Deprecation Notice: With the introduction of daal4py, a package that supersedes PyDAAL, Intel is deprecating PyDAAL and will discontinue support starting with Intel® DAAL 2021 and Intel® Distribution for Python 2021. Until then Intel will continue to provide compatible pyDAAL pip and conda packages for newer releases of Intel DAAL and make it available in open source. However, Intel will not add the new features of Intel DAAL to pyDAAL. Intel recommends developers switch to and use daal4py.

Note: To find daal4py examples, refer to daal4py documentation or browse github repository.

 # file:
 # Copyright 2014-2019 Intel Corporation.
 # This software and the related documents are Intel copyrighted  materials,  and
 # your use of  them is  governed by the  express license  under which  they were
 # provided to you (License).  Unless the License provides otherwise, you may not
 # use, modify, copy, publish, distribute,  disclose or transmit this software or
 # the related documents without Intel's prior written permission.
 # This software and the related documents  are provided as  is,  with no express
 # or implied  warranties,  other  than those  that are  expressly stated  in the
 # License.
 ## \example
 import os
 import sys
 import daal.algorithms.linear_regression as linear_regression
 import daal.algorithms.linear_regression.quality_metric_set as quality_metric_set
 from daal.algorithms.linear_regression import training, prediction
 from daal.algorithms.linear_regression.quality_metric import single_beta, group_of_betas
 from daal.data_management import (
     DataSourceIface, FileDataSource, HomogenNumericTable, MergedNumericTable,
     NumericTableIface, BlockDescriptor, readWrite
 utils_folder = os.path.realpath(os.path.abspath(os.path.dirname(os.path.dirname(__file__))))
 if utils_folder not in sys.path:
     sys.path.insert(0, utils_folder)
 from utils import printNumericTable
 trainDatasetFileName = os.path.join('..', 'data', 'batch', 'linear_regression_train.csv')
 nFeatures = 10
 nDependentVariables = 2
 trainingResult = None
 # predictionResult = None
 qmsResult = None
 trainData = None
 trainDependentVariables = None
 def trainModel(algorithm):
     global trainingResult, trainData, trainDependentVariables
     # Pass a training data set and dependent values to the algorithm
     algorithm.input.set(, trainData)
     algorithm.input.set(training.dependentVariables, trainDependentVariables)
     # Build the multiple linear regression model and retrieve the algorithm results
     trainingResult = algorithm.compute()
     printNumericTable(trainingResult.get(training.model).getBeta(), "Linear Regression coefficients:")
 def predictResults(trainData):
     # Create an algorithm object to predict values of multiple linear regression
     algorithm = prediction.Batch()
     # Pass a testing data set and the trained model to the algorithm
     algorithm.input.setTable(, trainData)
     algorithm.input.setModel(prediction.model, trainingResult.get(training.model))
     # Predict values of multiple linear regression and retrieve the algorithm results
     predictionResult = algorithm.compute()
     return predictionResult.get(prediction.prediction)
 def predictReducedModelResults(trainData):
     model = trainingResult.get(training.model)
     betas = model.getBeta()
     nBetas = model.getNumberOfBetas()
     j1 = 2
     j2 = 10
     savedBeta = [[None] * nBetas for _ in range(nDependentVariables)]
     block = BlockDescriptor()
     betas.getBlockOfRows(0, nDependentVariables, readWrite, block)
     pBeta = block.getArray()
     for i in range(0, nDependentVariables):
         savedBeta[i][j1] = pBeta[i][j1]
         savedBeta[i][j2] = pBeta[i][j2]
         pBeta[i][j1] = 0
         pBeta[i][j2] = 0
     predictedResults = predictResults(trainData)
     block = BlockDescriptor()
     betas.getBlockOfRows(0, nDependentVariables, readWrite, block)
     pBeta = block.getArray()
     for i in range(0, nDependentVariables):
         pBeta[i][j1] = savedBeta[i][j1]
         pBeta[i][j2] = savedBeta[i][j2]
     return predictedResults
 def testModelQuality():
     global trainingResult, qmsResult
     predictedResults = predictResults(trainData)
     printNumericTable(trainDependentVariables, "Expected responses (first 20 rows):", 20)
     printNumericTable(predictedResults, "Predicted responses (first 20 rows):", 20)
     model = trainingResult.get(
