ignite-commits mailing list archives

Site index · List index
Message view « Date » · « Thread »
Top « Date » · « Thread »
From sboi...@apache.org
Subject [12/15] ignite git commit: IGNITE-5217: Gradient descent for OLS lin reg
Date Fri, 29 Dec 2017 09:28:29 GMT
http://git-wip-us.apache.org/repos/asf/ignite/blob/b2060855/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
deleted file mode 100644
index aafeae8..0000000
--- a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegression.java
+++ /dev/null
@@ -1,257 +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.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;
-
-/**
- * This class is based on the corresponding class from Apache Common Math lib.
- * <p>Implements ordinary least squares (OLS) to estimate the parameters of a
- * multiple linear regression model.</p>
- *
- * <p>The regression coefficients, <code>b</code>, satisfy the normal equations:
- * <pre><code> X<sup>T</sup> X b = X<sup>T</sup> y </code></pre></p>
- *
- * <p>To solve the normal equations, this implementation uses QR decomposition
- * of the <code>X</code> matrix. (See {@link QRDecomposition} for details on the
- * decomposition algorithm.) The <code>X</code> matrix, also known as the <i>design matrix,</i>
- * has rows corresponding to sample observations and columns corresponding to independent
- * variables.  When the model is estimated using an intercept term (i.e. when
- * {@link #isNoIntercept() isNoIntercept} is false as it is by default), the <code>X</code>
- * matrix includes an initial column identically equal to 1.  We solve the normal equations
- * as follows:
- * <pre><code> X<sup>T</sup>X b = X<sup>T</sup> y
- * (QR)<sup>T</sup> (QR) b = (QR)<sup>T</sup>y
- * R<sup>T</sup> (Q<sup>T</sup>Q) R b = R<sup>T</sup> Q<sup>T</sup> y
- * R<sup>T</sup> R b = R<sup>T</sup> Q<sup>T</sup> y
- * (R<sup>T</sup>)<sup>-1</sup> R<sup>T</sup> R b = (R<sup>T</sup>)<sup>-1</sup> R<sup>T</sup> Q<sup>T</sup> y
- * R b = Q<sup>T</sup> y </code></pre></p>
- *
- * <p>Given <code>Q</code> and <code>R</code>, the last equation is solved by back-substitution.</p>
- */
-public class OLSMultipleLinearRegression extends AbstractMultipleLinearRegression {
-    /** Cached QR decomposition of X matrix */
-    private QRDSolver solver = null;
-
-    /** Singularity threshold for QR decomposition */
-    private final double threshold;
-
-    /**
-     * Create an empty OLSMultipleLinearRegression instance.
-     */
-    public OLSMultipleLinearRegression() {
-        this(0d);
-    }
-
-    /**
-     * Create an empty OLSMultipleLinearRegression instance, using the given
-     * singularity threshold for the QR decomposition.
-     *
-     * @param threshold the singularity threshold
-     */
-    public OLSMultipleLinearRegression(final double threshold) {
-        this.threshold = threshold;
-    }
-
-    /**
-     * Loads model x and y sample data, overriding any previous sample.
-     *
-     * Computes and caches QR decomposition of the X matrix.
-     *
-     * @param y the {@code n}-sized vector representing the y sample
-     * @param x the {@code n x k} matrix representing the x sample
-     * @throws MathIllegalArgumentException if the x and y array data are not compatible for the regression
-     */
-    public void newSampleData(Vector y, Matrix x) throws MathIllegalArgumentException {
-        validateSampleData(x, y);
-        newYSampleData(y);
-        newXSampleData(x);
-    }
-
-    /**
-     * {@inheritDoc}
-     * <p>This implementation computes and caches the QR decomposition of the X matrix.</p>
-     */
-    @Override public void newSampleData(double[] data, int nobs, int nvars, Matrix like) {
-        super.newSampleData(data, nobs, nvars, like);
-        QRDecomposition qr = new QRDecomposition(getX(), threshold);
-        solver = new QRDSolver(qr.getQ(), qr.getR());
-    }
-
-    /**
-     * <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() {
-        return solver.calculateHat();
-    }
-
-    /**
-     * <p>Returns the sum of squared deviations of Y from its mean.</p>
-     *
-     * <p>If the model has no intercept term, <code>0</code> is used for the
-     * mean of Y - i.e., what is returned is the sum of the squared Y values.</p>
-     *
-     * <p>The value returned by this method is the SSTO value used in
-     * the {@link #calculateRSquared() R-squared} computation.</p>
-     *
-     * @return SSTO - the total sum of squares
-     * @throws NullPointerException if the sample has not been set
-     * @see #isNoIntercept()
-     */
-    public double calculateTotalSumOfSquares() {
-        if (isNoIntercept())
-            return getY().foldMap(Functions.PLUS, Functions.SQUARE, 0.0);
-        else {
-            // TODO: IGNITE-5826, think about incremental update formula.
