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From ch...@apache.org
Subject [2/2] ignite git commit: IGNITE-6872: Linear regression should implement Model API
Date Thu, 07 Dec 2017 15:15:05 GMT
IGNITE-6872: Linear regression should implement Model API

This closes #3168


Project: http://git-wip-us.apache.org/repos/asf/ignite/repo
Commit: http://git-wip-us.apache.org/repos/asf/ignite/commit/c5c512e4
Tree: http://git-wip-us.apache.org/repos/asf/ignite/tree/c5c512e4
Diff: http://git-wip-us.apache.org/repos/asf/ignite/diff/c5c512e4

Branch: refs/heads/master
Commit: c5c512e460140c91fb77b527ff909ddbe3d1fd72
Parents: bbeb205
Author: Oleg Ignatenko <oignatenko@gridgain.com>
Authored: Thu Dec 7 18:14:51 2017 +0300
Committer: Yury Babak <ybabak@gridgain.com>
Committed: Thu Dec 7 18:14:51 2017 +0300

----------------------------------------------------------------------
 .../decompositions/QRDecompositionExample.java  |  82 ++++++
 .../DistributedRegressionExample.java           | 149 -----------
 .../examples/ml/math/trees/MNISTExample.java    | 261 -------------------
 .../examples/ml/math/trees/package-info.java    |  22 --
 .../apache/ignite/examples/ml/package-info.java |  22 ++
 .../DistributedRegressionExample.java           | 149 +++++++++++
 .../DistributedRegressionModelExample.java      | 134 ++++++++++
 .../examples/ml/regression/package-info.java    |  22 ++
 .../ignite/examples/ml/trees/MNISTExample.java  | 261 +++++++++++++++++++
 .../ignite/examples/ml/trees/package-info.java  |  22 ++
 .../ml/math/decompositions/QRDSolver.java       | 197 ++++++++++++++
 .../ml/math/decompositions/QRDecomposition.java |  54 +---
 .../AbstractMultipleLinearRegression.java       |  20 ++
 .../OLSMultipleLinearRegression.java            |  41 +--
 .../OLSMultipleLinearRegressionModel.java       |  77 ++++++
 .../OLSMultipleLinearRegressionModelFormat.java |  46 ++++
 .../OLSMultipleLinearRegressionTrainer.java     |  62 +++++
 .../org/apache/ignite/ml/IgniteMLTestSuite.java |   3 +-
 .../org/apache/ignite/ml/LocalModelsTest.java   |  99 +++++--
 .../ignite/ml/math/MathImplLocalTestSuite.java  |   2 +
 .../ml/math/decompositions/QRDSolverTest.java   |  87 +++++++
 ...tedBlockOLSMultipleLinearRegressionTest.java |  38 ++-
 ...tributedOLSMultipleLinearRegressionTest.java |  38 ++-
 .../OLSMultipleLinearRegressionModelTest.java   |  53 ++++
 .../ml/regressions/RegressionsTestSuite.java    |   5 +-
 25 files changed, 1371 insertions(+), 575 deletions(-)
----------------------------------------------------------------------


http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/examples/src/main/ml/org/apache/ignite/examples/ml/math/decompositions/QRDecompositionExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/ml/org/apache/ignite/examples/ml/math/decompositions/QRDecompositionExample.java b/examples/src/main/ml/org/apache/ignite/examples/ml/math/decompositions/QRDecompositionExample.java
new file mode 100644
index 0000000..bed99d1
--- /dev/null
+++ b/examples/src/main/ml/org/apache/ignite/examples/ml/math/decompositions/QRDecompositionExample.java
@@ -0,0 +1,82 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.examples.ml.math.decompositions;
+
+import org.apache.ignite.ml.math.Matrix;
+import org.apache.ignite.ml.math.Tracer;
+import org.apache.ignite.ml.math.decompositions.QRDecomposition;
+import org.apache.ignite.ml.math.impls.matrix.DenseLocalOnHeapMatrix;
+
+/**
+ * Example of using {@link QRDecomposition}.
+ */
+public class QRDecompositionExample {
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) {
+        System.out.println(">>> QR decomposition example started.");
+        Matrix m = new DenseLocalOnHeapMatrix(new double[][] {
+            {2.0d, -1.0d, 0.0d},
+            {-1.0d, 2.0d, -1.0d},
+            {0.0d, -1.0d, 2.0d}
+        });
+
+        System.out.println("\n>>> Input matrix:");
+        Tracer.showAscii(m);
+
+        QRDecomposition dec = new QRDecomposition(m);
+        System.out.println("\n>>> Value for full rank in decomposition: [" + dec.hasFullRank() + "].");
+
+        Matrix q = dec.getQ();
+        Matrix r = dec.getR();
+
+        System.out.println("\n>>> Orthogonal matrix Q:");
+        Tracer.showAscii(q);
+        System.out.println("\n>>> Upper triangular matrix R:");
+        Tracer.showAscii(r);
+
+        Matrix qSafeCp = safeCopy(q);
+
+        Matrix identity = qSafeCp.times(qSafeCp.transpose());
+
+        System.out.println("\n>>> Identity matrix obtained from Q:");
+        Tracer.showAscii(identity);
+
+        Matrix recomposed = qSafeCp.times(r);
+
+        System.out.println("\n>>> Recomposed input matrix:");
+        Tracer.showAscii(recomposed);
+
+        Matrix sol = dec.solve(new DenseLocalOnHeapMatrix(3, 10));
+
+        System.out.println("\n>>> Solved matrix:");
+        Tracer.showAscii(sol);
+
+        dec.destroy();
+
+        System.out.println("\n>>> QR decomposition example completed.");
+    }
+
+    /** */
+    private static Matrix safeCopy(Matrix orig) {
+        return new DenseLocalOnHeapMatrix(orig.rowSize(), orig.columnSize()).assign(orig);
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/examples/src/main/ml/org/apache/ignite/examples/ml/math/regression/DistributedRegressionExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/ml/org/apache/ignite/examples/ml/math/regression/DistributedRegressionExample.java b/examples/src/main/ml/org/apache/ignite/examples/ml/math/regression/DistributedRegressionExample.java
deleted file mode 100644
index de2c541..0000000
--- a/examples/src/main/ml/org/apache/ignite/examples/ml/math/regression/DistributedRegressionExample.java
+++ /dev/null
@@ -1,149 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one or more
- * contributor license agreements.  See the NOTICE file distributed with
- * this work for additional information regarding copyright ownership.
- * The ASF licenses this file to You under the Apache License, Version 2.0
- * (the "License"); you may not use this file except in compliance with
- * the License.  You may obtain a copy of the License at
- *
- *      http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-
-package org.apache.ignite.examples.ml.math.regression;
-
-import java.util.Arrays;
-import org.apache.ignite.Ignite;
-import org.apache.ignite.Ignition;
-import org.apache.ignite.examples.ml.math.matrix.SparseDistributedMatrixExample;
-import org.apache.ignite.ml.math.StorageConstants;
-import org.apache.ignite.ml.math.Tracer;
-import org.apache.ignite.ml.math.impls.matrix.SparseDistributedMatrix;
-import org.apache.ignite.ml.regressions.OLSMultipleLinearRegression;
-import org.apache.ignite.thread.IgniteThread;
-
-/**
- * Run linear regression over distributed matrix.
- *
- * TODO: IGNITE-6222, Currently works only in local mode.
- *
- * @see OLSMultipleLinearRegression
- */
-public class DistributedRegressionExample {
-    /** Run example. */
-    public static void main(String[] args) throws InterruptedException {
-        System.out.println();
-        System.out.println(">>> Linear regression over sparse distributed matrix API usage example started.");
-        // Start ignite grid.
-        try (Ignite ignite = Ignition.start("examples/config/example-ignite.xml")) {
-            System.out.println(">>> Ignite grid started.");
-            // Create IgniteThread, we must work with SparseDistributedMatrix inside IgniteThread
-            // because we create ignite cache internally.
-            IgniteThread igniteThread = new IgniteThread(ignite.configuration().getIgniteInstanceName(), SparseDistributedMatrixExample.class.getSimpleName(), () -> {
-
-                double[] data = {
-                    8, 78, 284, 9.100000381, 109,
-                    9.300000191, 68, 433, 8.699999809, 144,
-                    7.5, 70, 739, 7.199999809, 113,
-                    8.899999619, 96, 1792, 8.899999619, 97,
-                    10.19999981, 74, 477, 8.300000191, 206,
-                    8.300000191, 111, 362, 10.89999962, 124,
-                    8.800000191, 77, 671, 10, 152,
-                    8.800000191, 168, 636, 9.100000381, 162,
-                    10.69999981, 82, 329, 8.699999809, 150,
-                    11.69999981, 89, 634, 7.599999905, 134,
-                    8.5, 149, 631, 10.80000019, 292,
-                    8.300000191, 60, 257, 9.5, 108,
-                    8.199999809, 96, 284, 8.800000191, 111,
-                    7.900000095, 83, 603, 9.5, 182,
-                    10.30000019, 130, 686, 8.699999809, 129,
-                    7.400000095, 145, 345, 11.19999981, 158,
-                    9.600000381, 112, 1357, 9.699999809, 186,
-                    9.300000191, 131, 544, 9.600000381, 177,
-                    10.60000038, 80, 205, 9.100000381, 127,
-                    9.699999809, 130, 1264, 9.199999809, 179,
-                    11.60000038, 140, 688, 8.300000191, 80,
-                    8.100000381, 154, 354, 8.399999619, 103,
-                    9.800000191, 118, 1632, 9.399999619, 101,
-                    7.400000095, 94, 348, 9.800000191, 117,
-                    9.399999619, 119, 370, 10.39999962, 88,
-                    11.19999981, 153, 648, 9.899999619, 78,
-                    9.100000381, 116, 366, 9.199999809, 102,
-                    10.5, 97, 540, 10.30000019, 95,
-                    11.89999962, 176, 680, 8.899999619, 80,
-                    8.399999619, 75, 345, 9.600000381, 92,
-                    5, 134, 525, 10.30000019, 126,
-                    9.800000191, 161, 870, 10.39999962, 108,
-                    9.800000191, 111, 669, 9.699999809, 77,
-                    10.80000019, 114, 452, 9.600000381, 60,
-                    10.10000038, 142, 430, 10.69999981, 71,
-                    10.89999962, 238, 822, 10.30000019, 86,
-                    9.199999809, 78, 190, 10.69999981, 93,
-                    8.300000191, 196, 867, 9.600000381, 106,
-                    7.300000191, 125, 969, 10.5, 162,
-                    9.399999619, 82, 499, 7.699999809, 95,
-                    9.399999619, 125, 925, 10.19999981, 91,
-                    9.800000191, 129, 353, 9.899999619, 52,
-                    3.599999905, 84, 288, 8.399999619, 110,
-                    8.399999619, 183, 718, 10.39999962, 69,
-                    10.80000019, 119, 540, 9.199999809, 57,
-                    10.10000038, 180, 668, 13, 106,
-                    9, 82, 347, 8.800000191, 40,
-                    10, 71, 345, 9.199999809, 50,
-                    11.30000019, 118, 463, 7.800000191, 35,
-                    11.30000019, 121, 728, 8.199999809, 86,
-                    12.80000019, 68, 383, 7.400000095, 57,
-                    10, 112, 316, 10.39999962, 57,
-                    6.699999809, 109, 388, 8.899999619, 94
-                };
-
-                final int nobs = 53;
-                final int nvars = 4;
-
-                System.out.println(">>> Create new SparseDistributedMatrix inside IgniteThread.");
-                // Create SparseDistributedMatrix, new cache will be created automagically.
-                SparseDistributedMatrix distributedMatrix = new SparseDistributedMatrix(0, 0,
-                    StorageConstants.ROW_STORAGE_MODE, StorageConstants.RANDOM_ACCESS_MODE);
-
-                System.out.println(">>> Create new linear regression object");
-                OLSMultipleLinearRegression regression = new OLSMultipleLinearRegression();
-                regression.newSampleData(data, nobs, nvars, distributedMatrix);
-                System.out.println();
-
-                System.out.println(">>> Estimates the regression parameters b:");
-                System.out.println(Arrays.toString(regression.estimateRegressionParameters()));
-
-                System.out.println(">>> Estimates the residuals, ie u = y - X*b:");
-                System.out.println(Arrays.toString(regression.estimateResiduals()));
-
-                System.out.println(">>> Standard errors of the regression parameters:");
-                System.out.println(Arrays.toString(regression.estimateRegressionParametersStandardErrors()));
-
-                System.out.println(">>> Estimates the variance of the regression parameters, ie Var(b):");
-                Tracer.showAscii(regression.estimateRegressionParametersVariance());
-
-                System.out.println(">>> Estimates the standard error of the regression:");
-                System.out.println(regression.estimateRegressionStandardError());
-
-                System.out.println(">>> R-Squared statistic:");
-                System.out.println(regression.calculateRSquared());
-
-                System.out.println(">>> Adjusted R-squared statistic:");
-                System.out.println(regression.calculateAdjustedRSquared());
-
-                System.out.println(">>> Returns the variance of the regressand, ie Var(y):");
-                System.out.println(regression.estimateErrorVariance());
-            });
-
-            igniteThread.start();
-
-            igniteThread.join();
-        }
-    }
-
-}
\ No newline at end of file

