row from the test_table.
class_name The estimated variable.
class_value The estimated class for classification.
prob Probability of a given class.
rank

The rank of a given class based on the ordering of probabilities.

pred_type (optional)

TEXT, default: 'response'. The type of output desired, where 'response' gives the actual prediction and 'prob' gives the probability value for each class.

use_gpus (optional)

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.

Note
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.
class_values (optional)

TEXT[], default: NULL. Two dimensional list of class labels that were used while training the model for each dependent variable.

Note
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.
normalizing_const (optional)

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.

dependent_count (optional)
INTEGER, default: 1. The number of dependent variables in the model.

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.

Classification

  1. Create an input data set.
    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');
    
    Create a test/validation dataset from the training data:
    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;
    
     count
    ------+
       120
    
  2. Call the preprocessor for deep learning. For the training dataset:
    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
                                            );
    \x on
    SELECT * FROM iris_train_packed_summary;
    
    -[ RECORD 1 ]-----------+---------------------------------------------
    source_table            | iris_train
    output_table            | iris_train_packed
    dependent_varname       | {class_text}
    independent_varname     | {attributes}
    dependent_vartype       | {"character varying"}
    class_text_class_values | {Iris-setosa,Iris-versicolor,Iris-virginica}
    buffer_size             | 40
    normalizing_const       | 1
    num_classes             | {3}
    distribution_rules      | all_segments
    __internal_gpu_config__ | all_segments
    
    For the validation dataset:
    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;
    
    -[ RECORD 1 ]-----------+---------------------------------------------
    source_table            | iris_test
    output_table            | iris_test_packed
    dependent_varname       | {class_text}
    independent_varname     | {attributes}
    dependent_vartype       | {"character varying"}
    class_text_class_values | {Iris-setosa,Iris-versicolor,Iris-virginica}
    buffer_size             | 10
    normalizing_const       | 1
    num_classes             | {3}
    distribution_rules      | all_segments
    __internal_gpu_config__ | all_segments
    
  3. Define and load model architecture. Use Keras to define the model architecture:
    import keras
    from tensorflow.keras.models import Sequential
    from tensorflow.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()
    
    _________________________________________________________________
    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
    
    Export the model to JSON:
    model_simple.to_json()
    
    '{"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"}'
    
    Load into model architecture table:
    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
    );
    
  4. Train model and view summary table:
    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
                                    $$ loss='categorical_crossentropy', optimizer='adam', metrics=['categorical_accuracy'] $$,  -- compile_params
                                    $$ batch_size=5, epochs=3 $$,  -- fit_params
                                    10                    -- num_iterations
                                  );
    SELECT * FROM iris_model_summary;
    
    -[ 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=['categorical_accuracy']
    fit_params                |  batch_size=5, epochs=3
    num_iterations            | 10
    validation_table          |
    object_table              |
    metrics_compute_frequency | 10
    name                      |
    description               |
    model_type                | madlib_keras
    model_size                | 0.7900390625
    start_training_time       | 2021-02-01 15:58:43.760568
    end_training_time         | 2021-02-01 15:58:44.470054
    metrics_elapsed_time      | {0.709463119506836}
    madlib_version            | 2.1.0
    num_classes               | {3}
    dependent_vartype         | {"character varying"}
    normalizing_const         | 1
    metrics_type              | {accuracy}
    loss_type                 | categorical_crossentropy
    training_metrics_final    | 0.800000011920929
    training_loss_final       | 0.519745767116547
    training_metrics          | {0.800000011920929}
    training_loss             | {0.519745767116547}
    validation_metrics_final  |
    validation_loss_final     |
    validation_metrics        |
    validation_loss           |
    metrics_iters             | {10}
    class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}
    
  5. Use the test dataset to evaluate the model we built above:
    \x off
    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;
    
           loss        |      metric       | metrics_type |        loss_type
    -------------------+-------------------+--------------+--------------------------
     0.566911578178406 | 0.699999988079071 | {accuracy}   | categorical_crossentropy
    (1 row)
    
