Modified KolmogororSmirnovTest 2-sample test to use random jitter to break ties in input data. JIRA: MATH-1246.
This commit is contained in:
Phil Steitz
parent
5f9cfa6ebf
commit
f7ab3a70ec
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@ -60,7 +60,9 @@ If the output is not quite correct, check for invisible trailing spaces!
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synchronization is now performed on the coefficient list instead of the class.
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</action>
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<action dev="psteitz" type="update" issue="MATH-1246">
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Added bootstrap method to 2-sample KolmogorovSmirnovTest.
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Modified 2-sample KolmogorovSmirnovTest to handle ties in sample data. By default,
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ties are broken by adding random jitter to input data. Also added bootstrap method
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analogous to ks.boot in R Matching package.
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</action>
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<action dev="psteitz" type="update" issue="MATH-1287"> <!-- backported to 3.6 -->
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Added constructors taking sample data as arguments to enumerated real and integer distributions.
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@ -29,6 +29,23 @@ public class JDKRandomGenerator extends Random implements RandomGenerator {
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/** Serializable version identifier. */
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private static final long serialVersionUID = -7745277476784028798L;
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/**
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* Create a new JDKRandomGenerator with a default seed.
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*/
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public JDKRandomGenerator() {
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super();
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}
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/**
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* Create a new JDKRandomGenerator with the given seed.
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*
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* @param seed initial seed
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* @since 3.6
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*/
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public JDKRandomGenerator(int seed) {
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setSeed(seed);
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}
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/** {@inheritDoc} */
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@Override
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public void setSeed(int seed) {
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@ -24,8 +24,10 @@ import java.util.Iterator;
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import org.apache.commons.math4.distribution.EnumeratedRealDistribution;
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import org.apache.commons.math4.distribution.RealDistribution;
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import org.apache.commons.math4.distribution.UniformRealDistribution;
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import org.apache.commons.math4.exception.InsufficientDataException;
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import org.apache.commons.math4.exception.MathArithmeticException;
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import org.apache.commons.math4.exception.MathInternalError;
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import org.apache.commons.math4.exception.NullArgumentException;
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import org.apache.commons.math4.exception.NumberIsTooLargeException;
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import org.apache.commons.math4.exception.OutOfRangeException;
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@ -38,6 +40,7 @@ import org.apache.commons.math4.linear.Array2DRowFieldMatrix;
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import org.apache.commons.math4.linear.FieldMatrix;
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import org.apache.commons.math4.linear.MatrixUtils;
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import org.apache.commons.math4.linear.RealMatrix;
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import org.apache.commons.math4.random.JDKRandomGenerator;
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import org.apache.commons.math4.random.RandomGenerator;
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import org.apache.commons.math4.random.Well19937c;
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import org.apache.commons.math4.util.CombinatoricsUtils;
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@ -244,11 +247,21 @@ public class KolmogorovSmirnovTest {
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*/
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public double kolmogorovSmirnovTest(double[] x, double[] y, boolean strict) {
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final long lengthProduct = (long) x.length * y.length;
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double[] xa = null;
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double[] ya = null;
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if (lengthProduct < LARGE_SAMPLE_PRODUCT && hasTies(x,y)) {
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xa = MathArrays.copyOf(x);
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ya = MathArrays.copyOf(y);
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fixTies(xa, ya);
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} else {
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xa = x;
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ya = y;
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}
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if (lengthProduct < SMALL_SAMPLE_PRODUCT) {
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return integralExactP(integralKolmogorovSmirnovStatistic(x, y) + (strict?1l:0l), x.length, y.length);
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return integralExactP(integralKolmogorovSmirnovStatistic(xa, ya) + (strict?1l:0l), x.length, y.length);
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}
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if (lengthProduct < LARGE_SAMPLE_PRODUCT) {
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return integralMonteCarloP(integralKolmogorovSmirnovStatistic(x, y) + (strict?1l:0l), x.length, y.length, MONTE_CARLO_ITERATIONS);
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return integralMonteCarloP(integralKolmogorovSmirnovStatistic(xa, ya) + (strict?1l:0l), x.length, y.length, MONTE_CARLO_ITERATIONS);
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}
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return approximateP(kolmogorovSmirnovStatistic(x, y), x.length, y.length);
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}
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@ -1149,6 +1162,59 @@ public class KolmogorovSmirnovTest {
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return (double) tail / iterations;
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}
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/**
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* If there are no ties in the combined dataset formed from x and y, this
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* method is a no-op. If there are ties, a uniform random deviate in
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* (-minDelta / 2, minDelta / 2) - {0} is added to each value in x and y, where
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* minDelta is the minimum difference between unequal values in the combined
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* sample. A fixed seed is used to generate the jitter, so repeated activations
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* with the same input arrays result in the same values.