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/MNISTExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/MNISTExample.java b/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/MNISTExample.java
deleted file mode 100644
index 6aaadd9..0000000
--- a/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/MNISTExample.java
+++ /dev/null
@@ -1,261 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one or more
- * contributor license agreements.  See the NOTICE file distributed with
- * this work for additional information regarding copyright ownership.
- * The ASF licenses this file to You under the Apache License, Version 2.0
- * (the "License"); you may not use this file except in compliance with
- * the License.  You may obtain a copy of the License at
- *
- *      http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-
-package org.apache.ignite.examples.ml.math.trees;
-
-import java.io.IOException;
-import java.util.HashMap;
-import java.util.Iterator;
-import java.util.Random;
-import java.util.function.Function;
-import java.util.stream.Stream;
-import org.apache.commons.cli.BasicParser;
-import org.apache.commons.cli.CommandLine;
-import org.apache.commons.cli.CommandLineParser;
-import org.apache.commons.cli.Option;
-import org.apache.commons.cli.OptionBuilder;
-import org.apache.commons.cli.Options;
-import org.apache.commons.cli.ParseException;
-import org.apache.ignite.Ignite;
-import org.apache.ignite.IgniteCache;
-import org.apache.ignite.IgniteDataStreamer;
-import org.apache.ignite.Ignition;
-import org.apache.ignite.cache.CacheAtomicityMode;
-import org.apache.ignite.cache.CacheMode;
-import org.apache.ignite.cache.CacheWriteSynchronizationMode;
-import org.apache.ignite.configuration.CacheConfiguration;
-import org.apache.ignite.examples.ExampleNodeStartup;
-import org.apache.ignite.internal.util.IgniteUtils;
-import org.apache.ignite.lang.IgniteBiTuple;
-import org.apache.ignite.ml.Model;
-import org.apache.ignite.ml.estimators.Estimators;
-import org.apache.ignite.ml.math.Vector;
-import org.apache.ignite.ml.math.functions.IgniteTriFunction;
-import org.apache.ignite.ml.math.impls.vector.DenseLocalOnHeapVector;
-import org.apache.ignite.ml.trees.models.DecisionTreeModel;
-import org.apache.ignite.ml.trees.trainers.columnbased.BiIndex;
-import org.apache.ignite.ml.trees.trainers.columnbased.BiIndexedCacheColumnDecisionTreeTrainerInput;
-import org.apache.ignite.ml.trees.trainers.columnbased.ColumnDecisionTreeTrainer;
-import org.apache.ignite.ml.trees.trainers.columnbased.contsplitcalcs.ContinuousSplitCalculators;
-import org.apache.ignite.ml.trees.trainers.columnbased.contsplitcalcs.GiniSplitCalculator;
-import org.apache.ignite.ml.trees.trainers.columnbased.regcalcs.RegionCalculators;
-import org.apache.ignite.ml.util.MnistUtils;
-import org.jetbrains.annotations.NotNull;
-
-/**
- * <p>
- * Example of usage of decision trees algorithm for MNIST dataset
- * (it can be found here: http://yann.lecun.com/exdb/mnist/). </p>
- * <p>
- * Remote nodes should always be started with special configuration file which
- * enables P2P class loading: {@code 'ignite.{sh|bat} examples/config/example-ignite.xml'}.</p>
- * <p>
- * Alternatively you can run {@link ExampleNodeStartup} in another JVM which will start node
- * with {@code examples/config/example-ignite.xml} configuration.</p>
- * <p>
- * It is recommended to start at least one node prior to launching this example if you intend
- * to run it with default memory settings.</p>
- * <p>
- * This example should with program arguments, for example
- * -ts_i /path/to/train-images-idx3-ubyte
- * -ts_l /path/to/train-labels-idx1-ubyte
- * -tss_i /path/to/t10k-images-idx3-ubyte
- * -tss_l /path/to/t10k-labels-idx1-ubyte
- * -cfg examples/config/example-ignite.xml.</p>
- * <p>
- * -ts_i specifies path to training set images of MNIST;
- * -ts_l specifies path to training set labels of MNIST;
- * -tss_i specifies path to test set images of MNIST;
- * -tss_l specifies path to test set labels of MNIST;
- * -cfg specifies path to a config path.</p>
- */
-public class MNISTExample {
-    /** Name of parameter specifying path to training set images. */
-    private static final String MNIST_TRAINING_IMAGES_PATH = "ts_i";
-
-    /** Name of parameter specifying path to training set labels. */
-    private static final String MNIST_TRAINING_LABELS_PATH = "ts_l";
-
-    /** Name of parameter specifying path to test set images. */
-    private static final String MNIST_TEST_IMAGES_PATH = "tss_i";
-
-    /** Name of parameter specifying path to test set labels. */
-    private static final String MNIST_TEST_LABELS_PATH = "tss_l";
-
-    /** Name of parameter specifying path of Ignite config. */
-    private static final String CONFIG = "cfg";
-
-    /** Default config path. */
-    private static final String DEFAULT_CONFIG = "examples/config/example-ignite.xml";
-
-    /**
-     * Launches example.
-     *
-     * @param args Program arguments.
-     */
-    public static void main(String[] args) {
-        String igniteCfgPath;
-
-        CommandLineParser parser = new BasicParser();
-
-        String trainingImagesPath;
-        String trainingLabelsPath;
-
-        String testImagesPath;
-        String testLabelsPath;
-
-        try {
-            // Parse the command line arguments.
-            CommandLine line = parser.parse(buildOptions(), args);
-
-            trainingImagesPath = line.getOptionValue(MNIST_TRAINING_IMAGES_PATH);
-            trainingLabelsPath = line.getOptionValue(MNIST_TRAINING_LABELS_PATH);
-            testImagesPath = line.getOptionValue(MNIST_TEST_IMAGES_PATH);
-            testLabelsPath = line.getOptionValue(MNIST_TEST_LABELS_PATH);
-            igniteCfgPath = line.getOptionValue(CONFIG, DEFAULT_CONFIG);
-        }
-        catch (ParseException e) {
-            e.printStackTrace();
-            return;
-        }
-
-        try (Ignite ignite = Ignition.start(igniteCfgPath)) {
-            IgniteUtils.setCurrentIgniteName(ignite.configuration().getIgniteInstanceName());
-
-            int ptsCnt = 60000;
-            int featCnt = 28 * 28;
-
-            Stream<DenseLocalOnHeapVector> trainingMnistStream = MnistUtils.mnist(trainingImagesPath, trainingLabelsPath, new Random(123L), ptsCnt);
-            Stream<DenseLocalOnHeapVector> testMnistStream = MnistUtils.mnist(testImagesPath, testLabelsPath, new Random(123L), 10_000);
-
-            IgniteCache<BiIndex, Double> cache = createBiIndexedCache(ignite);
-
-            loadVectorsIntoBiIndexedCache(cache.getName(), trainingMnistStream.iterator(), featCnt + 1, ignite);
-
-            ColumnDecisionTreeTrainer<GiniSplitCalculator.GiniData> trainer =
-                new ColumnDecisionTreeTrainer<>(10, ContinuousSplitCalculators.GINI.apply(ignite), RegionCalculators.GINI, RegionCalculators.MOST_COMMON, ignite);
-
-            System.out.println(">>> Training started");
-            long before = System.currentTimeMillis();
-            DecisionTreeModel mdl = trainer.train(new BiIndexedCacheColumnDecisionTreeTrainerInput(cache, new HashMap<>(), ptsCnt, featCnt));
-            System.out.println(">>> Training finished in " + (System.currentTimeMillis() - before));
-
-            IgniteTriFunction<Model<Vector, Double>, Stream<IgniteBiTuple<Vector, Double>>, Function<Double, Double>, Double> mse = Estimators.errorsPercentage();
-            Double accuracy = mse.apply(mdl, testMnistStream.map(v -> new IgniteBiTuple<>(v.viewPart(0, featCnt), v.getX(featCnt))), Function.identity());
-            System.out.println(">>> Errs percentage: " + accuracy);
-        }
-        catch (IOException e) {
-            e.printStackTrace();
-        }
-    }
-
-    /**
-     * Build cli options.
-     */
-    @NotNull private static Options buildOptions() {
-        Options options = new Options();
-
-        Option trsImagesPathOpt = OptionBuilder.withArgName(MNIST_TRAINING_IMAGES_PATH).withLongOpt(MNIST_TRAINING_IMAGES_PATH).hasArg()
-            .withDescription("Path to the MNIST training set.")
-            .isRequired(true).create();
-
-        Option trsLabelsPathOpt = OptionBuilder.withArgName(MNIST_TRAINING_LABELS_PATH).withLongOpt(MNIST_TRAINING_LABELS_PATH).hasArg()
-            .withDescription("Path to the MNIST training set.")
-            .isRequired(true).create();
-
-        Option tssImagesPathOpt = OptionBuilder.withArgName(MNIST_TEST_IMAGES_PATH).withLongOpt(MNIST_TEST_IMAGES_PATH).hasArg()
-            .withDescription("Path to the MNIST test set.")
-            .isRequired(true).create();
-
-        Option tssLabelsPathOpt = OptionBuilder.withArgName(MNIST_TEST_LABELS_PATH).withLongOpt(MNIST_TEST_LABELS_PATH).hasArg()
-            .withDescription("Path to the MNIST test set.")
-            .isRequired(true).create();
-
-        Option configOpt = OptionBuilder.withArgName(CONFIG).withLongOpt(CONFIG).hasArg()
-            .withDescription("Path to the config.")
-            .isRequired(false).create();
-
-        options.addOption(trsImagesPathOpt);
-        options.addOption(trsLabelsPathOpt);
-        options.addOption(tssImagesPathOpt);
-        options.addOption(tssLabelsPathOpt);
-        options.addOption(configOpt);
-
-        return options;
-    }
-
-    /**
-     * Creates cache where data for training is stored.
-     *
-     * @param ignite Ignite instance.
-     * @return cache where data for training is stored.
-     */
-    private static IgniteCache<BiIndex, Double> createBiIndexedCache(Ignite ignite) {
-        CacheConfiguration<BiIndex, Double> cfg = new CacheConfiguration<>();
-
-        // Write to primary.
-        cfg.setWriteSynchronizationMode(CacheWriteSynchronizationMode.PRIMARY_SYNC);
-
-        // Atomic transactions only.
-        cfg.setAtomicityMode(CacheAtomicityMode.ATOMIC);
-
-        // No eviction.
-        cfg.setEvictionPolicy(null);
-
-        // No copying of values.
-        cfg.setCopyOnRead(false);
-
-        // Cache is partitioned.
-        cfg.setCacheMode(CacheMode.PARTITIONED);
-
-        cfg.setBackups(0);
-
-        cfg.setName("TMP_BI_INDEXED_CACHE");
-
-        return ignite.getOrCreateCache(cfg);
-    }
-
-    /**
-     * Loads vectors into cache.
-     *
-     * @param cacheName Name of cache.
-     * @param vectorsIterator Iterator over vectors to load.
-     * @param vectorSize Size of vector.
-     * @param ignite Ignite instance.
-     */
-    private static void loadVectorsIntoBiIndexedCache(String cacheName, Iterator<? extends Vector> vectorsIterator,
-        int vectorSize, Ignite ignite) {
-        try (IgniteDataStreamer<BiIndex, Double> streamer =
-                 ignite.dataStreamer(cacheName)) {
-            int sampleIdx = 0;
-
-            streamer.perNodeBufferSize(10000);
-
-            while (vectorsIterator.hasNext()) {
-                org.apache.ignite.ml.math.Vector next = vectorsIterator.next();
-
-                for (int i = 0; i < vectorSize; i++)
-                    streamer.addData(new BiIndex(sampleIdx, i), next.getX(i));
-
-                sampleIdx++;
-
-                if (sampleIdx % 1000 == 0)
-                    System.out.println("Loaded " + sampleIdx + " vectors.");
-            }
-        }
-    }
-}
\ No newline at end of file