-            final double mean = getY().sum() / getY().size();
-            return getY().foldMap(Functions.PLUS, x -> (mean - x) * (mean - x), 0.0);
-        }
-    }
-
-    /**
-     * Returns the sum of squared residuals.
-     *
-     * @return residual sum of squares
-     * @throws SingularMatrixException if the design matrix is singular
-     * @throws NullPointerException if the data for the model have not been loaded
-     */
-    public double calculateResidualSumOfSquares() {
-        final Vector residuals = calculateResiduals();
-        // No advertised DME, args are valid
-        return residuals.dot(residuals);
-    }
-
-    /**
-     * Returns the R-Squared statistic, defined by the formula <pre>
-     * R<sup>2</sup> = 1 - SSR / SSTO
-     * </pre>
-     * where SSR is the {@link #calculateResidualSumOfSquares() sum of squared residuals}
-     * and SSTO is the {@link #calculateTotalSumOfSquares() total sum of squares}
-     *
-     * <p>If there is no variance in y, i.e., SSTO = 0, NaN is returned.</p>
-     *
-     * @return R-square statistic
-     * @throws NullPointerException if the sample has not been set
-     * @throws SingularMatrixException if the design matrix is singular
-     */
-    public double calculateRSquared() {
-        return 1 - calculateResidualSumOfSquares() / calculateTotalSumOfSquares();
-    }
-
-    /**
-     * <p>Returns the adjusted R-squared statistic, defined by the formula <pre>
-     * R<sup>2</sup><sub>adj</sub> = 1 - [SSR (n - 1)] / [SSTO (n - p)]
-     * </pre>
-     * where SSR is the {@link #calculateResidualSumOfSquares() sum of squared residuals},
-     * SSTO is the {@link #calculateTotalSumOfSquares() total sum of squares}, n is the number
-     * of observations and p is the number of parameters estimated (including the intercept).</p>
-     *
-     * <p>If the regression is estimated without an intercept term, what is returned is <pre>
-     * <code> 1 - (1 - {@link #calculateRSquared()}) * (n / (n - p)) </code>
-     * </pre></p>
-     *
-     * <p>If there is no variance in y, i.e., SSTO = 0, NaN is returned.</p>
-     *
-     * @return adjusted R-Squared statistic
-     * @throws NullPointerException if the sample has not been set
-     * @throws SingularMatrixException if the design matrix is singular
-     * @see #isNoIntercept()
-     */
-    public double calculateAdjustedRSquared() {
-        final double n = getX().rowSize();
-        if (isNoIntercept())
-            return 1 - (1 - calculateRSquared()) * (n / (n - getX().columnSize()));
-        else
-            return 1 - (calculateResidualSumOfSquares() * (n - 1)) /
-                (calculateTotalSumOfSquares() * (n - getX().columnSize()));
-    }
-
-    /**
-     * {@inheritDoc}
-     * <p>This implementation computes and caches the QR decomposition of the X matrix
-     * once it is successfully loaded.</p>
-     */
-    @Override protected void newXSampleData(Matrix x) {
-        super.newXSampleData(x);
-        QRDecomposition qr = new QRDecomposition(getX());
-        solver = new QRDSolver(qr.getQ(), qr.getR());
-    }
-
-    /**
-     * Calculates the regression coefficients using OLS.