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*
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* NOTE: if there are ties in the data, this method overwrites the data in
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* x and y with the jittered values.
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*
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* @param x first sample
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* @param y second sample
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*/
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private static void fixTies(double[] x, double[] y) {
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final double[] values = MathArrays.unique(MathArrays.concatenate(x,y));
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if (values.length == x.length + y.length) {
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return; // There are no ties
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}
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// Find the smallest difference between values, or 1 if all values are the same
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double minDelta = 1;
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double prev = values[0];
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double delta = 1;
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for (int i = 1; i < values.length; i++) {
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delta = prev - values[i];
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if (delta < minDelta) {
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minDelta = delta;
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}
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prev = values[i];
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}
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minDelta /= 2;
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// Add jitter using a fixed seed (so same arguments always give same results),
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// low-initialization-overhead generator
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final RealDistribution dist =
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new UniformRealDistribution(new JDKRandomGenerator(100), -minDelta, minDelta);
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// It is theoretically possible that jitter does not break ties, so repeat
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// until all ties are gone. Bound the loop and throw MIE if bound is exceeded.
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int ct = 0;
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boolean ties = true;
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do {
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jitter(x, dist);
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jitter(y, dist);
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ties = hasTies(x, y);
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ct++;
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} while (ties && ct < 1000);
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if (ties) {
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throw new MathInternalError(); // Should never happen
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}
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}
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/**
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* Returns true iff there are ties in the combined sample
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* formed from x and y.
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@ -1157,8 +1223,8 @@ public class KolmogorovSmirnovTest {
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* @param y second sample
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* @return true if x and y together contain ties
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*/
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private boolean hasTies(double[] x, double[] y) {
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HashSet<Double> values = new HashSet<Double>();
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private static boolean hasTies(double[] x, double[] y) {
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final HashSet<Double> values = new HashSet<Double>();
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for (int i = 0; i < x.length; i++) {
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if (!values.add(x[i])) {
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return true;
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@ -1171,4 +1237,20 @@ public class KolmogorovSmirnovTest {
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}
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return false;
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}
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/**
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* Adds random jitter to {@code data} using deviates sampled from {@code dist}.
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* <p>
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* Note that jitter is applied in-place - i.e., the array
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* values are overwritten with the result of applying jitter.</p>
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*
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* @param data input/output data array - entries overwritten by the method
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* @param dist probability distribution to sample for jitter values
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* @throws NullPointerException if either of the parameters is null
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*/
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private static void jitter(double[] data, RealDistribution dist) {
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for (int i = 0; i < data.length; i++) {
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data[i] = data[i] + dist.sample();
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}
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}
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}
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@ -22,7 +22,9 @@ import java.util.ArrayList;
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import java.util.Arrays;
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import java.util.Collections;
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import java.util.Comparator;
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import java.util.Iterator;
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import java.util.List;
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import java.util.TreeSet;
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import org.apache.commons.math4.Field;
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import org.apache.commons.math4.distribution.UniformIntegerDistribution;
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@ -1876,4 +1878,60 @@ public class MathArrays {
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return verifyValues(values, begin, length, allowEmpty);
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}
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/**
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* Concatenates a sequence of arrays. The return array consists of the
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* entries of the input arrays concatenated in the order they appear in
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* the argument list. Null arrays cause NullPointerExceptions; zero
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* length arrays are allowed (contributing nothing to the output array).
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*
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* @param x list of double[] arrays to concatenate
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* @return a new array consisting of the entries of the argument arrays
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* @throws NullPointerException if any of the arrays are null
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* @since 3.6
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*/
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public static double[] concatenate(double[] ...x) {
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int combinedLength = 0;
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for (double[] a : x) {
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combinedLength += a.length;
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}
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int offset = 0;
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int curLength = 0;
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final double[] combined = new double[combinedLength];
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for (int i = 0; i < x.length; i++) {
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curLength = x[i].length;
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System.arraycopy(x[i], 0, combined, offset, curLength);
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offset += curLength;
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}
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return combined;
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}
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/**
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* Returns an array consisting of the unique values in {@code data}.