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/package-info.java
----------------------------------------------------------------------
diff --git a/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/package-info.java b/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/package-info.java
deleted file mode 100644
index 9b6867b..0000000
--- a/examples/src/main/ml/org/apache/ignite/examples/ml/math/trees/package-info.java
+++ /dev/null
@@ -1,22 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one or more
- * contributor license agreements.  See the NOTICE file distributed with
- * this work for additional information regarding copyright ownership.
- * The ASF licenses this file to You under the Apache License, Version 2.0
- * (the "License"); you may not use this file except in compliance with
- * the License.  You may obtain a copy of the License at
- *
- *      http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-
-/**
- * <!-- Package description. -->
- * Decision trees examples.
- */
-package org.apache.ignite.examples.ml.math.trees;

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/examples/src/main/ml/org/apache/ignite/examples/ml/package-info.java
----------------------------------------------------------------------
diff --git a/examples/src/main/ml/org/apache/ignite/examples/ml/package-info.java b/examples/src/main/ml/org/apache/ignite/examples/ml/package-info.java
new file mode 100644
index 0000000..52778b5
--- /dev/null
+++ b/examples/src/main/ml/org/apache/ignite/examples/ml/package-info.java
@@ -0,0 +1,22 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+/**
+ * <!-- Package description. -->
+ * Machine learning examples.
+ */
+package org.apache.ignite.examples.ml;
\ No newline at end of file