-     *
-     * <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 beta
-     * @throws SingularMatrixException if the design matrix is singular
-     * @throws NullPointerException if the data for the model have not been loaded
-     */
-    @Override protected Vector calculateBeta() {
-        return solver.solve(getY());
-    }
-
-    /**
-     * <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>
-     *
-     * @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
-     */
-    @Override protected Matrix calculateBetaVariance() {
-        return solver.calculateBetaVariance(getX().columnSize());
-    }
-
-    /** */
-    QRDSolver solver() {
-        return solver;
-    }
-}

http://git-wip-us.apache.org/repos/asf/ignite/blob/b2060855/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
deleted file mode 100644
index b95cbf3..0000000
--- a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionModel.java
+++ /dev/null
@@ -1,77 +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.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 apply(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/b2060855/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
deleted file mode 100644
index fc44968..0000000
--- a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionModelFormat.java
+++ /dev/null
@@ -1,46 +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.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/b2060855/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
deleted file mode 100644
index dde0aca..0000000
--- a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/OLSMultipleLinearRegressionTrainer.java
+++ /dev/null
@@ -1,62 +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.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/b2060855/modules/ml/src/main/java/org/apache/ignite/ml/regressions/RegressionsErrorMessages.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/RegressionsErrorMessages.java b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/RegressionsErrorMessages.java
deleted file mode 100644
index 883adca..0000000
--- a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/RegressionsErrorMessages.java
+++ /dev/null
@@ -1,28 +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.ml.regressions;
-
-/**
- * This class contains various messages used in regressions,
- */
-public class RegressionsErrorMessages {
-    /** Constant for string indicating that sample has insufficient observed points. */
-    static final String INSUFFICIENT_OBSERVED_POINTS_IN_SAMPLE = "Insufficient observed points in sample.";
-    /** */
-    static final String NOT_ENOUGH_DATA_FOR_NUMBER_OF_PREDICTORS = "Not enough data (%d rows) for this many predictors (%d predictors)";
-}

http://git-wip-us.apache.org/repos/asf/ignite/blob/b2060855/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/LinearRegressionModel.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/LinearRegressionModel.java b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/LinearRegressionModel.java
new file mode 100644
index 0000000..6586a81
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/LinearRegressionModel.java
@@ -0,0 +1,107 @@
+/*
+ * 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.linear;
+
+import java.io.Serializable;
+import java.util.Objects;
+import org.apache.ignite.ml.Exportable;
+import org.apache.ignite.ml.Exporter;
+import org.apache.ignite.ml.Model;
+import org.apache.ignite.ml.math.Vector;
+
+/**
+ * Simple linear regression model which predicts result value Y as a linear combination of input variables:
+ * Y = weights * X + intercept.
+ */
+public class LinearRegressionModel implements Model<Vector, Double>, Exportable<LinearRegressionModel>, Serializable {
+    /** */
+    private static final long serialVersionUID = -105984600091550226L;
+
+    /** Multiplier of the objects's vector required to make prediction.  */
+    private final Vector weights;
+
+    /** Intercept of the linear regression model */
+    private final double intercept;
+
+    /** */
+    public LinearRegressionModel(Vector weights, double intercept) {
+        this.weights = weights;
+        this.intercept = intercept;
+    }
+
+    /** */
+    public Vector getWeights() {
+        return weights;
+    }
+
+    /** */
+    public double getIntercept() {
+        return intercept;
+    }
+
+    /** {@inheritDoc} */
+    @Override public Double apply(Vector input) {
+        return input.dot(weights) + intercept;
+    }
+
+    /** {@inheritDoc} */
+    @Override public <P> void saveModel(Exporter<LinearRegressionModel, P> exporter, P path) {
+        exporter.save(this, path);
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean equals(Object o) {
+        if (this == o)
+            return true;
+        if (o == null || getClass() != o.getClass())
+            return false;
+        LinearRegressionModel mdl = (LinearRegressionModel)o;
+        return Double.compare(mdl.intercept, intercept) == 0 &&
+            Objects.equals(weights, mdl.weights);
+    }
+
+    /** {@inheritDoc} */
+    @Override public int hashCode() {
+
+        return Objects.hash(weights, intercept);
+    }
+
+    /** {@inheritDoc} */
+    @Override public String toString() {
+        if (weights.size() < 10) {
+            StringBuilder builder = new StringBuilder();
+
+            for (int i = 0; i < weights.size(); i++) {
+                double nextItem = i == weights.size() - 1 ? intercept : weights.get(i + 1);
+
+                builder.append(String.format("%.4f", Math.abs(weights.get(i))))
+                    .append("*x")
+                    .append(i)
+                    .append(nextItem > 0 ? " + " : " - ");
+            }
+
+            builder.append(String.format("%.4f", Math.abs(intercept)));
+            return builder.toString();
+        }
+
+        return "LinearRegressionModel{" +
+            "weights=" + weights +
+            ", intercept=" + intercept +
+            '}';
+    }
+}
\ No newline at end of file

http://git-wip-us.apache.org/repos/asf/ignite/blob/b2060855/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/LinearRegressionQRTrainer.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/LinearRegressionQRTrainer.java b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/LinearRegressionQRTrainer.java
new file mode 100644
index 0000000..5de3cda
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/LinearRegressionQRTrainer.java
@@ -0,0 +1,72 @@
+/*
+ * 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.linear;
+
+import org.apache.ignite.ml.Trainer;
+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.impls.vector.FunctionVector;
+
+/**
+ * Linear regression trainer based on least squares loss function and QR decomposition.