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* The return array is sorted in descending order. Empty arrays
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* are allowed, but null arrays result in NullPointerException.
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* Infinities are allowed. NaN values are allowed with maximum
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* sort order - i.e., if there are NaN values in {@code data},
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* {@code Double.NaN} will be the first element of the output array,
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* even if the array also contains {@code Double.POSITIVE_INFINITY}.
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*
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* @param data array to scan
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* @return descending list of values included in the input array
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* @throws NullPointerException if data is null
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* @since 3.6
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*/
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public static double[] unique(double[] data) {
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TreeSet<Double> values = new TreeSet<Double>();
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for (int i = 0; i < data.length; i++) {
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values.add(data[i]);
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}
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final int count = values.size();
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final double[] out = new double[count];
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Iterator<Double> iterator = values.descendingIterator();
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int i = 0;
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while (iterator.hasNext()) {
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out[i++] = iterator.next();
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}
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return out;
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}
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}
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@ -17,6 +17,7 @@
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package org.apache.commons.math4.stat.inference;
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import java.lang.reflect.Method;
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import java.util.Arrays;
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import org.apache.commons.math4.TestUtils;
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@ -27,6 +28,7 @@ import org.apache.commons.math4.random.Well19937c;
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import org.apache.commons.math4.stat.inference.KolmogorovSmirnovTest;
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import org.apache.commons.math4.util.CombinatoricsUtils;
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import org.apache.commons.math4.util.FastMath;
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import org.apache.commons.math4.util.MathArrays;
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import org.junit.Assert;
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import org.junit.Test;
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@ -567,6 +569,63 @@ public class KolmogorovSmirnovTestTest {
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Assert.assertEquals(0.06303, test.bootstrap(x, y, 10000, false), 1E-2);
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}
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@Test
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public void testFixTiesNoOp() throws Exception {
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final double[] x = {0, 1, 2, 3, 4};
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final double[] y = {5, 6, 7, 8};
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final double[] origX = MathArrays.copyOf(x);
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final double[] origY = MathArrays.copyOf(y);
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fixTies(x,y);
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Assert.assertArrayEquals(origX, x, 0);
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Assert.assertArrayEquals(origY, y, 0);
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}
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/**
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* Verify that fixTies is deterministic, i.e,
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* x = x', y = y' => fixTies(x,y) = fixTies(x', y')
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*/
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@Test
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public void testFixTiesConsistency() throws Exception {
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final double[] x = {0, 1, 2, 3, 4, 2};
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final double[] y = {5, 6, 7, 8, 1, 2};
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final double[] xP = MathArrays.copyOf(x);
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final double[] yP = MathArrays.copyOf(y);
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checkFixTies(x, y);
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final double[] fixedX = MathArrays.copyOf(x);
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final double[] fixedY = MathArrays.copyOf(y);
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checkFixTies(xP, yP);
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Assert.assertArrayEquals(fixedX, xP, 0);
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Assert.assertArrayEquals(fixedY, yP, 0);
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}
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@Test
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public void testFixTies() throws Exception {
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checkFixTies(new double[] {0, 1, 1, 4, 0}, new double[] {0, 5, 0.5, 0.55, 7});
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checkFixTies(new double[] {1, 1, 1, 1, 1}, new double[] {1, 1});
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checkFixTies(new double[] {1, 2, 3}, new double[] {1});
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checkFixTies(new double[] {1, 1, 0, 1, 0}, new double[] {});
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}
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/**
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* Checks that fixTies eliminates ties in the data but does not otherwise
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* perturb the ordering.
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*/
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private void checkFixTies(double[] x, double[] y) throws Exception {
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final double[] origCombined = MathArrays.concatenate(x, y);
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fixTies(x, y);
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Assert.assertFalse(hasTies(x, y));
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final double[] combined = MathArrays.concatenate(x, y);
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for (int i = 0; i < combined.length; i++) {
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for (int j = 0; j < i; j++) {
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Assert.assertTrue(combined[i] != combined[j]);
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if (combined[i] < combined[j])
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Assert.assertTrue(origCombined[i] < origCombined[j]
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|| origCombined[i] == origCombined[j]);
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}
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}
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}
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/**
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* Verifies the inequality exactP(criticalValue, n, m, true) < alpha < exactP(criticalValue, n,
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* m, false).