  6. 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:
    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, rank;
    
     id  | class_name |   class_value   |    prob     | rank
    -----+------------+-----------------+-------------+------
       4 | class_text | Iris-setosa     |   0.7689959 |    1
       4 | class_text | Iris-virginica  |  0.15600422 |    2
       4 | class_text | Iris-versicolor |  0.07499986 |    3
       9 | class_text | Iris-setosa     |   0.7642913 |    1
       9 | class_text | Iris-virginica  |  0.15844841 |    2
       9 | class_text | Iris-versicolor | 0.077260315 |    3
      13 | class_text | Iris-setosa     |   0.8160971 |    1
      13 | class_text | Iris-virginica  |  0.13053566 |    2
      13 | class_text | Iris-versicolor |  0.05336728 |    3
      14 | class_text | Iris-setosa     |    0.804419 |    1
      14 | class_text | Iris-virginica  |  0.13591427 |    2
      14 | class_text | Iris-versicolor |  0.05966685 |    3
      15 | class_text | Iris-setosa     |  0.88610095 |    1
      15 | class_text | Iris-virginica  |  0.08893245 |    2
      15 | class_text | Iris-versicolor | 0.024966586 |    3
      25 | class_text | Iris-setosa     |  0.68195176 |    1
      25 | class_text | Iris-virginica  |  0.20334557 |    2
      25 | class_text | Iris-versicolor | 0.114702694 |    3
      34 | class_text | Iris-setosa     |   0.8619849 |    1
      34 | class_text | Iris-virginica  |   0.1032386 |    2
      34 | class_text | Iris-versicolor | 0.034776475 |    3
      36 | class_text | Iris-setosa     |  0.84423053 |    1
      36 | class_text | Iris-virginica  | 0.114072084 |    2
      36 | class_text | Iris-versicolor |  0.04169741 |    3
      39 | class_text | Iris-setosa     |  0.79559565 |    1
      39 | class_text | Iris-virginica  |  0.13950573 |    2
      39 | class_text | Iris-versicolor | 0.064898595 |    3
      48 | class_text | Iris-setosa     |   0.8010248 |    1
      48 | class_text | Iris-virginica  |  0.13615999 |    2
      48 | class_text | Iris-versicolor |  0.06281526 |    3
      56 | class_text | Iris-versicolor |  0.47732472 |    1
      56 | class_text | Iris-virginica  |  0.46635315 |    2
      56 | class_text | Iris-setosa     | 0.056322116 |    3
      63 | class_text | Iris-virginica  |   0.5329179 |    1
      63 | class_text | Iris-versicolor |  0.38090497 |    2
      63 | class_text | Iris-setosa     | 0.086177126 |    3
      65 | class_text | Iris-virginica  |   0.4516514 |    1
      65 | class_text | Iris-versicolor |   0.4330772 |    2
      65 | class_text | Iris-setosa     |  0.11527142 |    3
      69 | class_text | Iris-virginica  |  0.57348573 |    1
      69 | class_text | Iris-versicolor |  0.36967018 |    2
      69 | class_text | Iris-setosa     |  0.05684407 |    3
      72 | class_text | Iris-virginica  |   0.4918356 |    1
      72 | class_text | Iris-versicolor |  0.42640963 |    2
      72 | class_text | Iris-setosa     |  0.08175478 |    3
      73 | class_text | Iris-virginica  |   0.5534297 |    1
      73 | class_text | Iris-versicolor |  0.39819974 |    2
      73 | class_text | Iris-setosa     |  0.04837051 |    3
      75 | class_text | Iris-virginica  |   0.4986787 |    1
      75 | class_text | Iris-versicolor |  0.43546444 |    2
      75 | class_text | Iris-setosa     |  0.06585683 |    3
      82 | class_text | Iris-virginica  |  0.47533202 |    1
      82 | class_text | Iris-versicolor |  0.43122545 |    2
      82 | class_text | Iris-setosa     |  0.09344252 |    3
      90 | class_text | Iris-virginica  |  0.47962278 |    1
      90 | class_text | Iris-versicolor |  0.45068985 |    2
      90 | class_text | Iris-setosa     |  0.06968742 |    3
      91 | class_text | Iris-virginica  |  0.47005868 |    1
      91 | class_text | Iris-versicolor |   0.4696341 |    2
      91 | class_text | Iris-setosa     | 0.060307216 |    3
      97 | class_text | Iris-versicolor |  0.49070656 |    1
      97 | class_text | Iris-virginica  |  0.44852367 |    2
      97 | class_text | Iris-setosa     | 0.060769808 |    3
     100 | class_text | Iris-versicolor |  0.47884703 |    1
     100 | class_text | Iris-virginica  |   0.4577389 |    2
     100 | class_text | Iris-setosa     |  0.06341412 |    3
     102 | class_text | Iris-virginica  |   0.5396443 |    1
     102 | class_text | Iris-versicolor |  0.40945858 |    2
     102 | class_text | Iris-setosa     | 0.050897114 |    3
     109 | class_text | Iris-virginica  |  0.61228466 |    1
     109 | class_text | Iris-versicolor |   0.3522025 |    2
     109 | class_text | Iris-setosa     |  0.03551281 |    3
     114 | class_text | Iris-virginica  |    0.562418 |    1
     114 | class_text | Iris-versicolor |  0.38269255 |    2
     114 | class_text | Iris-setosa     |  0.05488944 |    3
     128 | class_text | Iris-virginica  |  0.50814027 |    1
     128 | class_text | Iris-versicolor |  0.44240898 |    2
     128 | class_text | Iris-setosa     |  0.04945076 |    3
     138 | class_text | Iris-virginica  |  0.52319044 |    1
     138 | class_text | Iris-versicolor |  0.43786547 |    2
     138 | class_text | Iris-setosa     |  0.03894412 |    3
     140 | class_text | Iris-virginica  |   0.5677875 |    1
     140 | class_text | Iris-versicolor |   0.3936515 |    2
     140 | class_text | Iris-setosa     | 0.038560882 |    3
     141 | class_text | Iris-virginica  |  0.58414406 |    1
     141 | class_text | Iris-versicolor |   0.3770253 |    2
     141 | class_text | Iris-setosa     |  0.03883058 |    3
     150 | class_text | Iris-virginica  |   0.5025033 |    1
     150 | class_text | Iris-versicolor |   0.4495215 |    2
     150 | class_text | Iris-setosa     | 0.047975186 |    3
    (90 rows)
    