+ */
+public class LinearRegressionQRTrainer implements Trainer<LinearRegressionModel, Matrix> {
+    /**
+     * {@inheritDoc}
+     */
+    @Override public LinearRegressionModel train(Matrix data) {
+        Vector groundTruth = extractGroundTruth(data);
+        Matrix inputs = extractInputs(data);
+
+        QRDecomposition decomposition = new QRDecomposition(inputs);
+        QRDSolver solver = new QRDSolver(decomposition.getQ(), decomposition.getR());
+
+        Vector variables = solver.solve(groundTruth);
+        Vector weights = variables.viewPart(1, variables.size() - 1);
+
+        double intercept = variables.get(0);
+
+        return new LinearRegressionModel(weights, intercept);
+    }
+
+    /**
+     * Extracts first column with ground truth from the data set matrix.
+     *
+     * @param data data to build model
+     * @return Ground truth vector
+     */
+    private Vector extractGroundTruth(Matrix data) {
+        return data.getCol(0);
+    }
+
+    /**
+     * Extracts all inputs from data set matrix and updates matrix so that first column contains value 1.0.
+     *
+     * @param data data to build model
+     * @return Inputs matrix
+     */
+    private Matrix extractInputs(Matrix data) {
+        data = data.copy();
+
+        data.assignColumn(0, new FunctionVector(data.rowSize(), row -> 1.0));
+
+        return data;
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/b2060855/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/LinearRegressionSGDTrainer.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/LinearRegressionSGDTrainer.java b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/LinearRegressionSGDTrainer.java
new file mode 100644
index 0000000..aad4c7a
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/LinearRegressionSGDTrainer.java
@@ -0,0 +1,67 @@
+/*
+ * 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.linear;
+
+import org.apache.ignite.ml.Trainer;
+import org.apache.ignite.ml.math.Matrix;
+import org.apache.ignite.ml.math.Vector;
+import org.apache.ignite.ml.optimization.BarzilaiBorweinUpdater;
+import org.apache.ignite.ml.optimization.GradientDescent;
+import org.apache.ignite.ml.optimization.LeastSquaresGradientFunction;
+import org.apache.ignite.ml.optimization.SimpleUpdater;
+
+/**
+ * Linear regression trainer based on least squares loss function and gradient descent optimization algorithm.
+ */
+public class LinearRegressionSGDTrainer implements Trainer<LinearRegressionModel, Matrix> {
+    /**
+     * Gradient descent optimizer.
+     */
+    private final GradientDescent gradientDescent;
+
+    /** */
+    public LinearRegressionSGDTrainer(GradientDescent gradientDescent) {
+        this.gradientDescent = gradientDescent;
+    }
+
+    /** */
+    public LinearRegressionSGDTrainer(int maxIterations, double convergenceTol) {
+        this.gradientDescent = new GradientDescent(new LeastSquaresGradientFunction(), new BarzilaiBorweinUpdater())
+            .withMaxIterations(maxIterations)
+            .withConvergenceTol(convergenceTol);
+    }
+
+    /** */
+    public LinearRegressionSGDTrainer(int maxIterations, double convergenceTol, double learningRate) {
+        this.gradientDescent = new GradientDescent(new LeastSquaresGradientFunction(), new SimpleUpdater(learningRate))
+            .withMaxIterations(maxIterations)
+            .withConvergenceTol(convergenceTol);
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    @Override public LinearRegressionModel train(Matrix data) {
+        Vector variables = gradientDescent.optimize(data, data.likeVector(data.columnSize()));
+        Vector weights = variables.viewPart(1, variables.size() - 1);
+
+        double intercept = variables.get(0);
+
+        return new LinearRegressionModel(weights, intercept);
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/b2060855/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/package-info.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/package-info.java b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/package-info.java
new file mode 100644
index 0000000..086a824
--- /dev/null
+++ b/modules/ml/src/main/java/org/apache/ignite/ml/regressions/linear/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. -->
+ * Contains various linear regressions.