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@ -601,4 +660,24 @@ public class KolmogorovSmirnovTestTest {
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Assert.assertEquals(alpha, test.approximateP(criticalValue, n, m), epsilon);
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}
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/**
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* Reflection hack to expose private fixTies method for testing.
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*/
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private static void fixTies(double[] x, double[] y) throws Exception {
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Method method = KolmogorovSmirnovTest.class.getDeclaredMethod("fixTies",
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double[].class, double[].class);
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method.setAccessible(true);
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method.invoke(KolmogorovSmirnovTest.class, x, y);
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}
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/**
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* Reflection hack to expose private hasTies method.
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*/
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private static boolean hasTies(double[] x, double[] y) throws Exception {
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Method method = KolmogorovSmirnovTest.class.getDeclaredMethod("hasTies",
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double[].class, double[].class);
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method.setAccessible(true);
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return (boolean) method.invoke(KolmogorovSmirnovTest.class, x, y);
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}
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}
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@ -37,7 +37,7 @@ import org.junit.Test;
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*
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*/
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public class MathArraysTest {
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private double[] testArray = {0, 1, 2, 3, 4, 5};
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private double[] testWeightsArray = {0.3, 0.2, 1.3, 1.1, 1.0, 1.8};
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private double[] testNegativeWeightsArray = {-0.3, 0.2, -1.3, 1.1, 1.0, 1.8};
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@ -49,7 +49,7 @@ public class MathArraysTest {
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final double[] test = new double[] { -2.5, -1, 0, 1, 2.5 };
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final double[] correctTest = MathArrays.copyOf(test);
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final double[] correctScaled = new double[]{5.25, 2.1, 0, -2.1, -5.25};
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final double[] scaled = MathArrays.scale(-2.1, test);
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// Make sure test has not changed
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@ -62,7 +62,7 @@ public class MathArraysTest {
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Assert.assertEquals(correctScaled[i], scaled[i], 0);
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}
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}
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@Test
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public void testScaleInPlace() {
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final double[] test = new double[] { -2.5, -1, 0, 1, 2.5 };
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@ -74,7 +74,7 @@ public class MathArraysTest {
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Assert.assertEquals(correctScaled[i], test[i], 0);
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}
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}
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@Test(expected=DimensionMismatchException.class)
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public void testEbeAddPrecondition() {
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MathArrays.ebeAdd(new double[3], new double[4]);
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@ -353,7 +353,7 @@ public class MathArraysTest {
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new Double(-27.5) },
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MathArrays.OrderDirection.DECREASING, false));
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}
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@Test
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public void testCheckRectangular() {
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final long[][] rect = new long[][] {{0, 1}, {2, 3}};
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@ -373,9 +373,9 @@ public class MathArraysTest {
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Assert.fail("Expecting NullArgumentException");
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} catch (NullArgumentException ex) {
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// Expected
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}
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}
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}
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@Test
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public void testCheckPositive() {
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final double[] positive = new double[] {1, 2, 3};