    Count missclassifications:
    SELECT COUNT(*) FROM iris_predict JOIN iris_test USING (id)
    WHERE iris_predict.class_value != iris_test.class_text AND iris_predict.rank = 1;
    
     count
    -------+
         9
    (1 row)
    
    Accuracy:
    SELECT round(count(*)*100/(150*0.2),2) as test_accuracy_percent from
        (select iris_test.class_text as actual, iris_predict.class_value as estimated
         from iris_predict inner join iris_test
         on iris_test.id=iris_predict.id where iris_predict.rank = 1) q
    WHERE q.actual=q.estimated;
    
     test_accuracy_percent
    -----------------------+
                     70.00
    (1 row)
    
  7. Predict BYOM. We will use the validation dataset for prediction as well, which is not usual but serves to show the syntax. See Define Model Architectures for details on how to load the model architecture and weights. In this example we will use weights we already have:
    UPDATE model_arch_library
    SET model_weights = iris_model.model_weights
    FROM iris_model
    WHERE model_arch_library.model_id = 1;
    
    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 'training_preprocessor_dl()' 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.
    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[ARRAY['Iris-setosa', 'Iris-versicolor', 'Iris-virginica']], -- class values
                                             1.0                   -- normalizing const
                                       );
    SELECT * FROM iris_predict_byom ORDER BY id;
    