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/examples/src/main/ml/org/apache/ignite/examples/ml/regression/DistributedRegressionExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/ml/org/apache/ignite/examples/ml/regression/DistributedRegressionExample.java b/examples/src/main/ml/org/apache/ignite/examples/ml/regression/DistributedRegressionExample.java
new file mode 100644
index 0000000..3e65527
--- /dev/null
+++ b/examples/src/main/ml/org/apache/ignite/examples/ml/regression/DistributedRegressionExample.java
@@ -0,0 +1,149 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.examples.ml.regression;
+
+import java.util.Arrays;
+import org.apache.ignite.Ignite;
+import org.apache.ignite.Ignition;
+import org.apache.ignite.examples.ml.math.matrix.SparseDistributedMatrixExample;
+import org.apache.ignite.ml.math.StorageConstants;
+import org.apache.ignite.ml.math.Tracer;
+import org.apache.ignite.ml.math.impls.matrix.SparseDistributedMatrix;
+import org.apache.ignite.ml.regressions.OLSMultipleLinearRegression;
+import org.apache.ignite.thread.IgniteThread;
+
+/**
+ * Run linear regression over distributed matrix.
+ *
+ * TODO: IGNITE-6222, Currently works only in local mode.
+ *
+ * @see OLSMultipleLinearRegression
+ */
+public class DistributedRegressionExample {
+    /** Run example. */
+    public static void main(String[] args) throws InterruptedException {
+        System.out.println();
+        System.out.println(">>> Linear regression over sparse distributed matrix API usage example started.");
+        // Start ignite grid.
+        try (Ignite ignite = Ignition.start("examples/config/example-ignite.xml")) {
+            System.out.println(">>> Ignite grid started.");
+            // Create IgniteThread, we must work with SparseDistributedMatrix inside IgniteThread
+            // because we create ignite cache internally.
+            IgniteThread igniteThread = new IgniteThread(ignite.configuration().getIgniteInstanceName(), SparseDistributedMatrixExample.class.getSimpleName(), () -> {
+
+                double[] data = {
+                    8, 78, 284, 9.100000381, 109,
+                    9.300000191, 68, 433, 8.699999809, 144,
+                    7.5, 70, 739, 7.199999809, 113,
+                    8.899999619, 96, 1792, 8.899999619, 97,
+                    10.19999981, 74, 477, 8.300000191, 206,
+                    8.300000191, 111, 362, 10.89999962, 124,
+                    8.800000191, 77, 671, 10, 152,
+                    8.800000191, 168, 636, 9.100000381, 162,
+                    10.69999981, 82, 329, 8.699999809, 150,
+                    11.69999981, 89, 634, 7.599999905, 134,
+                    8.5, 149, 631, 10.80000019, 292,
+                    8.300000191, 60, 257, 9.5, 108,
+                    8.199999809, 96, 284, 8.800000191, 111,
+                    7.900000095, 83, 603, 9.5, 182,
+                    10.30000019, 130, 686, 8.699999809, 129,
+                    7.400000095, 145, 345, 11.19999981, 158,
+                    9.600000381, 112, 1357, 9.699999809, 186,
+                    9.300000191, 131, 544, 9.600000381, 177,
+                    10.60000038, 80, 205, 9.100000381, 127,
+                    9.699999809, 130, 1264, 9.199999809, 179,
+                    11.60000038, 140, 688, 8.300000191, 80,
+                    8.100000381, 154, 354, 8.399999619, 103,
+                    9.800000191, 118, 1632, 9.399999619, 101,
+                    7.400000095, 94, 348, 9.800000191, 117,
+                    9.399999619, 119, 370, 10.39999962, 88,
+                    11.19999981, 153, 648, 9.899999619, 78,
+                    9.100000381, 116, 366, 9.199999809, 102,
+                    10.5, 97, 540, 10.30000019, 95,
+                    11.89999962, 176, 680, 8.899999619, 80,
+                    8.399999619, 75, 345, 9.600000381, 92,
+                    5, 134, 525, 10.30000019, 126,
+                    9.800000191, 161, 870, 10.39999962, 108,
+                    9.800000191, 111, 669, 9.699999809, 77,
+                    10.80000019, 114, 452, 9.600000381, 60,
+                    10.10000038, 142, 430, 10.69999981, 71,
+                    10.89999962, 238, 822, 10.30000019, 86,
+                    9.199999809, 78, 190, 10.69999981, 93,
+                    8.300000191, 196, 867, 9.600000381, 106,
+                    7.300000191, 125, 969, 10.5, 162,
+                    9.399999619, 82, 499, 7.699999809, 95,
+                    9.399999619, 125, 925, 10.19999981, 91,
+                    9.800000191, 129, 353, 9.899999619, 52,
+                    3.599999905, 84, 288, 8.399999619, 110,
+                    8.399999619, 183, 718, 10.39999962, 69,
+                    10.80000019, 119, 540, 9.199999809, 57,
+                    10.10000038, 180, 668, 13, 106,
+                    9, 82, 347, 8.800000191, 40,
+                    10, 71, 345, 9.199999809, 50,
+                    11.30000019, 118, 463, 7.800000191, 35,
+                    11.30000019, 121, 728, 8.199999809, 86,
+                    12.80000019, 68, 383, 7.400000095, 57,
+                    10, 112, 316, 10.39999962, 57,
+                    6.699999809, 109, 388, 8.899999619, 94
+                };
+
+                final int nobs = 53;
+                final int nvars = 4;
+
+                System.out.println(">>> Create new SparseDistributedMatrix inside IgniteThread.");
+                // Create SparseDistributedMatrix, new cache will be created automagically.
+                SparseDistributedMatrix distributedMatrix = new SparseDistributedMatrix(0, 0,
+                    StorageConstants.ROW_STORAGE_MODE, StorageConstants.RANDOM_ACCESS_MODE);
+
+                System.out.println(">>> Create new linear regression object");
+                OLSMultipleLinearRegression regression = new OLSMultipleLinearRegression();
+                regression.newSampleData(data, nobs, nvars, distributedMatrix);
+                System.out.println();
+
+                System.out.println(">>> Estimates the regression parameters b:");
+                System.out.println(Arrays.toString(regression.estimateRegressionParameters()));
+
+                System.out.println(">>> Estimates the residuals, ie u = y - X*b:");
+                System.out.println(Arrays.toString(regression.estimateResiduals()));
+
+                System.out.println(">>> Standard errors of the regression parameters:");
+                System.out.println(Arrays.toString(regression.estimateRegressionParametersStandardErrors()));
+
+                System.out.println(">>> Estimates the variance of the regression parameters, ie Var(b):");
+                Tracer.showAscii(regression.estimateRegressionParametersVariance());
+
+                System.out.println(">>> Estimates the standard error of the regression:");
+                System.out.println(regression.estimateRegressionStandardError());
+
+                System.out.println(">>> R-Squared statistic:");
+                System.out.println(regression.calculateRSquared());
+
+                System.out.println(">>> Adjusted R-squared statistic:");
+                System.out.println(regression.calculateAdjustedRSquared());
+
+                System.out.println(">>> Returns the variance of the regressand, ie Var(y):");
+                System.out.println(regression.estimateErrorVariance());
+            });
+
+            igniteThread.start();
+
+            igniteThread.join();
+        }
+    }
+
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/examples/src/main/ml/org/apache/ignite/examples/ml/regression/DistributedRegressionModelExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/ml/org/apache/ignite/examples/ml/regression/DistributedRegressionModelExample.java b/examples/src/main/ml/org/apache/ignite/examples/ml/regression/DistributedRegressionModelExample.java
new file mode 100644
index 0000000..ab1b17d
--- /dev/null
+++ b/examples/src/main/ml/org/apache/ignite/examples/ml/regression/DistributedRegressionModelExample.java
@@ -0,0 +1,134 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.examples.ml.regression;
+
+import org.apache.ignite.Ignite;
+import org.apache.ignite.Ignition;
+import org.apache.ignite.examples.ml.math.matrix.SparseDistributedMatrixExample;
+import org.apache.ignite.ml.math.StorageConstants;
+import org.apache.ignite.ml.math.Tracer;
+import org.apache.ignite.ml.math.Vector;
+import org.apache.ignite.ml.math.impls.matrix.SparseDistributedMatrix;
+import org.apache.ignite.ml.math.impls.vector.SparseDistributedVector;
+import org.apache.ignite.ml.regressions.OLSMultipleLinearRegressionModel;
+import org.apache.ignite.ml.regressions.OLSMultipleLinearRegressionTrainer;
+import org.apache.ignite.thread.IgniteThread;
+
+/**
+ * Run linear regression model over distributed matrix.
+ *
+ * @see OLSMultipleLinearRegressionModel
+ */
+public class DistributedRegressionModelExample {
+    /** Run example. */
+    public static void main(String[] args) throws InterruptedException {
+        System.out.println();
+        System.out.println(">>> Linear regression model over sparse distributed matrix API usage example started.");
+        // Start ignite grid.
+        try (Ignite ignite = Ignition.start("examples/config/example-ignite.xml")) {
+            System.out.println(">>> Ignite grid started.");
+            // Create IgniteThread, we must work with SparseDistributedMatrix inside IgniteThread
+            // because we create ignite cache internally.
+            IgniteThread igniteThread = new IgniteThread(ignite.configuration().getIgniteInstanceName(),
+                SparseDistributedMatrixExample.class.getSimpleName(), () -> {
+                double[] data = {
+                    8, 78, 284, 9.100000381, 109,
+                    9.300000191, 68, 433, 8.699999809, 144,
+                    7.5, 70, 739, 7.199999809, 113,
+                    8.899999619, 96, 1792, 8.899999619, 97,
+                    10.19999981, 74, 477, 8.300000191, 206,
+                    8.300000191, 111, 362, 10.89999962, 124,
+                    8.800000191, 77, 671, 10, 152,
+                    8.800000191, 168, 636, 9.100000381, 162,
+                    10.69999981, 82, 329, 8.699999809, 150,
+                    11.69999981, 89, 634, 7.599999905, 134,
+                    8.5, 149, 631, 10.80000019, 292,
+                    8.300000191, 60, 257, 9.5, 108,
+                    8.199999809, 96, 284, 8.800000191, 111,
+                    7.900000095, 83, 603, 9.5, 182,
+                    10.30000019, 130, 686, 8.699999809, 129,
+                    7.400000095, 145, 345, 11.19999981, 158,
+                    9.600000381, 112, 1357, 9.699999809, 186,
+                    9.300000191, 131, 544, 9.600000381, 177,
+                    10.60000038, 80, 205, 9.100000381, 127,
+                    9.699999809, 130, 1264, 9.199999809, 179,
+                    11.60000038, 140, 688, 8.300000191, 80,
+                    8.100000381, 154, 354, 8.399999619, 103,
+                    9.800000191, 118, 1632, 9.399999619, 101,
+                    7.400000095, 94, 348, 9.800000191, 117,
+                    9.399999619, 119, 370, 10.39999962, 88,
+                    11.19999981, 153, 648, 9.899999619, 78,
+                    9.100000381, 116, 366, 9.199999809, 102,
+                    10.5, 97, 540, 10.30000019, 95,
+                    11.89999962, 176, 680, 8.899999619, 80,
+                    8.399999619, 75, 345, 9.600000381, 92,
+                    5, 134, 525, 10.30000019, 126,
+                    9.800000191, 161, 870, 10.39999962, 108,
+                    9.800000191, 111, 669, 9.699999809, 77,
+                    10.80000019, 114, 452, 9.600000381, 60,
+                    10.10000038, 142, 430, 10.69999981, 71,
+                    10.89999962, 238, 822, 10.30000019, 86,
+                    9.199999809, 78, 190, 10.69999981, 93,
+                    8.300000191, 196, 867, 9.600000381, 106,
+                    7.300000191, 125, 969, 10.5, 162,
+                    9.399999619, 82, 499, 7.699999809, 95,
+                    9.399999619, 125, 925, 10.19999981, 91,
+                    9.800000191, 129, 353, 9.899999619, 52,
+                    3.599999905, 84, 288, 8.399999619, 110,
+                    8.399999619, 183, 718, 10.39999962, 69,
+                    10.80000019, 119, 540, 9.199999809, 57,
+                    10.10000038, 180, 668, 13, 106,
+                    9, 82, 347, 8.800000191, 40,
+                    10, 71, 345, 9.199999809, 50,
+                    11.30000019, 118, 463, 7.800000191, 35,
+                    11.30000019, 121, 728, 8.199999809, 86,
+                    12.80000019, 68, 383, 7.400000095, 57,
+                    10, 112, 316, 10.39999962, 57,
+                    6.699999809, 109, 388, 8.899999619, 94
+                };
+
+                final int nobs = 53;
+                final int nvars = 4;
+
+                System.out.println(">>> Create new SparseDistributedMatrix inside IgniteThread.");
+                // Create SparseDistributedMatrix, new cache will be created automagically.
+                SparseDistributedMatrix distributedMatrix = new SparseDistributedMatrix(0, 0,
+                    StorageConstants.ROW_STORAGE_MODE, StorageConstants.RANDOM_ACCESS_MODE);
+
+                System.out.println(">>> Create new linear regression trainer object.");
+                OLSMultipleLinearRegressionTrainer trainer
+                    = new OLSMultipleLinearRegressionTrainer(0, nobs, nvars, distributedMatrix);
+                System.out.println(">>> Perform the training to get the model.");
+                OLSMultipleLinearRegressionModel mdl = trainer.train(data);
+                System.out.println();
+
+                Vector val = new SparseDistributedVector(nobs).assign((i) -> data[i * (nvars + 1)]);
+
+                System.out.println(">>> The input data:");
+                Tracer.showAscii(val);
+
+                System.out.println(">>> Trained model prediction results:");
+                Tracer.showAscii(mdl.predict(val));
+            });
+
+            igniteThread.start();
+
+            igniteThread.join();
+        }
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/examples/src/main/ml/org/apache/ignite/examples/ml/regression/package-info.java
----------------------------------------------------------------------
diff --git a/examples/src/main/ml/org/apache/ignite/examples/ml/regression/package-info.java b/examples/src/main/ml/org/apache/ignite/examples/ml/regression/package-info.java
new file mode 100644
index 0000000..c89c80c
--- /dev/null
+++ b/examples/src/main/ml/org/apache/ignite/examples/ml/regression/package-info.java
@@ -0,0 +1,22 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+/**
+ * <!-- Package description. -->
+ * ML regression examples.
+ */
+package org.apache.ignite.examples.ml.regression;