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@ -397,7 +397,7 @@ public class MathArraysTest {
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// Expected
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}
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}
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@Test
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public void testCheckNonNegative() {
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final long[] nonNegative = new long[] {0, 1};
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@ -419,7 +419,7 @@ public class MathArraysTest {
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// Expected
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}
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}
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@Test
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public void testCheckNonNegative2D() {
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final long[][] nonNegative = new long[][] {{0, 1}, {1, 0}};
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@ -554,7 +554,7 @@ public class MathArraysTest {
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Assert.assertEquals(25, x2[0], FastMath.ulp(1d));
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Assert.assertEquals(125, x3[0], FastMath.ulp(1d));
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}
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@Test
|
||||
/** Example in javadoc */
|
||||
public void testSortInPlaceExample() {
|
||||
|
|
@ -569,7 +569,7 @@ public class MathArraysTest {
|
|||
Assert.assertTrue(Arrays.equals(sy, y));
|
||||
Assert.assertTrue(Arrays.equals(sz, z));
|
||||
}
|
||||
|
||||
|
||||
@Test
|
||||
public void testSortInPlaceFailures() {
|
||||
final double[] nullArray = null;
|
||||
|
|
@ -1047,7 +1047,7 @@ public class MathArraysTest {
|
|||
Assert.fail("expecting MathIllegalArgumentException");
|
||||
} catch (MathIllegalArgumentException ex) {}
|
||||
}
|
||||
|
||||
|
||||
@Test
|
||||
public void testConvolve() {
|
||||
/* Test Case (obtained via SciPy)
|
||||
|
|
@ -1066,10 +1066,10 @@ public class MathArraysTest {
|
|||
double[] x2 = { 1, 2, 3 };
|
||||
double[] h2 = { 0, 1, 0.5 };
|
||||
double[] y2 = { 0, 1, 2.5, 4, 1.5 };
|
||||
|
||||
|
||||
yActual = MathArrays.convolve(x2, h2);
|
||||
Assert.assertArrayEquals(y2, yActual, tolerance);
|
||||
|
||||
|
||||
try {
|
||||
MathArrays.convolve(new double[]{1, 2}, null);
|
||||
Assert.fail("an exception should have been thrown");
|
||||
|
|
@ -1187,7 +1187,7 @@ public class MathArraysTest {
|
|||
final int[] seq = MathArrays.sequence(0, 12345, 6789);
|
||||
Assert.assertEquals(0, seq.length);
|
||||
}
|
||||
|
||||
|
||||
@Test
|
||||
public void testVerifyValuesPositive() {
|
||||
for (int j = 0; j < 6; j++) {
|
||||
|
|
@ -1252,4 +1252,69 @@ public class MathArraysTest {
|
|||
// expected
|
||||
}
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testConcatenate() {
|
||||
final double[] u = new double[] {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
|
||||
final double[] x = new double[] {0, 1, 2};
|
||||
final double[] y = new double[] {3, 4, 5, 6, 7, 8};
|
||||
final double[] z = new double[] {9};
|
||||
Assert.assertArrayEquals(u, MathArrays.concatenate(x, y, z), 0);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testConcatentateSingle() {
|
||||
final double[] x = new double[] {0, 1, 2};
|
||||
Assert.assertArrayEquals(x, MathArrays.concatenate(x), 0);
|
||||
}
|
||||
|
||||
public void testConcatenateEmptyArguments() {
|
||||
final double[] x = new double[] {0, 1, 2};
|
||||
final double[] y = new double[] {3};
|
||||
final double[] z = new double[] {};
|
||||
final double[] u = new double[] {0, 1, 2, 3};
|
||||
Assert.assertArrayEquals(u, MathArrays.concatenate(x, z, y), 0);
|
||||
Assert.assertArrayEquals(u, MathArrays.concatenate(x, y, z), 0);
|
||||
Assert.assertArrayEquals(u, MathArrays.concatenate(z, x, y), 0);
|
||||
Assert.assertEquals(0, MathArrays.concatenate(z, z, z).length);
|
||||
}
|
||||
|
||||
@Test(expected=NullPointerException.class)
|
||||
public void testConcatenateNullArguments() {
|
||||
final double[] x = new double[] {0, 1, 2};
|
||||
MathArrays.concatenate(x, null);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testUnique() {
|
||||
final double[] x = {0, 9, 3, 0, 11, 7, 3, 5, -1, -2};
|
||||
final double[] values = {11, 9, 7, 5, 3, 0, -1, -2};
|
||||
Assert.assertArrayEquals(values, MathArrays.unique(x), 0);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testUniqueInfiniteValues() {
|
||||
final double [] x = {0, Double.NEGATIVE_INFINITY, 3, Double.NEGATIVE_INFINITY,
|
||||
3, Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY};
|
||||
final double[] u = {Double.POSITIVE_INFINITY, 3, 0, Double.NEGATIVE_INFINITY};
|
||||
Assert.assertArrayEquals(u , MathArrays.unique(x), 0);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testUniqueNaNValues() {
|
||||
final double[] x = new double[] {10, 2, Double.NaN, Double.NaN, Double.NaN,
|
||||
Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY, Double.NEGATIVE_INFINITY};
|
||||
final double[] u = MathArrays.unique(x);
|
||||
Assert.assertEquals(5, u.length);
|
||||
Assert.assertTrue(Double.isNaN(u[0]));
|
||||
Assert.assertEquals(Double.POSITIVE_INFINITY, u[1], 0);
|
||||
Assert.assertEquals(10, u[2], 0);
|
||||
Assert.assertEquals(2, u[3], 0);
|
||||
Assert.assertEquals(Double.NEGATIVE_INFINITY, u[4], 0);
|
||||
}
|
||||
|
||||
@Test(expected=NullPointerException.class)
|
||||
public void testUniqueNullArgument() {
|
||||
MathArrays.unique(null);
|
||||
}
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue