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author | Doris Xin <doris.s.xin@gmail.com> | 2014-08-11 19:22:14 -0700 |
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committer | Xiangrui Meng <meng@databricks.com> | 2014-08-11 19:22:14 -0700 |
commit | 32638b5e74e02410831b391f555223f90c830498 (patch) | |
tree | 5fabdd0a7b2741da6e84160f3121b6908a86f78b /mllib | |
parent | 7712e724ad69dd0b83754e938e9799d13a4d43b9 (diff) | |
download | spark-32638b5e74e02410831b391f555223f90c830498.tar.gz spark-32638b5e74e02410831b391f555223f90c830498.tar.bz2 spark-32638b5e74e02410831b391f555223f90c830498.zip |
[SPARK-2515][mllib] Chi Squared test
Author: Doris Xin <doris.s.xin@gmail.com>
Closes #1733 from dorx/chisquare and squashes the following commits:
cafb3a7 [Doris Xin] fixed p-value for extreme case.
d286783 [Doris Xin] Merge branch 'master' into chisquare
e95e485 [Doris Xin] reviewer comments.
7dde711 [Doris Xin] ChiSqTestResult renaming and changed to Class
80d03e2 [Doris Xin] Reviewer comments.
c39eeb5 [Doris Xin] units passed with updated API
e90d90a [Doris Xin] Merge branch 'master' into chisquare
7eea80b [Doris Xin] WIP
d64c2fb [Doris Xin] Merge branch 'master' into chisquare
5686082 [Doris Xin] facelift
bc7eb2e [Doris Xin] unit passed; still need docs and some refactoring
50703a5 [Doris Xin] merge master
4e4e361 [Doris Xin] WIP
e6b83f3 [Doris Xin] reviewer comments
3d61582 [Doris Xin] input names
706d436 [Doris Xin] Added API for RDD[Vector]
6598379 [Doris Xin] API and code structure.
ff17423 [Doris Xin] WIP
Diffstat (limited to 'mllib')
4 files changed, 512 insertions, 0 deletions
diff --git a/mllib/src/main/scala/org/apache/spark/mllib/stat/Statistics.scala b/mllib/src/main/scala/org/apache/spark/mllib/stat/Statistics.scala index f416a9fbb3..cf8679610e 100644 --- a/mllib/src/main/scala/org/apache/spark/mllib/stat/Statistics.scala +++ b/mllib/src/main/scala/org/apache/spark/mllib/stat/Statistics.scala @@ -19,7 +19,9 @@ package org.apache.spark.mllib.stat import org.apache.spark.annotation.Experimental import org.apache.spark.mllib.linalg.{Matrix, Vector} +import org.apache.spark.mllib.regression.LabeledPoint import org.apache.spark.mllib.stat.correlation.Correlations +import org.apache.spark.mllib.stat.test.{ChiSqTest, ChiSqTestResult} import org.apache.spark.rdd.RDD /** @@ -89,4 +91,66 @@ object Statistics { */ @Experimental def corr(x: RDD[Double], y: RDD[Double], method: String): Double = Correlations.corr(x, y, method) + + /** + * :: Experimental :: + * Conduct Pearson's chi-squared goodness of fit test of the observed data against the + * expected distribution. + * + * Note: the two input Vectors need to have the same size. + * `observed` cannot contain negative values. + * `expected` cannot contain nonpositive values. + * + * @param observed Vector containing the observed categorical counts/relative frequencies. + * @param expected Vector containing the expected categorical counts/relative frequencies. + * `expected` is rescaled if the `expected` sum differs from the `observed` sum. + * @return ChiSquaredTest object containing the test statistic, degrees of freedom, p-value, + * the method used, and the null hypothesis. + */ + @Experimental + def chiSqTest(observed: Vector, expected: Vector): ChiSqTestResult = { + ChiSqTest.chiSquared(observed, expected) + } + + /** + * :: Experimental :: + * Conduct Pearson's chi-squared goodness of fit test of the observed data against the uniform + * distribution, with each category having an expected frequency of `1 / observed.size`. + * + * Note: `observed` cannot contain negative values. + * + * @param observed Vector containing the observed categorical counts/relative frequencies. + * @return ChiSquaredTest object containing the test statistic, degrees of freedom, p-value, + * the method used, and the null hypothesis. + */ + @Experimental + def chiSqTest(observed: Vector): ChiSqTestResult = ChiSqTest.chiSquared(observed) + + /** + * :: Experimental :: + * Conduct Pearson's independence test on the input contingency matrix, which cannot contain + * negative entries or columns or rows that sum up to 0. + * + * @param observed The contingency matrix (containing either counts or relative frequencies). + * @return ChiSquaredTest object containing the test statistic, degrees of freedom, p-value, + * the method used, and the null hypothesis. + */ + @Experimental + def chiSqTest(observed: Matrix): ChiSqTestResult = ChiSqTest.chiSquaredMatrix(observed) + + /** + * :: Experimental :: + * Conduct Pearson's independence test for every feature against the label across the input RDD. + * For each feature, the (feature, label) pairs are converted into a contingency matrix for which + * the chi-squared statistic is computed. + * + * @param data an `RDD[LabeledPoint]` containing the labeled dataset with categorical features. + * Real-valued features will be treated as categorical for each distinct value. + * @return an array containing the ChiSquaredTestResult for every feature against the label. + * The order of the elements in the returned array reflects the order of input features. + */ + @Experimental + def chiSqTest(data: RDD[LabeledPoint]): Array[ChiSqTestResult] = { + ChiSqTest.chiSquaredFeatures(data) + } } diff --git a/mllib/src/main/scala/org/apache/spark/mllib/stat/test/ChiSqTest.scala b/mllib/src/main/scala/org/apache/spark/mllib/stat/test/ChiSqTest.scala new file mode 100644 index 0000000000..8f67527374 --- /dev/null +++ b/mllib/src/main/scala/org/apache/spark/mllib/stat/test/ChiSqTest.scala @@ -0,0 +1,221 @@ +/* + * 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.spark.mllib.stat.test + +import breeze.linalg.{DenseMatrix => BDM} +import cern.jet.stat.Probability.chiSquareComplemented + +import org.apache.spark.Logging +import org.apache.spark.mllib.linalg.{Matrices, Matrix, Vector, Vectors} +import org.apache.spark.mllib.regression.LabeledPoint +import org.apache.spark.rdd.RDD + +/** + * Conduct the chi-squared test for the input RDDs using the specified method. + * Goodness-of-fit test is conducted on two `Vectors`, whereas test of independence is conducted + * on an input of type `Matrix` in which independence between columns is assessed. + * We also provide a method for computing the chi-squared statistic between each feature and the + * label for an input `RDD[LabeledPoint]`, return an `Array[ChiSquaredTestResult]` of size = + * number of features in the inpuy RDD. + * + * Supported methods for goodness of fit: `pearson` (default) + * Supported methods for independence: `pearson` (default) + * + * More information on Chi-squared test: http://en.wikipedia.org/wiki/Chi-squared_test + */ +private[stat] object ChiSqTest extends Logging { + + /** + * @param name String name for the method. + * @param chiSqFunc Function for computing the statistic given the observed and expected counts. + */ + case class Method(name: String, chiSqFunc: (Double, Double) => Double) + + // Pearson's chi-squared test: http://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test + val PEARSON = new Method("pearson", (observed: Double, expected: Double) => { + val dev = observed - expected + dev * dev / expected + }) + + // Null hypothesis for the two different types of chi-squared tests to be included in the result. + object NullHypothesis extends Enumeration { + type NullHypothesis = Value + val goodnessOfFit = Value("observed follows the same distribution as expected.") + val independence = Value("observations in each column are statistically independent.") + } + + // Method identification based on input methodName string + private def methodFromString(methodName: String): Method = { + methodName match { + case PEARSON.name => PEARSON + case _ => throw new IllegalArgumentException("Unrecognized method for Chi squared test.") + } + } + + /** + * Conduct Pearson's independence test for each feature against the label across the input RDD. + * The contingency table is constructed from the raw (feature, label) pairs and used to conduct + * the independence test. + * Returns an array containing the ChiSquaredTestResult for every feature against the label. + */ + def chiSquaredFeatures(data: RDD[LabeledPoint], + methodName: String = PEARSON.name): Array[ChiSqTestResult] = { + val numCols = data.first().features.size + val results = new Array[ChiSqTestResult](numCols) + var labels: Map[Double, Int] = null + // At most 100 columns at a time + val batchSize = 100 + var batch = 0 + while (batch * batchSize < numCols) { + // The following block of code can be cleaned up and made public as + // chiSquared(data: RDD[(V1, V2)]) + val startCol = batch * batchSize + val endCol = startCol + math.min(batchSize, numCols - startCol) + val pairCounts = data.flatMap { p => + // assume dense vectors + p.features.toArray.slice(startCol, endCol).zipWithIndex.map { case (feature, col) => + (col, feature, p.label) + } + }.countByValue() + + if (labels == null) { + // Do this only once for the first column since labels are invariant across features. + labels = + pairCounts.keys.filter(_._1 == startCol).map(_._3).toArray.distinct.zipWithIndex.toMap + } + val numLabels = labels.size + pairCounts.keys.groupBy(_._1).map { case (col, keys) => + val features = keys.map(_._2).toArray.distinct.zipWithIndex.toMap + val numRows = features.size + val contingency = new BDM(numRows, numLabels, new Array[Double](numRows * numLabels)) + keys.foreach { case (_, feature, label) => + val i = features(feature) + val j = labels(label) + contingency(i, j) += pairCounts((col, feature, label)) + } + results(col) = chiSquaredMatrix(Matrices.fromBreeze(contingency), methodName) + } + batch += 1 + } + results + } + + /* + * Pearon's goodness of fit test on the input observed and expected counts/relative frequencies. + * Uniform distribution is assumed when `expected` is not passed in. + */ + def chiSquared(observed: Vector, + expected: Vector = Vectors.dense(Array[Double]()), + methodName: String = PEARSON.name): ChiSqTestResult = { + + // Validate input arguments + val method = methodFromString(methodName) + if (expected.size != 0 && observed.size != expected.size) { + throw new IllegalArgumentException("observed and expected must be of the same size.") + } + val size = observed.size + if (size > 1000) { + logWarning("Chi-squared approximation may not be accurate due to low expected frequencies " + + s" as a result of a large number of categories: $size.") + } + val obsArr = observed.toArray + val expArr = if (expected.size == 0) Array.tabulate(size)(_ => 1.0 / size) else expected.toArray + if (!obsArr.forall(_ >= 0.0)) { + throw new IllegalArgumentException("Negative entries disallowed in the observed vector.") + } + if (expected.size != 0 && ! expArr.forall(_ >= 0.0)) { + throw new IllegalArgumentException("Negative entries disallowed in the expected vector.") + } + + // Determine the scaling factor for expected + val obsSum = obsArr.sum + val expSum = if (expected.size == 0.0) 1.0 else expArr.sum + val scale = if (math.abs(obsSum - expSum) < 1e-7) 1.0 else obsSum / expSum + + // compute chi-squared statistic + val statistic = obsArr.zip(expArr).foldLeft(0.0) { case (stat, (obs, exp)) => + if (exp == 0.0) { + if (obs == 0.0) { + throw new IllegalArgumentException("Chi-squared statistic undefined for input vectors due" + + " to 0.0 values in both observed and expected.") + } else { + return new ChiSqTestResult(0.0, size - 1, Double.PositiveInfinity, PEARSON.name, + NullHypothesis.goodnessOfFit.toString) + } + } + if (scale == 1.0) { + stat + method.chiSqFunc(obs, exp) + } else { + stat + method.chiSqFunc(obs, exp * scale) + } + } + val df = size - 1 + val pValue = chiSquareComplemented(df, statistic) + new ChiSqTestResult(pValue, df, statistic, PEARSON.name, NullHypothesis.goodnessOfFit.toString) + } + + /* + * Pearon's independence test on the input contingency matrix. + * TODO: optimize for SparseMatrix when it becomes supported. + */ + def chiSquaredMatrix(counts: Matrix, methodName:String = PEARSON.name): ChiSqTestResult = { + val method = methodFromString(methodName) + val numRows = counts.numRows + val numCols = counts.numCols + + // get row and column sums + val colSums = new Array[Double](numCols) + val rowSums = new Array[Double](numRows) + val colMajorArr = counts.toArray + var i = 0 + while (i < colMajorArr.size) { + val elem = colMajorArr(i) + if (elem < 0.0) { + throw new IllegalArgumentException("Contingency table cannot contain negative entries.") + } + colSums(i / numRows) += elem + rowSums(i % numRows) += elem + i += 1 + } + val total = colSums.sum + + // second pass to collect statistic + var statistic = 0.0 + var j = 0 + while (j < colMajorArr.size) { + val col = j / numRows + val colSum = colSums(col) + if (colSum == 0.0) { + throw new IllegalArgumentException("Chi-squared statistic undefined for input matrix due to" + + s"0 sum in column [$col].") + } + val row = j % numRows + val rowSum = rowSums(row) + if (rowSum == 0.0) { + throw new IllegalArgumentException("Chi-squared statistic undefined for input matrix due to" + + s"0 sum in row [$row].") + } + val expected = colSum * rowSum / total + statistic += method.chiSqFunc(colMajorArr(j), expected) + j += 1 + } + val df = (numCols - 1) * (numRows - 1) + val pValue = chiSquareComplemented(df, statistic) + new ChiSqTestResult(pValue, df, statistic, methodName, NullHypothesis.independence.toString) + } +} diff --git a/mllib/src/main/scala/org/apache/spark/mllib/stat/test/TestResult.scala b/mllib/src/main/scala/org/apache/spark/mllib/stat/test/TestResult.scala new file mode 100644 index 0000000000..2f27862133 --- /dev/null +++ b/mllib/src/main/scala/org/apache/spark/mllib/stat/test/TestResult.scala @@ -0,0 +1,88 @@ +/* + * 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.spark.mllib.stat.test + +import org.apache.spark.annotation.Experimental + +/** + * :: Experimental :: + * Trait for hypothesis test results. + * @tparam DF Return type of `degreesOfFreedom`. + */ +@Experimental +trait TestResult[DF] { + + /** + * The probability of obtaining a test statistic result at least as extreme as the one that was + * actually observed, assuming that the null hypothesis is true. + */ + def pValue: Double + + /** + * Returns the degree(s) of freedom of the hypothesis test. + * Return type should be