+ */
+package org.apache.ignite.ml.regressions.linear;
\ No newline at end of file

http://git-wip-us.apache.org/repos/asf/ignite/blob/b2060855/modules/ml/src/test/java/org/apache/ignite/ml/LocalModelsTest.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/test/java/org/apache/ignite/ml/LocalModelsTest.java b/modules/ml/src/test/java/org/apache/ignite/ml/LocalModelsTest.java
index 37dec77..862a9c1 100644
--- a/modules/ml/src/test/java/org/apache/ignite/ml/LocalModelsTest.java
+++ b/modules/ml/src/test/java/org/apache/ignite/ml/LocalModelsTest.java
@@ -28,9 +28,8 @@ import org.apache.ignite.ml.knn.models.KNNModelFormat;
 import org.apache.ignite.ml.knn.models.KNNStrategy;
 import org.apache.ignite.ml.math.distances.EuclideanDistance;
 import org.apache.ignite.ml.math.impls.matrix.DenseLocalOnHeapMatrix;
-import org.apache.ignite.ml.regressions.OLSMultipleLinearRegressionModel;
-import org.apache.ignite.ml.regressions.OLSMultipleLinearRegressionModelFormat;
-import org.apache.ignite.ml.regressions.OLSMultipleLinearRegressionTrainer;
+import org.apache.ignite.ml.math.impls.vector.DenseLocalOnHeapVector;
+import org.apache.ignite.ml.regressions.linear.LinearRegressionModel;
 import org.apache.ignite.ml.structures.LabeledDataset;
 import org.junit.Assert;
 import org.junit.Test;
@@ -63,21 +62,16 @@ public class LocalModelsTest {
 
     /** */
     @Test
-    public void importExportOLSMultipleLinearRegressionModelTest() throws IOException {
+    public void importExportLinearRegressionModelTest() throws IOException {
         executeModelTest(mdlFilePath -> {
-            OLSMultipleLinearRegressionModel mdl = getAbstractMultipleLinearRegressionModel();
+            LinearRegressionModel model = new LinearRegressionModel(new DenseLocalOnHeapVector(new double[]{1, 2}), 3);
+            Exporter<LinearRegressionModel, String> exporter = new FileExporter<>();
+            model.saveModel(exporter, mdlFilePath);
 
-            Exporter<OLSMultipleLinearRegressionModelFormat, String> exporter = new FileExporter<>();
-
-            mdl.saveModel(exporter, mdlFilePath);
-
-            OLSMultipleLinearRegressionModelFormat load = exporter.load(mdlFilePath);
+            LinearRegressionModel load = exporter.load(mdlFilePath);
 
             Assert.assertNotNull(load);
-
-            OLSMultipleLinearRegressionModel importedMdl = load.getOLSMultipleLinearRegressionModel();
-
-            Assert.assertTrue("", mdl.equals(importedMdl));
+            Assert.assertEquals("", model, load);
 
             return null;
         });
@@ -114,24 +108,6 @@ public class LocalModelsTest {
     }
 
     /** */
-    private OLSMultipleLinearRegressionModel getAbstractMultipleLinearRegressionModel() {
-        double[] data = new double[] {
-            0, 0, 0, 0, 0, 0, // IMPL NOTE values in this row are later replaced (with 1.0)
-            0, 2.0, 0, 0, 0, 0,
-            0, 0, 3.0, 0, 0, 0,
-            0, 0, 0, 4.0, 0, 0,
-            0, 0, 0, 0, 5.0, 0,
-            0, 0, 0, 0, 0, 6.0};
-
-        final int nobs = 6, nvars = 5;
-
-        OLSMultipleLinearRegressionTrainer trainer
-            = new OLSMultipleLinearRegressionTrainer(0, nobs, nvars, new DenseLocalOnHeapMatrix(1, 1));
-
-        return trainer.train(data);
-    }
-
-    /** */
     @Test
     public void importExportKNNModelTest() throws IOException {
         executeModelTest(mdlFilePath -> {

http://git-wip-us.apache.org/repos/asf/ignite/blob/b2060855/modules/ml/src/test/java/org/apache/ignite/ml/optimization/GradientDescentTest.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/test/java/org/apache/ignite/ml/optimization/GradientDescentTest.java b/modules/ml/src/test/java/org/apache/ignite/ml/optimization/GradientDescentTest.java
new file mode 100644
index 0000000..f6f4775
--- /dev/null
+++ b/modules/ml/src/test/java/org/apache/ignite/ml/optimization/GradientDescentTest.java
@@ -0,0 +1,64 @@
+/*
+ * 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.optimization;
+
+import org.apache.ignite.ml.TestUtils;
+import org.apache.ignite.ml.math.Vector;
+import org.apache.ignite.ml.math.impls.matrix.DenseLocalOnHeapMatrix;
+import org.apache.ignite.ml.math.impls.vector.DenseLocalOnHeapVector;
+import org.junit.Test;
+
+/**
+ * Tests for {@link GradientDescent}.