    The prediction is in the 'estimated_dependent_var' column:
     id  |  class_name   |   class_value   |    prob
    -----+---------------+-----------------+------------
       4 | dependent_var | Iris-setosa     |  0.7689959
       9 | dependent_var | Iris-setosa     |  0.7642913
      13 | dependent_var | Iris-setosa     |  0.8160971
      14 | dependent_var | Iris-setosa     |   0.804419
      15 | dependent_var | Iris-setosa     | 0.88610095
      25 | dependent_var | Iris-setosa     | 0.68195176
      34 | dependent_var | Iris-setosa     |  0.8619849
      36 | dependent_var | Iris-setosa     | 0.84423053
      39 | dependent_var | Iris-setosa     | 0.79559565
      48 | dependent_var | Iris-setosa     |  0.8010248
      56 | dependent_var | Iris-versicolor | 0.47732472
      63 | dependent_var | Iris-virginica  |  0.5329179
      65 | dependent_var | Iris-virginica  |  0.4516514
      69 | dependent_var | Iris-virginica  | 0.57348573
      72 | dependent_var | Iris-virginica  |  0.4918356
      73 | dependent_var | Iris-virginica  |  0.5534297
      75 | dependent_var | Iris-virginica  |  0.4986787
      82 | dependent_var | Iris-virginica  | 0.47533202
      90 | dependent_var | Iris-virginica  | 0.47962278
      91 | dependent_var | Iris-virginica  | 0.47005868
      97 | dependent_var | Iris-versicolor | 0.49070656
     100 | dependent_var | Iris-versicolor | 0.47884703
     102 | dependent_var | Iris-virginica  |  0.5396443
     109 | dependent_var | Iris-virginica  | 0.61228466
     114 | dependent_var | Iris-virginica  |   0.562418
     128 | dependent_var | Iris-virginica  | 0.50814027
     138 | dependent_var | Iris-virginica  | 0.52319044
     140 | dependent_var | Iris-virginica  |  0.5677875
     141 | dependent_var | Iris-virginica  | 0.58414406
     150 | dependent_var | Iris-virginica  |  0.5025033
    (30 rows)
     
    Count missclassifications:
    SELECT COUNT(*) FROM iris_predict_byom JOIN iris_test USING (id)
    WHERE iris_predict_byom.class_value != iris_test.class_text;
    
     count
    -------+
         9
    (1 row)
    
    Accuracy:
    SELECT round(count(*)*100/(150*0.2),2) as test_accuracy_percent from
        (select iris_test.class_text as actual, iris_predict_byom.class_value as estimated
         from iris_predict_byom inner join iris_test
         on iris_test.id=iris_predict_byom.id) q
    WHERE q.actual=q.estimated;
    
     test_accuracy_percent
    -----------------------+
                     70.00
    (1 row)
    

Classification with Other Parameters

  1. 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.
    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
                                    $$ loss='categorical_crossentropy', optimizer='adam', metrics=['categorical_accuracy'] $$,  -- 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
                                  );
    \x on
    SELECT * FROM iris_model_summary;
    
    -[ 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=['categorical_accuracy']
    fit_params                |  batch_size=5, epochs=3
    num_iterations            | 10
    validation_table          | iris_test_packed
    object_table              |
    metrics_compute_frequency | 3
    name                      | Sophie L.
    description               | Simple MLP for iris dataset
    model_type                | madlib_keras
    model_size                | 0.7900390625
    start_training_time       | 2021-01-29 14:41:16.943861
    end_training_time         | 2021-01-29 14:41:19.478149
    metrics_elapsed_time      | {2.3377411365509,2.42358803749084,2.49885511398315,2.53427410125732}
    madlib_version            | 2.1.0
    num_classes               | {3}
    dependent_vartype         | {"character varying"}
    normalizing_const         | 1
    metrics_type              | {accuracy}
    loss_type                 | categorical_crossentropy
    training_metrics_final    | 0.883333325386047
    training_loss_final       | 0.584357917308807
    training_metrics          | {0.733333349227905,0.774999976158142,0.883333325386047,0.883333325386047}
    training_loss             | {0.765825688838959,0.664925456047058,0.605871021747589,0.584357917308807}
    validation_metrics_final  | 0.899999976158142
    validation_loss_final     | 0.590348184108734
    validation_metrics        | {0.699999988079071,0.866666674613953,0.899999976158142,0.899999976158142}
    validation_loss           | {0.81381630897522,0.691304981708527,0.616305589675903,0.590348184108734}
    metrics_iters             | {3,6,9,10}
    class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}
    