     predictedReducedModelResults = predictReducedModelResults(trainData)
     printNumericTable(predictedReducedModelResults, "Responses predicted with reduced model (first 20 rows):", 20)
     # Create a quality metric set object to compute quality metrics of the linear regression algorithm
     nBetaReducedModel = model.getNumberOfBetas() - 2
     qualityMetricSet = quality_metric_set.Batch(model.getNumberOfBetas(), nBetaReducedModel)
     singleBeta = single_beta.Input.downCast(qualityMetricSet.getInputDataCollection().getInput(quality_metric_set.singleBeta))
     singleBeta.setDataInput(single_beta.expectedResponses, trainDependentVariables)
     singleBeta.setDataInput(single_beta.predictedResponses, predictedResults)
     singleBeta.setModelInput(single_beta.model, model)
     # Set input for a group of betas metrics algorithm
     groupOfBetas = group_of_betas.Input.downCast(qualityMetricSet.getInputDataCollection().getInput(quality_metric_set.groupOfBetas))
     groupOfBetas.set(group_of_betas.expectedResponses, trainDependentVariables)
     groupOfBetas.set(group_of_betas.predictedResponses, predictedResults)
     groupOfBetas.set(group_of_betas.predictedReducedModelResponses, predictedReducedModelResults)
     # Compute quality metrics
     # Retrieve the quality metrics
     qmsResult = qualityMetricSet.getResultCollection()
 def printResults():
     # Print the quality metrics for a single beta
     print ("Quality metrics for a single beta")
     result = single_beta.Result.downCast(qmsResult.getResult(quality_metric_set.singleBeta))
     printNumericTable(result.getResult(single_beta.rms), "Root means square errors for each response (dependent variable):")
     printNumericTable(result.getResult(single_beta.variance), "Variance for each response (dependent variable):")
     printNumericTable(result.getResult(single_beta.zScore), "Z-score statistics:")
     printNumericTable(result.getResult(single_beta.confidenceIntervals), "Confidence intervals for each beta coefficient:")
     printNumericTable(result.getResult(single_beta.inverseOfXtX), "Inverse(Xt * X) matrix:")
     coll = result.getResultDataCollection(single_beta.betaCovariances)
     for i in range(0, coll.size()):
         message = "Variance-covariance matrix for betas of " + str(i) + "-th response\n"
         betaCov = result.get(single_beta.betaCovariances, i)
         printNumericTable(betaCov, message)
     # Print quality metrics for a group of betas
     print ("Quality metrics for a group of betas")
     result = group_of_betas.Result.downCast(qmsResult.getResult(quality_metric_set.groupOfBetas))
     printNumericTable(result.get(group_of_betas.expectedMeans), "Means of expected responses for each dependent variable:", 0, 0, 20)
     printNumericTable(result.get(group_of_betas.expectedVariance), "Variance of expected responses for each dependent variable:", 0, 0, 20)
     printNumericTable(result.get(group_of_betas.regSS), "Regression sum of squares of expected responses:", 0, 0, 20)
     printNumericTable(result.get(group_of_betas.resSS), "Sum of squares of residuals for each dependent variable:", 0, 0, 20)
     printNumericTable(result.get(group_of_betas.tSS), "Total sum of squares for each dependent variable:", 0, 0, 20)
     printNumericTable(result.get(group_of_betas.determinationCoeff), "Determination coefficient for each dependent variable:", 0, 0, 20)
     printNumericTable(result.get(group_of_betas.fStatistics), "F-statistics for each dependent variable:", 0, 0, 20)
 if __name__ == "__main__":
     # Initialize FileDataSource<CSVFeatureManager> to retrieve the input data from a .csv file
     dataSource = FileDataSource(trainDatasetFileName,
     # Create Numeric Tables for data and values for dependent variable
     trainData = HomogenNumericTable(nFeatures, 0, NumericTableIface.doNotAllocate)
     trainDependentVariables = HomogenNumericTable(nDependentVariables, 0, NumericTableIface.doNotAllocate)
     mergedData = MergedNumericTable(trainData, trainDependentVariables)
     # Retrieve the data from the input file
     for i in range(0, 2):
         if i == 0:
             print ("Train model with normal equation algorithm.")
             algorithm = training.Batch()
             print ("Train model with QR algorithm.")
             algorithm = training.Batch(method=training.qrDense)
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