+ */
+public class GradientDescentTest {
+    /** */
+    private static final double PRECISION = 1e-6;
+
+    /**
+     * Test gradient descent optimization on function y = x^2 with gradient function 2 * x.
+     */
+    @Test
+    public void testOptimize() {
+        GradientDescent gradientDescent = new GradientDescent(
+            (inputs, groundTruth, point) -> point.times(2),
+            new SimpleUpdater(0.01)
+        );
+
+        Vector res = gradientDescent.optimize(new DenseLocalOnHeapMatrix(new double[1][1]),
+            new DenseLocalOnHeapVector(new double[]{ 2.0 }));
+
+        TestUtils.assertEquals(0, res.get(0), PRECISION);
+    }
+
+    /**
+     * Test gradient descent optimization on function y = (x - 2)^2 with gradient function 2 * (x - 2).
+     */
+    @Test
+    public void testOptimizeWithOffset() {
+        GradientDescent gradientDescent = new GradientDescent(
+            (inputs, groundTruth, point) -> point.minus(new DenseLocalOnHeapVector(new double[]{ 2.0 })).times(2.0),
+            new SimpleUpdater(0.01)
+        );
+
+        Vector res = gradientDescent.optimize(new DenseLocalOnHeapMatrix(new double[1][1]),
+            new DenseLocalOnHeapVector(new double[]{ 2.0 }));
+
+        TestUtils.assertEquals(2, res.get(0), PRECISION);
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/b2060855/modules/ml/src/test/java/org/apache/ignite/ml/optimization/util/SparseDistributedMatrixMapReducerTest.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/test/java/org/apache/ignite/ml/optimization/util/SparseDistributedMatrixMapReducerTest.java b/modules/ml/src/test/java/org/apache/ignite/ml/optimization/util/SparseDistributedMatrixMapReducerTest.java
new file mode 100644
index 0000000..9017c43
--- /dev/null
+++ b/modules/ml/src/test/java/org/apache/ignite/ml/optimization/util/SparseDistributedMatrixMapReducerTest.java
@@ -0,0 +1,135 @@
+/*
+ * 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.optimization.util;
+
+import org.apache.ignite.Ignite;
+import org.apache.ignite.internal.util.IgniteUtils;
+import org.apache.ignite.ml.math.impls.matrix.SparseDistributedMatrix;
+import org.apache.ignite.testframework.junits.common.GridCommonAbstractTest;
+
+/**
+ * Tests for {@link SparseDistributedMatrixMapReducer}.
+ */
+public class SparseDistributedMatrixMapReducerTest extends GridCommonAbstractTest {
+    /** Number of nodes in grid */
+    private static final int NODE_COUNT = 2;
+
+    /** */
+    private Ignite ignite;
+
+    /** {@inheritDoc} */
+    @Override protected void beforeTestsStarted() throws Exception {
+        for (int i = 1; i <= NODE_COUNT; i++)
+            startGrid(i);
+    }
+
+    /** {@inheritDoc} */
+    @Override protected void afterTestsStopped() {
+        stopAllGrids();
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    @Override protected void beforeTest() throws Exception {
+        /* Grid instance. */
+        ignite = grid(NODE_COUNT);
+        ignite.configuration().setPeerClassLoadingEnabled(true);
+        IgniteUtils.setCurrentIgniteName(ignite.configuration().getIgniteInstanceName());
+    }
+
+    /**
+     * Tests that matrix 100x100 filled by "1.0" and distributed across nodes successfully processed (calculate sum of
+     * all elements) via {@link SparseDistributedMatrixMapReducer}.
+     */
+    public void testMapReduce() {
+        IgniteUtils.setCurrentIgniteName(ignite.configuration().getIgniteInstanceName());
+        SparseDistributedMatrix distributedMatrix = new SparseDistributedMatrix(100, 100);
+        for (int i = 0; i < 100; i++)
+            for (int j = 0; j < 100; j++)
+                distributedMatrix.set(i, j, 1);
+        SparseDistributedMatrixMapReducer mapReducer = new SparseDistributedMatrixMapReducer(distributedMatrix);
+        double total = mapReducer.mapReduce(
+            (matrix, args) -> {
+                double partialSum = 0.0;
+                for (int i = 0; i < matrix.rowSize(); i++)
+                    for (int j = 0; j < matrix.columnSize(); j++)
+                        partialSum += matrix.get(i, j);
+                return partialSum;
+            },
+            sums -> {
+                double totalSum = 0;
+                for (Double partialSum : sums)
+                    if (partialSum != null)
+                        totalSum += partialSum;
+                return totalSum;
+            }, 0.0);
+        assertEquals(100.0 * 100.0, total, 1e-18);
+    }
+
+    /**
+     * Tests that matrix 100x100 filled by "1.0" and distributed across nodes successfully processed via
+     * {@link SparseDistributedMatrixMapReducer} even when mapping function returns {@code null}.
+     */
+    public void testMapReduceWithNullValues() {
+        IgniteUtils.setCurrentIgniteName(ignite.configuration().getIgniteInstanceName());
+        SparseDistributedMatrix distributedMatrix = new SparseDistributedMatrix(100, 100);
+        for (int i = 0; i < 100; i++)
+            for (int j = 0; j < 100; j++)
+                distributedMatrix.set(i, j, 1);
+        SparseDistributedMatrixMapReducer mapReducer = new SparseDistributedMatrixMapReducer(distributedMatrix);
+        double total = mapReducer.mapReduce(
+            (matrix, args) -> null,
+            sums -> {
+                double totalSum = 0;
+                for (Double partialSum : sums)
+                    if (partialSum != null)
+                        totalSum += partialSum;
+                return totalSum;
+            }, 0.0);
+        assertEquals(0, total, 1e-18);
+    }
+
+    /**
+     * Tests that matrix 1x100 filled by "1.0" and distributed across nodes successfully processed (calculate sum of
+     * all elements) via {@link SparseDistributedMatrixMapReducer} even when not all nodes contains data.
+     */
+    public void testMapReduceWithOneEmptyNode() {
+        IgniteUtils.setCurrentIgniteName(ignite.configuration().getIgniteInstanceName());
+        SparseDistributedMatrix distributedMatrix = new SparseDistributedMatrix(1, 100);
+        for (int j = 0; j < 100; j++)
+            distributedMatrix.set(0, j, 1);
+        SparseDistributedMatrixMapReducer mapReducer = new SparseDistributedMatrixMapReducer(distributedMatrix);
+        double total = mapReducer.mapReduce(
+            (matrix, args) -> {
+                double partialSum = 0.0;
+                for (int i = 0; i < matrix.rowSize(); i++)
+                    for (int j = 0; j < matrix.columnSize(); j++)
+                        partialSum += matrix.get(i, j);
+                return partialSum;
+            },
+            sums -> {
+                double totalSum = 0;
+                for (Double partialSum : sums)
+                    if (partialSum != null)
+                        totalSum += partialSum;
+                return totalSum;
+            }, 0.0);
+        assertEquals(100.0, total, 1e-18);
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/b2060855/modules/ml/src/test/java/org/apache/ignite/ml/regressions/AbstractMultipleLinearRegressionTest.java
----------------------------------------------------------------------
diff --git a/modules/ml/src/test/java/org/apache/ignite/ml/regressions/AbstractMultipleLinearRegressionTest.java b/modules/ml/src/test/java/org/apache/ignite/ml/regressions/AbstractMultipleLinearRegressionTest.java
deleted file mode 100644
index 6ad56a5..0000000
--- a/modules/ml/src/test/java/org/apache/ignite/ml/regressions/AbstractMultipleLinearRegressionTest.java
+++ /dev/null
@@ -1,164 +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.ml.regressions;
-
-import org.apache.ignite.ml.math.Matrix;
-import org.apache.ignite.ml.math.Vector;
-import org.apache.ignite.ml.math.exceptions.MathIllegalArgumentException;
-import org.apache.ignite.ml.math.exceptions.NullArgumentException;
-import org.apache.ignite.ml.math.impls.matrix.DenseLocalOnHeapMatrix;
-import org.apache.ignite.ml.math.impls.vector.DenseLocalOnHeapVector;
-import org.junit.Assert;
-import org.junit.Before;
-import org.junit.Test;
-
-/**
- * This class is based on the corresponding class from Apache Common Math lib.
- * Abstract base class for implementations of {@link MultipleLinearRegression}.
- */
-public abstract class AbstractMultipleLinearRegressionTest {
-    /** */
-    protected AbstractMultipleLinearRegression regression;
-
-    /** */
-    @Before
-    public void setUp() {
-        regression = createRegression();
-    }
-
-    /** */
-    protected abstract AbstractMultipleLinearRegression createRegression();
-
-    /** */
-    protected abstract int getNumberOfRegressors();
-
-    /** */
-    protected abstract int getSampleSize();
-
-    /** */
-    @Test
-    public void canEstimateRegressionParameters() {
-        double[] beta = regression.estimateRegressionParameters();
-        Assert.assertEquals(getNumberOfRegressors(), beta.length);
-    }
-
-    /** */
-    @Test
-    public void canEstimateResiduals() {
-        double[] e = regression.estimateResiduals();
-        Assert.assertEquals(getSampleSize(), e.length);
-    }
-
-    /** */
-    @Test
-    public void canEstimateRegressionParametersVariance() {
-        Matrix var = regression.estimateRegressionParametersVariance();
-        Assert.assertEquals(getNumberOfRegressors(), var.rowSize());
-    }
-
-    /** */
-    @Test
-    public void canEstimateRegressandVariance() {
-        if (getSampleSize() > getNumberOfRegressors()) {
-            double variance = regression.estimateRegressandVariance();
-            Assert.assertTrue(variance > 0.0);
-        }
-    }
-
-    /**
-     * Verifies that newSampleData methods consistently insert unitary columns
-     * in design matrix.  Confirms the fix for MATH-411.
-     */
-    @Test
-    public void testNewSample() {
-        double[] design = new double[] {
-            1, 19, 22, 33,
-            2, 20, 30, 40,
-            3, 25, 35, 45,
-            4, 27, 37, 47
-        };
-
-        double[] y = new double[] {1, 2, 3, 4};
-
-        double[][] x = new double[][] {
-            {19, 22, 33},
-            {20, 30, 40},
-            {25, 35, 45},
-            {27, 37, 47}
-        };
-
-        AbstractMultipleLinearRegression regression = createRegression();
-        regression.newSampleData(design, 4, 3, new DenseLocalOnHeapMatrix());
-
-        Matrix flatX = regression.getX().copy();
-        Vector flatY = regression.getY().copy();
-
-        regression.newXSampleData(new DenseLocalOnHeapMatrix(x));
-        regression.newYSampleData(new DenseLocalOnHeapVector(y));
-
-        Assert.assertEquals(flatX, regression.getX());
-        Assert.assertEquals(flatY, regression.getY());
-
-        // No intercept
-        regression.setNoIntercept(true);
-        regression.newSampleData(design, 4, 3, new DenseLocalOnHeapMatrix());
-
-        flatX = regression.getX().copy();
-        flatY = regression.getY().copy();
-
-        regression.newXSampleData(new DenseLocalOnHeapMatrix(x));
-        regression.newYSampleData(new DenseLocalOnHeapVector(y));
-
-        Assert.assertEquals(flatX, regression.getX());
-        Assert.assertEquals(flatY, regression.getY());
-    }
-
-    /** */
-    @Test(expected = NullArgumentException.class)
-    public void testNewSampleNullData() {
-        double[] data = null;
-        createRegression().newSampleData(data, 2, 3, new DenseLocalOnHeapMatrix());
-    }
-
-    /** */
-    @Test(expected = MathIllegalArgumentException.class)
-    public void testNewSampleInvalidData() {
-        double[] data = new double[] {1, 2, 3, 4};
-        createRegression().newSampleData(data, 2, 3, new DenseLocalOnHeapMatrix());
-    }
-
-    /** */
-    @Test(expected = MathIllegalArgumentException.class)
-    public void testNewSampleInsufficientData() {
-        double[] data = new double[] {1, 2, 3, 4};
-        createRegression().newSampleData(data, 1, 3, new DenseLocalOnHeapMatrix());
-    }
-
-    /** */
-    @Test(expected = NullArgumentException.class)
-    public void testXSampleDataNull() {
-        createRegression().newXSampleData(null);
-    }
-
-    /** */
-    @Test(expected = NullArgumentException.class)
-    public void testYSampleDataNull() {
-        createRegression().newYSampleData(null);
-    }
-
-}


Mime
View raw message