  2. Predict probabilities for each class:
    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
                                       );
    \x off
    SELECT * FROM iris_predict ORDER BY id;
    
     id  | class_name |   class_value   |    prob     | rank
    -----+------------+-----------------+-------------+------
       4 | class_text | Iris-versicolor |  0.34548566 |    2
       4 | class_text | Iris-setosa     |  0.57626975 |    1
       4 | class_text | Iris-virginica  |  0.07824467 |    3
       7 | class_text | Iris-versicolor |  0.34442508 |    2
       7 | class_text | Iris-setosa     |  0.57735515 |    1
       7 | class_text | Iris-virginica  | 0.078219764 |    3
       9 | class_text | Iris-versicolor |   0.3453845 |    2
       9 | class_text | Iris-virginica  |  0.08293749 |    3
       9 | class_text | Iris-setosa     |  0.57167804 |    1
      12 | class_text | Iris-versicolor |  0.34616387 |    2
      12 | class_text | Iris-setosa     |   0.5793855 |    1
      12 | class_text | Iris-virginica  | 0.074450605 |    3
      18 | class_text | Iris-versicolor |  0.34597218 |    2
      18 | class_text | Iris-virginica  |  0.07100027 |    3
      18 | class_text | Iris-setosa     |  0.58302754 |    1
      20 | class_text | Iris-versicolor |  0.34480608 |    2
      20 | class_text | Iris-setosa     |   0.5856424 |    1
      20 | class_text | Iris-virginica  |  0.06955151 |    3
      24 | class_text | Iris-versicolor |  0.38339624 |    2
      24 | class_text | Iris-setosa     |   0.5330486 |    1
      24 | class_text | Iris-virginica  | 0.083555184 |    3
      30 | class_text | Iris-versicolor |  0.35101113 |    2
      30 | class_text | Iris-setosa     |  0.56958234 |    1
      30 | class_text | Iris-virginica  |  0.07940655 |    3
      31 | class_text | Iris-versicolor |   0.3503181 |    2
      31 | class_text | Iris-setosa     |   0.5733414 |    1
      31 | class_text | Iris-virginica  |  0.07634052 |    3
      33 | class_text | Iris-versicolor |  0.34489658 |    2
      33 | class_text | Iris-setosa     |   0.5847962 |    1
      33 | class_text | Iris-virginica  |  0.07030724 |    3
      35 | class_text | Iris-versicolor |  0.34719768 |    2
      35 | class_text | Iris-setosa     |    0.577414 |    1
      35 | class_text | Iris-virginica  |  0.07538838 |    3
      40 | class_text | Iris-versicolor |   0.3464746 |    2
      40 | class_text | Iris-setosa     |  0.58250487 |    1
      40 | class_text | Iris-virginica  | 0.071020484 |    3
      41 | class_text | Iris-versicolor |  0.34581655 |    2
      41 | class_text | Iris-setosa     |   0.5805128 |    1
      41 | class_text | Iris-virginica  |  0.07367061 |    3
      45 | class_text | Iris-versicolor |  0.38146245 |    2
      45 | class_text | Iris-setosa     |  0.52559936 |    1
      45 | class_text | Iris-virginica  |  0.09293811 |    3