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/examples/src/main/ml/org/apache/ignite/examples/ml/trees/MNISTExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/ml/org/apache/ignite/examples/ml/trees/MNISTExample.java b/examples/src/main/ml/org/apache/ignite/examples/ml/trees/MNISTExample.java
new file mode 100644
index 0000000..6ff121e
--- /dev/null
+++ b/examples/src/main/ml/org/apache/ignite/examples/ml/trees/MNISTExample.java
@@ -0,0 +1,261 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.examples.ml.trees;
+
+import java.io.IOException;
+import java.util.HashMap;
+import java.util.Iterator;
+import java.util.Random;
+import java.util.function.Function;
+import java.util.stream.Stream;
+import org.apache.commons.cli.BasicParser;
+import org.apache.commons.cli.CommandLine;
+import org.apache.commons.cli.CommandLineParser;
+import org.apache.commons.cli.Option;
+import org.apache.commons.cli.OptionBuilder;
+import org.apache.commons.cli.Options;
+import org.apache.commons.cli.ParseException;
+import org.apache.ignite.Ignite;
+import org.apache.ignite.IgniteCache;
+import org.apache.ignite.IgniteDataStreamer;
+import org.apache.ignite.Ignition;
+import org.apache.ignite.cache.CacheAtomicityMode;
+import org.apache.ignite.cache.CacheMode;
+import org.apache.ignite.cache.CacheWriteSynchronizationMode;
+import org.apache.ignite.configuration.CacheConfiguration;
+import org.apache.ignite.examples.ExampleNodeStartup;
+import org.apache.ignite.internal.util.IgniteUtils;
+import org.apache.ignite.lang.IgniteBiTuple;
+import org.apache.ignite.ml.Model;
+import org.apache.ignite.ml.estimators.Estimators;
+import org.apache.ignite.ml.math.Vector;
+import org.apache.ignite.ml.math.functions.IgniteTriFunction;
+import org.apache.ignite.ml.math.impls.vector.DenseLocalOnHeapVector;
+import org.apache.ignite.ml.trees.models.DecisionTreeModel;
+import org.apache.ignite.ml.trees.trainers.columnbased.BiIndex;
+import org.apache.ignite.ml.trees.trainers.columnbased.BiIndexedCacheColumnDecisionTreeTrainerInput;
+import org.apache.ignite.ml.trees.trainers.columnbased.ColumnDecisionTreeTrainer;
+import org.apache.ignite.ml.trees.trainers.columnbased.contsplitcalcs.ContinuousSplitCalculators;
+import org.apache.ignite.ml.trees.trainers.columnbased.contsplitcalcs.GiniSplitCalculator;
+import org.apache.ignite.ml.trees.trainers.columnbased.regcalcs.RegionCalculators;
+import org.apache.ignite.ml.util.MnistUtils;
+import org.jetbrains.annotations.NotNull;
+
+/**
+ * <p>
+ * Example of usage of decision trees algorithm for MNIST dataset
+ * (it can be found here: http://yann.lecun.com/exdb/mnist/). </p>
+ * <p>
+ * Remote nodes should always be started with special configuration file which
+ * enables P2P class loading: {@code 'ignite.{sh|bat} examples/config/example-ignite.xml'}.</p>
+ * <p>
+ * Alternatively you can run {@link ExampleNodeStartup} in another JVM which will start node
+ * with {@code examples/config/example-ignite.xml} configuration.</p>
+ * <p>
+ * It is recommended to start at least one node prior to launching this example if you intend
+ * to run it with default memory settings.</p>
+ * <p>
+ * This example should with program arguments, for example
+ * -ts_i /path/to/train-images-idx3-ubyte
+ * -ts_l /path/to/train-labels-idx1-ubyte
+ * -tss_i /path/to/t10k-images-idx3-ubyte
+ * -tss_l /path/to/t10k-labels-idx1-ubyte
+ * -cfg examples/config/example-ignite.xml.</p>
+ * <p>
+ * -ts_i specifies path to training set images of MNIST;
+ * -ts_l specifies path to training set labels of MNIST;
+ * -tss_i specifies path to test set images of MNIST;
+ * -tss_l specifies path to test set labels of MNIST;
+ * -cfg specifies path to a config path.</p>
+ */
+public class MNISTExample {
+    /** Name of parameter specifying path to training set images. */
+    private static final String MNIST_TRAINING_IMAGES_PATH = "ts_i";
+
+    /** Name of parameter specifying path to training set labels. */
+    private static final String MNIST_TRAINING_LABELS_PATH = "ts_l";
+
+    /** Name of parameter specifying path to test set images. */
+    private static final String MNIST_TEST_IMAGES_PATH = "tss_i";
+
+    /** Name of parameter specifying path to test set labels. */
+    private static final String MNIST_TEST_LABELS_PATH = "tss_l";
+
+    /** Name of parameter specifying path of Ignite config. */
+    private static final String CONFIG = "cfg";
+
+    /** Default config path. */
+    private static final String DEFAULT_CONFIG = "examples/config/example-ignite.xml";
+
+    /**
+     * Launches example.
+     *
+     * @param args Program arguments.
+     */
+    public static void main(String[] args) {
+        String igniteCfgPath;
+
+        CommandLineParser parser = new BasicParser();
+
+        String trainingImagesPath;
+        String trainingLabelsPath;
+
+        String testImagesPath;
+        String testLabelsPath;
+
+        try {
+            // Parse the command line arguments.
+            CommandLine line = parser.parse(buildOptions(), args);
+
+            trainingImagesPath = line.getOptionValue(MNIST_TRAINING_IMAGES_PATH);
+            trainingLabelsPath = line.getOptionValue(MNIST_TRAINING_LABELS_PATH);
+            testImagesPath = line.getOptionValue(MNIST_TEST_IMAGES_PATH);
+            testLabelsPath = line.getOptionValue(MNIST_TEST_LABELS_PATH);
+            igniteCfgPath = line.getOptionValue(CONFIG, DEFAULT_CONFIG);
+        }
+        catch (ParseException e) {
+            e.printStackTrace();
+            return;
+        }
+
+        try (Ignite ignite = Ignition.start(igniteCfgPath)) {
+            IgniteUtils.setCurrentIgniteName(ignite.configuration().getIgniteInstanceName());
+
+            int ptsCnt = 60000;
+            int featCnt = 28 * 28;
+
+            Stream<DenseLocalOnHeapVector> trainingMnistStream = MnistUtils.mnist(trainingImagesPath, trainingLabelsPath, new Random(123L), ptsCnt);
+            Stream<DenseLocalOnHeapVector> testMnistStream = MnistUtils.mnist(testImagesPath, testLabelsPath, new Random(123L), 10_000);
+
+            IgniteCache<BiIndex, Double> cache = createBiIndexedCache(ignite);
+
+            loadVectorsIntoBiIndexedCache(cache.getName(), trainingMnistStream.iterator(), featCnt + 1, ignite);
+
+            ColumnDecisionTreeTrainer<GiniSplitCalculator.GiniData> trainer =
+                new ColumnDecisionTreeTrainer<>(10, ContinuousSplitCalculators.GINI.apply(ignite), RegionCalculators.GINI, RegionCalculators.MOST_COMMON, ignite);
+
+            System.out.println(">>> Training started");
+            long before = System.currentTimeMillis();
+            DecisionTreeModel mdl = trainer.train(new BiIndexedCacheColumnDecisionTreeTrainerInput(cache, new HashMap<>(), ptsCnt, featCnt));
+            System.out.println(">>> Training finished in " + (System.currentTimeMillis() - before));
+
+            IgniteTriFunction<Model<Vector, Double>, Stream<IgniteBiTuple<Vector, Double>>, Function<Double, Double>, Double> mse = Estimators.errorsPercentage();
+            Double accuracy = mse.apply(mdl, testMnistStream.map(v -> new IgniteBiTuple<>(v.viewPart(0, featCnt), v.getX(featCnt))), Function.identity());
+            System.out.println(">>> Errs percentage: " + accuracy);
+        }
+        catch (IOException e) {
+            e.printStackTrace();
+        }
+    }
+
+    /**
+     * Build cli options.
+     */
+    @NotNull private static Options buildOptions() {
+        Options options = new Options();
+
+        Option trsImagesPathOpt = OptionBuilder.withArgName(MNIST_TRAINING_IMAGES_PATH).withLongOpt(MNIST_TRAINING_IMAGES_PATH).hasArg()
+            .withDescription("Path to the MNIST training set.")
+            .isRequired(true).create();
+
+        Option trsLabelsPathOpt = OptionBuilder.withArgName(MNIST_TRAINING_LABELS_PATH).withLongOpt(MNIST_TRAINING_LABELS_PATH).hasArg()
+            .withDescription("Path to the MNIST training set.")
+            .isRequired(true).create();
+
+        Option tssImagesPathOpt = OptionBuilder.withArgName(MNIST_TEST_IMAGES_PATH).withLongOpt(MNIST_TEST_IMAGES_PATH).hasArg()
+            .withDescription("Path to the MNIST test set.")
+            .isRequired(true).create();
+
+        Option tssLabelsPathOpt = OptionBuilder.withArgName(MNIST_TEST_LABELS_PATH).withLongOpt(MNIST_TEST_LABELS_PATH).hasArg()
+            .withDescription("Path to the MNIST test set.")
+            .isRequired(true).create();
+
+        Option configOpt = OptionBuilder.withArgName(CONFIG).withLongOpt(CONFIG).hasArg()
+            .withDescription("Path to the config.")
+            .isRequired(false).create();
+
+        options.addOption(trsImagesPathOpt);
+        options.addOption(trsLabelsPathOpt);
+        options.addOption(tssImagesPathOpt);
+        options.addOption(tssLabelsPathOpt);
+        options.addOption(configOpt);
+
+        return options;
+    }
+
+    /**
+     * Creates cache where data for training is stored.
+     *
+     * @param ignite Ignite instance.
+     * @return cache where data for training is stored.
+     */
+    private static IgniteCache<BiIndex, Double> createBiIndexedCache(Ignite ignite) {
+        CacheConfiguration<BiIndex, Double> cfg = new CacheConfiguration<>();
+
+        // Write to primary.
+        cfg.setWriteSynchronizationMode(CacheWriteSynchronizationMode.PRIMARY_SYNC);
+
+        // Atomic transactions only.
+        cfg.setAtomicityMode(CacheAtomicityMode.ATOMIC);
+
+        // No eviction.
+        cfg.setEvictionPolicy(null);
+
+        // No copying of values.
+        cfg.setCopyOnRead(false);
+
+        // Cache is partitioned.
+        cfg.setCacheMode(CacheMode.PARTITIONED);
+
+        cfg.setBackups(0);
+
+        cfg.setName("TMP_BI_INDEXED_CACHE");
+
+        return ignite.getOrCreateCache(cfg);
+    }
+
+    /**
+     * Loads vectors into cache.
+     *
+     * @param cacheName Name of cache.
+     * @param vectorsIterator Iterator over vectors to load.
+     * @param vectorSize Size of vector.
+     * @param ignite Ignite instance.
+     */
+    private static void loadVectorsIntoBiIndexedCache(String cacheName, Iterator<? extends Vector> vectorsIterator,
+        int vectorSize, Ignite ignite) {
+        try (IgniteDataStreamer<BiIndex, Double> streamer =
+                 ignite.dataStreamer(cacheName)) {
+            int sampleIdx = 0;
+
+            streamer.perNodeBufferSize(10000);
+
+            while (vectorsIterator.hasNext()) {
+                org.apache.ignite.ml.math.Vector next = vectorsIterator.next();
+
+                for (int i = 0; i < vectorSize; i++)
+                    streamer.addData(new BiIndex(sampleIdx, i), next.getX(i));
+
+                sampleIdx++;
+
+                if (sampleIdx % 1000 == 0)
+                    System.out.println("Loaded " + sampleIdx + " vectors.");
+            }
+        }
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/examples/src/main/ml/org/apache/ignite/examples/ml/trees/package-info.java
----------------------------------------------------------------------
diff --git a/examples/src/main/ml/org/apache/ignite/examples/ml/trees/package-info.java b/examples/src/main/ml/org/apache/ignite/examples/ml/trees/package-info.java
new file mode 100644
index 0000000..d944f60
--- /dev/null
+++ b/examples/src/main/ml/org/apache/ignite/examples/ml/trees/package-info.java
@@ -0,0 +1,22 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+/**
+ * <!-- Package description. -->
+ * Decision trees examples.
+ */
+package org.apache.ignite.examples.ml.trees;