Number(e.g. Int, Double) or tuples of Numbers for toString compatibility. + */ + def degreesOfFreedom: DF + + /** + * Test statistic. + */ + def statistic: Double + + /** + * String explaining the hypothesis test result. + * Specific classes implementing this trait should override this method to output test-specific + * information. + */ + override def toString: String = { + + // String explaining what the p-value indicates. + val pValueExplain = if (pValue <= 0.01) { + "Very strong presumption against null hypothesis." + } else if (0.01 < pValue && pValue <= 0.05) { + "Strong presumption against null hypothesis." + } else if (0.05 < pValue && pValue <= 0.01) { + "Low presumption against null hypothesis." + } else { + "No presumption against null hypothesis." + } + + s"degrees of freedom = ${degreesOfFreedom.toString} \n" + + s"statistic = $statistic \n" + + s"pValue = $pValue \n" + pValueExplain + } +} + +/** + * :: Experimental :: + * Object containing the test results for the chi squared hypothesis test. + */ +@Experimental +class ChiSqTestResult(override val pValue: Double, + override val degreesOfFreedom: Int, + override val statistic: Double, + val method: String, + val nullHypothesis: String) extends TestResult[Int] { + + override def toString: String = { + "Chi squared test summary: \n" + + s"method: $method \n" + + s"null hypothesis: $nullHypothesis \n" + + super.toString + } +} diff --git a/mllib/src/test/scala/org/apache/spark/mllib/stat/HypothesisTestSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/stat/HypothesisTestSuite.scala new file mode 100644 index 0000000000..5bd0521298 --- /dev/null +++ b/mllib/src/test/scala/org/apache/spark/mllib/stat/HypothesisTestSuite.scala @@ -0,0 +1,139 @@ +/* + * 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.spark.mllib.stat + +import org.scalatest.FunSuite + +import org.apache.spark.mllib.linalg.{DenseVector, Matrices, Vectors} +import org.apache.spark.mllib.regression.LabeledPoint +import org.apache.spark.mllib.stat.test.ChiSqTest +import org.apache.spark.mllib.util.LocalSparkContext +import org.apache.spark.mllib.util.TestingUtils._ + +class HypothesisTestSuite extends FunSuite with LocalSparkContext { + + test("chi squared pearson goodness of fit") { + + val observed = new DenseVector(Array[Double](4, 6, 5)) + val pearson = Statistics.chiSqTest(observed) + + // Results validated against the R command `chisq.test(c(4, 6, 5), p=c(1/3, 1/3, 1/3))` + assert(pearson.statistic === 0.4) + assert(pearson.degreesOfFreedom === 2) + assert(pearson.pValue ~== 0.8187 relTol 1e-4) + assert(pearson.method === ChiSqTest.PEARSON.name) + assert(pearson.nullHypothesis === ChiSqTest.NullHypothesis.goodnessOfFit.toString) + + // different expected and observed sum + val observed1 = new DenseVector(Array[Double](21, 38, 43, 80)) + val expected1 = new DenseVector(Array[Double](3, 5, 7, 20)) + val pearson1 = Statistics.chiSqTest(observed1, expected1) + + // Results validated against the R command + // `chisq.test(c(21, 38, 43, 80), p=c(3/35, 1/7, 1/5, 4/7))` + assert(pearson1.statistic ~== 14.1429 relTol 1e-4) + assert(pearson1.degreesOfFreedom === 3) + assert(pearson1.pValue ~== 0.002717 relTol 1e-4) + assert(pearson1.method === ChiSqTest.PEARSON.name) + assert(pearson1.nullHypothesis === ChiSqTest.NullHypothesis.goodnessOfFit.toString) + + // Vectors with different sizes + val observed3 = new DenseVector(Array(1.0, 2.0, 3.0)) + val expected3 = new DenseVector(Array(1.0, 2.0, 3.0, 4.0)) + intercept[IllegalArgumentException](Statistics.chiSqTest(observed3, expected3)) + + // negative