      51 | class_text | Iris-virginica  |  0.41811863 |    2
      51 | class_text | Iris-setosa     |  0.07617204 |    3
      51 | class_text | Iris-versicolor |   0.5057093 |    1
      53 | class_text | Iris-virginica  |  0.47048044 |    2
      53 | class_text | Iris-versicolor |  0.47150916 |    1
      53 | class_text | Iris-setosa     | 0.058010455 |    3
      57 | class_text | Iris-versicolor |   0.4443615 |    2
      57 | class_text | Iris-setosa     | 0.055230834 |    3
      57 | class_text | Iris-virginica  |   0.5004077 |    1
      58 | class_text | Iris-virginica  |  0.35905617 |    2
      58 | class_text | Iris-setosa     |  0.15329117 |    3
      58 | class_text | Iris-versicolor |   0.4876526 |    1
      69 | class_text | Iris-versicolor |   0.4485282 |    2
      69 | class_text | Iris-virginica  |   0.4913048 |    1
      69 | class_text | Iris-setosa     | 0.060167026 |    3
      72 | class_text | Iris-virginica  |  0.38764492 |    2
      72 | class_text | Iris-versicolor |   0.5052213 |    1
      72 | class_text | Iris-setosa     |  0.10713379 |    3
      74 | class_text | Iris-versicolor |  0.44894043 |    2
      74 | class_text | Iris-setosa     |  0.06307102 |    3
      74 | class_text | Iris-virginica  |  0.48798853 |    1
      93 | class_text | Iris-virginica  |  0.40836224 |    2
      93 | class_text | Iris-setosa     | 0.102442265 |    3
      93 | class_text | Iris-versicolor |  0.48919544 |    1
      94 | class_text | Iris-virginica  |  0.35238466 |    2
      94 | class_text | Iris-versicolor |  0.49192256 |    1
      94 | class_text | Iris-setosa     |  0.15569273 |    3
     110 | class_text | Iris-versicolor |   0.2917817 |    2
     110 | class_text | Iris-virginica  |   0.6972358 |    1
     110 | class_text | Iris-setosa     | 0.010982483 |    3
     113 | class_text | Iris-versicolor |  0.35037678 |    2
     113 | class_text | Iris-setosa     | 0.021288367 |    3
     113 | class_text | Iris-virginica  |   0.6283349 |    1
     117 | class_text | Iris-versicolor |  0.35009244 |    2
     117 | class_text | Iris-virginica  |   0.6264066 |    1
     117 | class_text | Iris-setosa     | 0.023500985 |    3
     123 | class_text | Iris-versicolor |   0.2849912 |    2
     123 | class_text | Iris-virginica  |  0.70571697 |    1
     123 | class_text | Iris-setosa     | 0.009291774 |    3
     127 | class_text | Iris-versicolor |   0.4041788 |    2
     127 | class_text | Iris-virginica  |  0.55537915 |    1
     127 | class_text | Iris-setosa     | 0.040441982 |    3
     130 | class_text | Iris-versicolor |  0.38396156 |    2
     130 | class_text | Iris-virginica  |  0.59018326 |    1
     130 | class_text | Iris-setosa     | 0.025855187 |    3
     143 | class_text | Iris-versicolor |  0.33123586 |    2
     143 | class_text | Iris-virginica  |   0.6445185 |    1
     143 | class_text | Iris-setosa     | 0.024245638 |    3
    (30 rows)
    