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/modules/ml/src/main/java/org/apache/ignite/ml/math/decompositions/QRDSolver.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/decompositions/QRDSolver.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/decompositions/QRDSolver.java
new file mode 100644
index 0000000..bb591ee
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/decompositions/QRDSolver.java
@@ -0,0 +1,197 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml.math.decompositions;
+
+import java.io.Serializable;
+import org.apache.ignite.ml.math.Matrix;
+import org.apache.ignite.ml.math.Vector;
+import org.apache.ignite.ml.math.exceptions.NoDataException;
+import org.apache.ignite.ml.math.exceptions.NullArgumentException;
+import org.apache.ignite.ml.math.exceptions.SingularMatrixException;
+import org.apache.ignite.ml.math.functions.Functions;
+import org.apache.ignite.ml.math.util.MatrixUtil;
+
+import static org.apache.ignite.ml.math.util.MatrixUtil.like;
+
+/**
+ * For an {@code m x n} matrix {@code A} with {@code m >= n}, the QR decomposition
+ * is an {@code m x n} orthogonal matrix {@code Q} and an {@code n x n} upper
+ * triangular matrix {@code R} so that {@code A = Q*R}.
+ */
+public class QRDSolver implements Serializable {
+    /** */
+    private final Matrix q;
+
+    /** */
+    private final Matrix r;
+
+    /**
+     * Constructs a new QR decomposition solver object.
+     *
+     * @param q An orthogonal matrix.
+     * @param r An upper triangular matrix
+     */
+    public QRDSolver(Matrix q, Matrix r) {
+        this.q = q;
+        this.r = r;
+    }
+
+    /**
+     * Least squares solution of {@code A*X = B}; {@code returns X}.
+     *
+     * @param mtx A matrix with as many rows as {@code A} and any number of cols.
+     * @return {@code X<} that minimizes the two norm of {@code Q*R*X - B}.
+     * @throws IllegalArgumentException if {@code B.rows() != A.rows()}.
+     */
+    public Matrix solve(Matrix mtx) {
+        if (mtx.rowSize() != q.rowSize())
+            throw new IllegalArgumentException("Matrix row dimensions must agree.");
+
+        int cols = mtx.columnSize();
+        Matrix x = like(r, r.columnSize(), cols);
+
+        Matrix qt = q.transpose();
+        Matrix y = qt.times(mtx);
+
+        for (int k = Math.min(r.columnSize(), q.rowSize()) - 1; k >= 0; k--) {
+            // X[k,] = Y[k,] / R[k,k], note that X[k,] starts with 0 so += is same as =
+            x.viewRow(k).map(y.viewRow(k), Functions.plusMult(1 / r.get(k, k)));
+
+            if (k == 0)
+                continue;
+
+            // Y[0:(k-1),] -= R[0:(k-1),k] * X[k,]
+            Vector rCol = r.viewColumn(k).viewPart(0, k);
+
+            for (int c = 0; c < cols; c++)
+                y.viewColumn(c).viewPart(0, k).map(rCol, Functions.plusMult(-x.get(k, c)));
+        }
+
+        return x;
+    }
+
+    /**
+     * Least squares solution of {@code A*X = B}; {@code returns X}.
+     *
+     * @param vec A vector with as many rows as {@code A}.
+     * @return {@code X<} that minimizes the two norm of {@code Q*R*X - B}.
+     * @throws IllegalArgumentException if {@code B.rows() != A.rows()}.
+     */
+    public Vector solve(Vector vec) {
+        if (vec == null)
+            throw new NullArgumentException();
+        if (vec.size() == 0)
+            throw new NoDataException();
+        // TODO: IGNITE-5826, Should we copy here?
+
+        Matrix res = solve(vec.likeMatrix(vec.size(), 1).assignColumn(0, vec));
+
+        return vec.like(res.rowSize()).assign(res.viewColumn(0));
+    }
+
+    /**
+     * <p>Compute the "hat" matrix.
+     * </p>
+     * <p>The hat matrix is defined in terms of the design matrix X
+     * by X(X<sup>T</sup>X)<sup>-1</sup>X<sup>T</sup>
+     * </p>
+     * <p>The implementation here uses the QR decomposition to compute the
+     * hat matrix as Q I<sub>p</sub>Q<sup>T</sup> where I<sub>p</sub> is the
+     * p-dimensional identity matrix augmented by 0's.  This computational
+     * formula is from "The Hat Matrix in Regression and ANOVA",
+     * David C. Hoaglin and Roy E. Welsch,
+     * <i>The American Statistician</i>, Vol. 32, No. 1 (Feb., 1978), pp. 17-22.
+     * </p>
+     * <p>Data for the model must have been successfully loaded using one of
+     * the {@code newSampleData} methods before invoking this method; otherwise
+     * a {@code NullPointerException} will be thrown.</p>
+     *
+     * @return the hat matrix
+     * @throws NullPointerException unless method {@code newSampleData} has been called beforehand.
+     */
+    public Matrix calculateHat() {
+        // Create augmented identity matrix
+        // No try-catch or advertised NotStrictlyPositiveException - NPE above if n < 3
+        Matrix augI = MatrixUtil.like(q, q.columnSize(), q.columnSize());
+
+        int n = augI.columnSize();
+        int p = r.columnSize();
+
+        for (int i = 0; i < n; i++)
+            for (int j = 0; j < n; j++)
+                if (i == j && i < p)
+                    augI.setX(i, j, 1d);
+                else
+                    augI.setX(i, j, 0d);
+
+        // Compute and return Hat matrix
+        // No DME advertised - args valid if we get here
+        return q.times(augI).times(q.transpose());
+    }
+
+    /**
+     * <p>Calculates the variance-covariance matrix of the regression parameters.
+     * </p>
+     * <p>Var(b) = (X<sup>T</sup>X)<sup>-1</sup>
+     * </p>
+     * <p>Uses QR decomposition to reduce (X<sup>T</sup>X)<sup>-1</sup>
+     * to (R<sup>T</sup>R)<sup>-1</sup>, with only the top p rows of
+     * R included, where p = the length of the beta vector.</p>
+     *
+     * <p>Data for the model must have been successfully loaded using one of
+     * the {@code newSampleData} methods before invoking this method; otherwise
+     * a {@code NullPointerException} will be thrown.</p>
+     *
+     * @param p Size of the beta variance-covariance matrix
+     * @return The beta variance-covariance matrix
+     * @throws SingularMatrixException if the design matrix is singular
+     * @throws NullPointerException if the data for the model have not been loaded
+     */
+    public Matrix calculateBetaVariance(int p) {
+        Matrix rAug = MatrixUtil.copy(r.viewPart(0, p, 0, p));
+        Matrix rInv = rAug.inverse();
+
+        return rInv.times(rInv.transpose());
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean equals(Object o) {
+        if (this == o)
+            return true;
+        if (o == null || getClass() != o.getClass())
+            return false;
+
+        QRDSolver solver = (QRDSolver)o;
+
+        return q.equals(solver.q) && r.equals(solver.r);
+    }
+
+    /** {@inheritDoc} */
+    @Override public int hashCode() {
+        int res = q.hashCode();
+        res = 31 * res + r.hashCode();
+        return res;
+    }
+
+    /**
+     * Returns a rough string rendition of a QRD solver.
+     */
+    @Override public String toString() {
+        return String.format("QRD Solver(%d x %d)", q.rowSize(), r.columnSize());
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/modules/ml/src/main/java/org/apache/ignite/ml/math/decompositions/QRDecomposition.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/math/decompositions/QRDecomposition.java b/modules/ml/src/main/java/org/apache/ignite/ml/math/decompositions/QRDecomposition.java
index 3d0bb5d..c069683 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/math/decompositions/QRDecomposition.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/math/decompositions/QRDecomposition.java
@@ -46,8 +46,6 @@ public class QRDecomposition implements Destroyable {
     private final int rows;
     /** */
     private final int cols;
-    /** */
-    private double threshold;
 