counts in observed + val negObs = new DenseVector(Array(1.0, 2.0, 3.0, -4.0)) + intercept[IllegalArgumentException](Statistics.chiSqTest(negObs, expected1)) + + // count = 0.0 in expected but not observed + val zeroExpected = new DenseVector(Array(1.0, 0.0, 3.0)) + val inf = Statistics.chiSqTest(observed, zeroExpected) + assert(inf.statistic === Double.PositiveInfinity) + assert(inf.degreesOfFreedom === 2) + assert(inf.pValue === 0.0) + assert(inf.method === ChiSqTest.PEARSON.name) + assert(inf.nullHypothesis === ChiSqTest.NullHypothesis.goodnessOfFit.toString) + + // 0.0 in expected and observed simultaneously + val zeroObserved = new DenseVector(Array(2.0, 0.0, 1.0)) + intercept[IllegalArgumentException](Statistics.chiSqTest(zeroObserved, zeroExpected)) + } + + test("chi squared pearson matrix independence") { + val data = Array(40.0, 24.0, 29.0, 56.0, 32.0, 42.0, 31.0, 10.0, 0.0, 30.0, 15.0, 12.0) + // [[40.0, 56.0, 31.0, 30.0], + // [24.0, 32.0, 10.0, 15.0], + // [29.0, 42.0, 0.0, 12.0]] + val chi = Statistics.chiSqTest(Matrices.dense(3, 4, data)) + // Results validated against R command + // `chisq.test(rbind(c(40, 56, 31, 30),c(24, 32, 10, 15), c(29, 42, 0, 12)))` + assert(chi.statistic ~== 21.9958 relTol 1e-4) + assert(chi.degreesOfFreedom === 6) + assert(chi.pValue ~== 0.001213 relTol 1e-4) + assert(chi.method === ChiSqTest.PEARSON.name) + assert(chi.nullHypothesis === ChiSqTest.NullHypothesis.independence.toString) + + // Negative counts + val negCounts = Array(4.0, 5.0, 3.0, -3.0) + intercept[IllegalArgumentException](Statistics.chiSqTest(Matrices.dense(2, 2, negCounts))) + + // Row sum = 0.0 + val rowZero = Array(0.0, 1.0, 0.0, 2.0) + intercept[IllegalArgumentException](Statistics.chiSqTest(Matrices.dense(2, 2, rowZero))) + + // Column sum = 0.0 + val colZero = Array(0.0, 0.0, 2.0, 2.0) + // IllegalArgumentException thrown here since it's thrown on driver, not inside a task + intercept[IllegalArgumentException](Statistics.chiSqTest(Matrices.dense(2, 2, colZero))) + } + + test("chi squared pearson RDD[LabeledPoint]") { + // labels: 1.0 (2 / 6), 0.0 (4 / 6) + // feature1: 0.5 (1 / 6), 1.5 (2 / 6), 3.5 (3 / 6) + // feature2: 10.0 (1 / 6), 20.0 (1 / 6), 30.0 (2 / 6), 40.0 (2 / 6) + val data = Array(new LabeledPoint(0.0, Vectors.dense(0.5, 10.0)), + new LabeledPoint(0.0, Vectors.dense(1.5, 20.0)), + new LabeledPoint(1.0, Vectors.dense(1.5, 30.0)), + new LabeledPoint(0.0, Vectors.dense(3.5, 30.0)), + new LabeledPoint(0.0, Vectors.dense(3.5, 40.0)), + new LabeledPoint(1.0, Vectors.dense(3.5, 40.0))) + for (numParts <- List(2, 4, 6, 8)) { + val chi = Statistics.chiSqTest(sc.parallelize(data, numParts)) + val feature1 = chi(0) + assert(feature1.statistic === 0.75) + assert(feature1.degreesOfFreedom === 2) + assert(feature1.pValue ~== 0.6873 relTol 1e-4) + assert(feature1.method === ChiSqTest.PEARSON.name) + assert(feature1.nullHypothesis === ChiSqTest.NullHypothesis.independence.toString) + val feature2 = chi(1) + assert(feature2.statistic === 1.5) + assert(feature2.degreesOfFreedom === 3) + assert(feature2.pValue ~== 0.6823 relTol 1e-4) + assert(feature2.method === ChiSqTest.PEARSON.name) + assert(feature2.nullHypothesis === ChiSqTest.NullHypothesis.independence.toString) + } + + // Test that the right number of results is returned + val numCols = 321 + val sparseData = Array(new LabeledPoint(0.0, Vectors.sparse(numCols, Seq((100, 2.0)))), + new LabeledPoint(0.0, Vectors.sparse(numCols, Seq((200, 1.0))))) + val chi = Statistics.chiSqTest(sc.parallelize(sparseData)) + assert(chi.size === numCols) + } +} |