  3. 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:
    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
                                    $$ loss='categorical_crossentropy', optimizer='adam', metrics=['categorical_accuracy'] $$,  -- 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
                                  );
    \x on
    SELECT * FROM iris_model_summary;
    
    -[ 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=['categorical_accuracy']
    fit_params                |  batch_size=5, epochs=3
    num_iterations            | 5
    validation_table          | iris_test_packed
    object_table              |
    metrics_compute_frequency | 1
    name                      | Sophie L.
    description               | Simple MLP for iris dataset
    model_type                | madlib_keras
    model_size                | 0.7900390625
    start_training_time       | 2021-01-29 14:42:28.780276
    end_training_time         | 2021-01-29 14:42:31.177561
    metrics_elapsed_time      | {2.24628114700317,2.28473520278931,2.32178020477295,2.35844302177429,2.39726710319519}
    madlib_version            | 2.1.0
    num_classes               | {3}
    dependent_vartype         | {"character varying"}
    normalizing_const         | 1
    metrics_type              | {accuracy}
    loss_type                 | categorical_crossentropy
    training_metrics_final    | 0.916666686534882
    training_loss_final       | 0.456518471240997
    training_metrics          | {0.883333325386047,0.891666650772095,0.908333361148834,0.916666686534882,0.916666686534882}
    training_loss             | {0.559914350509644,0.537041485309601,0.513083755970001,0.47985765337944,0.456518471240997}
    validation_metrics_final  | 0.966666638851166
    validation_loss_final     | 0.432968735694885
    validation_metrics        | {0.899999976158142,0.899999976158142,0.933333337306976,0.966666638851166,0.966666638851166}
    validation_loss           | {0.558336615562439,0.529355347156525,0.496939331293106,0.462678134441376,0.432968735694885}
    metrics_iters             | {1,2,3,4,5}
    class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}
    
    Note that the loss and accuracy values pick up from where the previous run left off.

Transfer Learning

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.

  1. Define and load a model architecture with the 1st hidden layer frozen:
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()
_________________________________________________________________
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

Export the model to JSON:

model_simple.to_json()
'{"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"}'

Load into model architecture table:

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
);

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.)

UPDATE model_arch_library
SET model_weights = iris_model.model_weights
FROM iris_model
WHERE model_arch_library.model_id = 2;

Now train the model using the transfer model and the pre-trained weights:

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
                                $$ loss='categorical_crossentropy', optimizer='adam', metrics=['categorical_accuracy'] $$,  -- compile_params
                                $$ batch_size=5, epochs=3 $$,  -- fit_params
                                10                    -- num_iterations
                              );
\x on
SELECT * FROM iris_model_summary;
-[ 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=['categorical_accuracy']
fit_params                |  batch_size=5, epochs=3
num_iterations            | 10
validation_table          |
object_table              |
metrics_compute_frequency | 10
name                      |
description               |
model_type                | madlib_keras
model_size                | 0.7900390625
start_training_time       | 2021-01-29 14:44:51.176983
end_training_time         | 2021-01-29 14:44:53.666457
metrics_elapsed_time      | {2.48945999145508}
madlib_version            | 2.1.0
num_classes               | {3}
dependent_vartype         | {"character varying"}
normalizing_const         | 1
metrics_type              | {accuracy}
loss_type                 | categorical_crossentropy
training_metrics_final    | 0.949999988079071
training_loss_final       | 0.340020209550858
training_metrics          | {0.949999988079071}
training_loss             | {0.340020209550858}
validation_metrics_final  |
validation_loss_final     |
validation_metrics        |
validation_loss           |
metrics_iters             | {10}
class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}

Notes
  1. Refer to the deep learning section of the Apache MADlib wiki [5] for important information including supported libraries and versions.
  2. Classification is currently supported, not regression.
  3. Reminder about the distinction between warm start and transfer learning. Warm start uses model state (weights) from the model output table from a previous training run - set the 'warm_start' parameter to TRUE in the fit function. Transfer learning uses initial model state (weights) stored in the 'model_arch_table' - in this case set the 'warm_start' parameter to FALSE in the fit function.

Technical Background

For an introduction to deep learning foundations, including MLP and CNN, refer to [6].

This module trains a single large model across the database cluster using the bulk synchronous parallel (BSP) approach, with model averaging [7].

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.

Alternatively, to train multiple models at the same time for model architecture search or hyperparameter tuning, you can use the methods in Train Multiple Models, which does not do model averaging and hence may have better covergence efficiency.

Literature

[1] https://keras.io/

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

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

[4] https://keras.io/models/model/

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

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

[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 https://adalabucsd.github.io/papers/TR_2019_Cerebro.pdf.

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

Related Topics

File madlib_keras.sql_in documenting the training, evaluate and predict functions.