     /**
      * @param v Value to be checked for being an ordinary double.
@@ -89,7 +87,6 @@ public class QRDecomposition implements Destroyable {
         boolean fullRank = true;
 
         r = like(mtx, min, cols);
-        this.threshold = threshold;
 
         for (int i = 0; i < min; i++) {
             Vector qi = qTmp.viewColumn(i);
@@ -129,6 +126,8 @@ public class QRDecomposition implements Destroyable {
         else
             q = qTmp;
 
+        verifyNonSingularR(threshold);
+
         this.fullRank = fullRank;
     }
 
@@ -170,32 +169,7 @@ public class QRDecomposition implements Destroyable {
      * @throws IllegalArgumentException if {@code B.rows() != A.rows()}.
      */
     public Matrix solve(Matrix mtx) {
-        if (mtx.rowSize() != rows)
-            throw new IllegalArgumentException("Matrix row dimensions must agree.");
-
-        int cols = mtx.columnSize();
-        Matrix r = getR();
-        checkSingular(r, threshold, true);
-        Matrix x = like(mType, this.cols, cols);
-
-        Matrix qt = getQ().transpose();
-        Matrix y = qt.times(mtx);
-
-        for (int k = Math.min(this.cols, rows) - 1; k >= 0; k--) {
-            // X[k,] = Y[k,] / R[k,k], note that X[k,] starts with 0 so += is same as =
-            x.viewRow(k).map(y.viewRow(k), Functions.plusMult(1 / r.get(k, k)));
-
-            if (k == 0)
-                continue;
-
-            // Y[0:(k-1),] -= R[0:(k-1),k] * X[k,]
-            Vector rCol = r.viewColumn(k).viewPart(0, k);
-
-            for (int c = 0; c < cols; c++)
-                y.viewColumn(c).viewPart(0, k).map(rCol, Functions.plusMult(-x.get(k, c)));
-        }
-
-        return x;
+        return new QRDSolver(q, r).solve(mtx);
     }
 
     /**
@@ -206,8 +180,7 @@ public class QRDecomposition implements Destroyable {
      * @throws IllegalArgumentException if {@code B.rows() != A.rows()}.
      */
     public Vector solve(Vector vec) {
-        Matrix res = solve(vec.likeMatrix(vec.size(), 1).assignColumn(0, vec));
-        return vec.like(res.rowSize()).assign(res.viewColumn(0));
+        return new QRDSolver(q, r).solve(vec);
     }
 
     /**
@@ -220,27 +193,20 @@ public class QRDecomposition implements Destroyable {
     /**
      * Check singularity.
      *
-     * @param r R matrix.
      * @param min Singularity threshold.
-     * @param raise Whether to raise a {@link SingularMatrixException} if any element of the diagonal fails the check.
-     * @return {@code true} if any element of the diagonal is smaller or equal to {@code min}.
      * @throws SingularMatrixException if the matrix is singular and {@code raise} is {@code true}.
      */
-    private static boolean checkSingular(Matrix r, double min, boolean raise) {
-        // TODO: IGNITE-5828, Not a very fast approach for distributed matrices. would be nice if we could independently check
-        // parts on different nodes for singularity and do fold with 'or'.
+    private void verifyNonSingularR(double min) {
+        // TODO: IGNITE-5828, Not a very fast approach for distributed matrices. would be nice if we could independently
+        // check parts on different nodes for singularity and do fold with 'or'.
 
-        final int len = r.columnSize();
+        final int len = r.columnSize() > r.rowSize() ? r.rowSize() : r.columnSize();
         for (int i = 0; i < len; i++) {
             final double d = r.getX(i, i);
             if (Math.abs(d) <= min)
-                if (raise)
-                    throw new SingularMatrixException("Number is too small (%f, while " +
-                        "threshold is %f). Index of diagonal element is (%d, %d)", d, min, i, i);
-                else
-                    return true;
+                throw new SingularMatrixException("Number is too small (%f, while " +
+                    "threshold is %f). Index of diagonal element is (%d, %d)", d, min, i, i);
 
         }
-        return false;
     }
 }

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/modules/ml/src/main/java/org/apache/ignite/ml/regressions/AbstractMultipleLinearRegression.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/AbstractMultipleLinearRegression.java b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/AbstractMultipleLinearRegression.java
index a2a8f16..5bc92c9 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/AbstractMultipleLinearRegression.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/AbstractMultipleLinearRegression.java
@@ -355,4 +355,24 @@ public abstract class AbstractMultipleLinearRegression implements MultipleLinear
         return yVector.minus(xMatrix.times(b));
     }
 
+    /** {@inheritDoc} */
+    @Override public boolean equals(Object o) {
+        if (this == o)
+            return true;
+        if (o == null || getClass() != o.getClass())
+            return false;
+
+        AbstractMultipleLinearRegression that = (AbstractMultipleLinearRegression)o;
+
+        return noIntercept == that.noIntercept && xMatrix.equals(that.xMatrix);
+    }
+
+    /** {@inheritDoc} */
+    @Override public int hashCode() {
+        int res = xMatrix.hashCode();
+
+        res = 31 * res + (noIntercept ? 1 : 0);
+
+        return res;
+    }
 }

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegression.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegression.java b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegression.java
index 36d5f2c..aafeae8 100644
--- a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegression.java
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegression.java
@@ -18,11 +18,11 @@ package org.apache.ignite.ml.regressions;
 
 import org.apache.ignite.ml.math.Matrix;
 import org.apache.ignite.ml.math.Vector;
+import org.apache.ignite.ml.math.decompositions.QRDSolver;
 import org.apache.ignite.ml.math.decompositions.QRDecomposition;
 import org.apache.ignite.ml.math.exceptions.MathIllegalArgumentException;
 import org.apache.ignite.ml.math.exceptions.SingularMatrixException;
 import org.apache.ignite.ml.math.functions.Functions;
-import org.apache.ignite.ml.math.util.MatrixUtil;
 
 /**
  * This class is based on the corresponding class from Apache Common Math lib.
@@ -51,7 +51,7 @@ import org.apache.ignite.ml.math.util.MatrixUtil;
  */
 public class OLSMultipleLinearRegression extends AbstractMultipleLinearRegression {
     /** Cached QR decomposition of X matrix */
-    private QRDecomposition qr = null;
+    private QRDSolver solver = null;
 
     /** Singularity threshold for QR decomposition */
     private final double threshold;
@@ -94,7 +94,8 @@ public class OLSMultipleLinearRegression extends AbstractMultipleLinearRegressio
      */
     @Override public void newSampleData(double[] data, int nobs, int nvars, Matrix like) {
         super.newSampleData(data, nobs, nvars, like);
-        qr = new QRDecomposition(getX(), threshold);
+        QRDecomposition qr = new QRDecomposition(getX(), threshold);
+        solver = new QRDSolver(qr.getQ(), qr.getR());
     }
 
     /**
@@ -118,24 +119,7 @@ public class OLSMultipleLinearRegression extends AbstractMultipleLinearRegressio
      * @throws NullPointerException unless method {@code newSampleData} has been called beforehand.
      */
     public Matrix calculateHat() {
-        // Create augmented identity matrix
-        // No try-catch or advertised NotStrictlyPositiveException - NPE above if n < 3
-        Matrix q = qr.getQ();
-        Matrix augI = MatrixUtil.like(q, q.columnSize(), q.columnSize());
-
-        int n = augI.columnSize();
-        int p = qr.getR().columnSize();
-
-        for (int i = 0; i < n; i++)
-            for (int j = 0; j < n; j++)
-                if (i == j && i < p)
-                    augI.setX(i, j, 1d);
-                else
-                    augI.setX(i, j, 0d);
-
-        // Compute and return Hat matrix
-        // No DME advertised - args valid if we get here
-        return q.times(augI).times(q.transpose());
+        return solver.calculateHat();
     }
 
     /**
@@ -226,7 +210,8 @@ public class OLSMultipleLinearRegression extends AbstractMultipleLinearRegressio
      */
     @Override protected void newXSampleData(Matrix x) {
         super.newXSampleData(x);
-        qr = new QRDecomposition(getX());
+        QRDecomposition qr = new QRDecomposition(getX());
+        solver = new QRDSolver(qr.getQ(), qr.getR());
     }
 
     /**
@@ -241,7 +226,7 @@ public class OLSMultipleLinearRegression extends AbstractMultipleLinearRegressio
      * @throws NullPointerException if the data for the model have not been loaded
      */
     @Override protected Vector calculateBeta() {
-        return qr.solve(getY());
+        return solver.solve(getY());
     }
 
     /**
@@ -262,11 +247,11 @@ public class OLSMultipleLinearRegression extends AbstractMultipleLinearRegressio
      * @throws NullPointerException if the data for the model have not been loaded
      */
     @Override protected Matrix calculateBetaVariance() {
-        int p = getX().columnSize();
-
-        Matrix rAug = MatrixUtil.copy(qr.getR().viewPart(0, p, 0, p));
-        Matrix rInv = rAug.inverse();
+        return solver.calculateBetaVariance(getX().columnSize());
+    }
 
-        return rInv.times(rInv.transpose());
+    /** */
+    QRDSolver solver() {
+        return solver;
     }
 }

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionModel.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionModel.java b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionModel.java
new file mode 100644
index 0000000..76a90fc
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionModel.java
@@ -0,0 +1,77 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml.regressions;
+
+import org.apache.ignite.ml.Exportable;
+import org.apache.ignite.ml.Exporter;
+import org.apache.ignite.ml.Model;
+import org.apache.ignite.ml.math.Matrix;
+import org.apache.ignite.ml.math.Vector;
+import org.apache.ignite.ml.math.decompositions.QRDSolver;
+import org.apache.ignite.ml.math.decompositions.QRDecomposition;
+
+/**
+ * Model for linear regression.
+ */
+public class OLSMultipleLinearRegressionModel implements Model<Vector, Vector>,
+    Exportable<OLSMultipleLinearRegressionModelFormat> {
+    /** */
+    private final Matrix xMatrix;
+    /** */
+    private final QRDSolver solver;
+
+    /**
+     * Construct linear regression model.
+     *
+     * @param xMatrix See {@link QRDecomposition#QRDecomposition(Matrix)}.
+     * @param solver Linear regression solver object.
+     */
+    public OLSMultipleLinearRegressionModel(Matrix xMatrix, QRDSolver solver) {
+        this.xMatrix = xMatrix;
+        this.solver = solver;
+    }
+
+    /** {@inheritDoc} */
+    @Override public Vector predict(Vector val) {
+        return xMatrix.times(solver.solve(val));
+    }
+
+    /** {@inheritDoc} */
+    @Override public <P> void saveModel(Exporter<OLSMultipleLinearRegressionModelFormat, P> exporter, P path) {
+        exporter.save(new OLSMultipleLinearRegressionModelFormat(xMatrix, solver), path);
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean equals(Object o) {
+        if (this == o)
+            return true;
+        if (o == null || getClass() != o.getClass())
+            return false;
+
+        OLSMultipleLinearRegressionModel mdl = (OLSMultipleLinearRegressionModel)o;
+
+        return xMatrix.equals(mdl.xMatrix) && solver.equals(mdl.solver);
+    }
+
+    /** {@inheritDoc} */
+    @Override public int hashCode() {
+        int res = xMatrix.hashCode();
+        res = 31 * res + solver.hashCode();
+        return res;
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionModelFormat.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionModelFormat.java b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionModelFormat.java
new file mode 100644
index 0000000..fc44968
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionModelFormat.java
@@ -0,0 +1,46 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml.regressions;
+
+import java.io.Serializable;
+import org.apache.ignite.ml.math.Matrix;
+import org.apache.ignite.ml.math.decompositions.QRDSolver;
+
+/**
+ * Linear regression model representation.
+ *
+ * @see OLSMultipleLinearRegressionModel
+ */
+public class OLSMultipleLinearRegressionModelFormat implements Serializable {
+    /** X sample data. */
+    private final Matrix xMatrix;
+
+    /** Whether or not the regression model includes an intercept.  True means no intercept. */
+    private final QRDSolver solver;
+
+    /** */
+    public OLSMultipleLinearRegressionModelFormat(Matrix xMatrix, QRDSolver solver) {
+        this.xMatrix = xMatrix;
+        this.solver = solver;
+    }
+
+    /** */
+    public OLSMultipleLinearRegressionModel getOLSMultipleLinearRegressionModel() {
+        return new OLSMultipleLinearRegressionModel(xMatrix, solver);
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionTrainer.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionTrainer.java b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionTrainer.java
new file mode 100644
index 0000000..dde0aca
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionTrainer.java
@@ -0,0 +1,62 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.ignite.ml.regressions;
+
+import org.apache.ignite.ml.Trainer;
+import org.apache.ignite.ml.math.Matrix;
+
+/**
+ * Trainer for linear regression.
+ */
+public class OLSMultipleLinearRegressionTrainer implements Trainer<OLSMultipleLinearRegressionModel, double[]> {
+    /** */
+    private final double threshold;
+
+    /** */
+    private final int nobs;
+
+    /** */
+    private final int nvars;
+
+    /** */
+    private final Matrix like;
+
+    /**
+     * Construct linear regression trainer.
+     *
+     * @param threshold the singularity threshold for QR decomposition
+     * @param nobs number of observations (rows)
+     * @param nvars number of independent variables (columns, not counting y)
+     * @param like matrix(maybe empty) indicating how data should be stored
+     */
+    public OLSMultipleLinearRegressionTrainer(double threshold, int nobs, int nvars, Matrix like) {
+        this.threshold = threshold;
+        this.nobs = nobs;
+        this.nvars = nvars;
+        this.like = like;
+    }
+
+    /** {@inheritDoc} */
+    @Override public OLSMultipleLinearRegressionModel train(double[] data) {
+        OLSMultipleLinearRegression regression = new OLSMultipleLinearRegression(threshold);
+
+        regression.newSampleData(data, nobs, nvars, like);
+
+        return new OLSMultipleLinearRegressionModel(regression.getX(), regression.solver());
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/c5c512e4/modules/ml/src/test/java/org/apache/ignite/ml/IgniteMLTestSuite.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/test/java/org/apache/ignite/ml/IgniteMLTestSuite.java b/modules/ml/src/test/java/org/apache/ignite/ml/IgniteMLTestSuite.java
index 47910c8..7a61bad 100644
--- a/modules/ml/src/test/java/org/apache/ignite/ml/IgniteMLTestSuite.java
+++ b/modules/ml/src/test/java/org/apache/ignite/ml/IgniteMLTestSuite.java
@@ -32,7 +32,8 @@ import org.junit.runners.Suite;
     MathImplMainTestSuite.class,
     RegressionsTestSuite.class,
     ClusteringTestSuite.class,
-    DecisionTreesTestSuite.class
+    DecisionTreesTestSuite.class,
+    LocalModelsTest.class
 })
 public class IgniteMLTestSuite {
     // No-op.


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