Basic Statistics

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Table of Contents

Correlation
Hypothesis testing
Summarizer

Correlation

Calculating the correlation between two series of data is a common operation in Statistics. In spark.ml we provide the flexibility to calculate pairwise correlations among many series. The supported correlation methods are currently Pearson’s and Spearman’s correlation.

Correlation computes the correlation matrix for the input Dataset of Vectors using the specified method. The output will be a DataFrame that contains the correlation matrix of the column of vectors.

import org.apache.spark.ml.linalg.{Matrix, Vectors}
import org.apache.spark.ml.stat.Correlation
import org.apache.spark.sql.Row

val data = Seq(
  Vectors.sparse(4, Seq((0, 1.0), (3, -2.0))),
  Vectors.dense(4.0, 5.0, 0.0, 3.0),
  Vectors.dense(6.0, 7.0, 0.0, 8.0),
  Vectors.sparse(4, Seq((0, 9.0), (3, 1.0)))
)

val df = data.map(Tuple1.apply).toDF("features")
val Row(coeff1: Matrix) = Correlation.corr(df, "features").head
println(s"Pearson correlation matrix:\n $coeff1")

val Row(coeff2: Matrix) = Correlation.corr(df, "features", "spearman").head
println(s"Spearman correlation matrix:\n $coeff2")

Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/CorrelationExample.scala" in the Spark repo.

import java.util.Arrays;
import java.util.List;

import org.apache.spark.ml.linalg.Vectors;
import org.apache.spark.ml.linalg.VectorUDT;
import org.apache.spark.ml.stat.Correlation;
import org.apache.spark.sql.Dataset;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.*;

List<Row> data = Arrays.asList(
  RowFactory.create(Vectors.sparse(4, new int[]{0, 3}, new double[]{1.0, -2.0})),
  RowFactory.create(Vectors.dense(4.0, 5.0, 0.0, 3.0)),
  RowFactory.create(Vectors.dense(6.0, 7.0, 0.0, 8.0)),
  RowFactory.create(Vectors.sparse(4, new int[]{0, 3}, new double[]{9.0, 1.0}))
);

StructType schema = new StructType(new StructField[]{
  new StructField("features", new VectorUDT(), false, Metadata.empty()),
});

Dataset<Row> df = spark.createDataFrame(data, schema);
Row r1 = Correlation.corr(df, "features").head();
System.out.println("Pearson correlation matrix:\n" + r1.get(0).toString());

Row r2 = Correlation.corr(df, "features", "spearman").head();
System.out.println("Spearman correlation matrix:\n" + r2.get(0).toString());

Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaCorrelationExample.java" in the Spark repo.

from pyspark.ml.linalg import Vectors
from pyspark.ml.stat import Correlation

data = [(Vectors.sparse(4, [(0, 1.0), (3, -2.0)]),),
        (Vectors.dense([4.0, 5.0, 0.0, 3.0]),),
        (Vectors.dense([6.0, 7.0, 0.0, 8.0]),),
        (Vectors.sparse(4, [(0, 9.0), (3, 1.0)]),)]
df = spark.createDataFrame(data, ["features"])

r1 = Correlation.corr(df, "features").head()
print("Pearson correlation matrix:\n" + str(r1[0]))

r2 = Correlation.corr(df, "features", "spearman").head()
print("Spearman correlation matrix:\n" + str(r2[0]))

Find full example code at "examples/src/main/python/ml/correlation_example.py" in the Spark repo.

Hypothesis testing

Hypothesis testing is a powerful tool in statistics to determine whether a result is statistically significant, whether this result occurred by chance or not. spark.ml currently supports Pearson’s Chi-squared ( $\chi^2$) tests for independence.

ChiSquareTest conducts Pearson’s independence test for every feature against the label. For each feature, the (feature, label) pairs are converted into a contingency matrix for which the Chi-squared statistic is computed. All label and feature values must be categorical.

Refer to the ChiSquareTest Scala docs for details on the API.

import org.apache.spark.ml.linalg.{Vector, Vectors}
import org.apache.spark.ml.stat.ChiSquareTest

val data = Seq(
  (0.0, Vectors.dense(0.5, 10.0)),
  (0.0, Vectors.dense(1.5, 20.0)),
  (1.0, Vectors.dense(1.5, 30.0)),
  (0.0, Vectors.dense(3.5, 30.0)),
  (0.0, Vectors.dense(3.5, 40.0)),
  (1.0, Vectors.dense(3.5, 40.0))
)

val df = data.toDF("label", "features")
val chi = ChiSquareTest.test(df, "features", "label").head
println(s"pValues = ${chi.getAs[Vector](0)}")
println(s"degreesOfFreedom ${chi.getSeq[Int](1).mkString("[", ",", "]")}")
println(s"statistics ${chi.getAs[Vector](2)}")

Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/ChiSquareTestExample.scala" in the Spark repo.

Refer to the ChiSquareTest Java docs for details on the API.

import java.util.Arrays;
import java.util.List;

import org.apache.spark.ml.linalg.Vectors;
import org.apache.spark.ml.linalg.VectorUDT;
import org.apache.spark.ml.stat.ChiSquareTest;
import org.apache.spark.sql.Dataset;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.*;

List<Row> data = Arrays.asList(
  RowFactory.create(0.0, Vectors.dense(0.5, 10.0)),
  RowFactory.create(0.0, Vectors.dense(1.5, 20.0)),
  RowFactory.create(1.0, Vectors.dense(1.5, 30.0)),
  RowFactory.create(0.0, Vectors.dense(3.5, 30.0)),
  RowFactory.create(0.0, Vectors.dense(3.5, 40.0)),
  RowFactory.create(1.0, Vectors.dense(3.5, 40.0))
);

StructType schema = new StructType(new StructField[]{
  new StructField("label", DataTypes.DoubleType, false, Metadata.empty()),
  new StructField("features", new VectorUDT(), false, Metadata.empty()),
});

Dataset<Row> df = spark.createDataFrame(data, schema);
Row r = ChiSquareTest.test(df, "features", "label").head();
System.out.println("pValues: " + r.get(0).toString());
System.out.println("degreesOfFreedom: " + r.getList(1).toString());
System.out.println("statistics: " + r.get(2).toString());

Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaChiSquareTestExample.java" in the Spark repo.

Refer to the ChiSquareTest Python docs for details on the API.

from pyspark.ml.linalg import Vectors
from pyspark.ml.stat import ChiSquareTest

data = [(0.0, Vectors.dense(0.5, 10.0)),
        (0.0, Vectors.dense(1.5, 20.0)),
        (1.0, Vectors.dense(1.5, 30.0)),
        (0.0, Vectors.dense(3.5, 30.0)),
        (0.0, Vectors.dense(3.5, 40.0)),
        (1.0, Vectors.dense(3.5, 40.0))]
df = spark.createDataFrame(data, ["label", "features"])

r = ChiSquareTest.test(df, "features", "label").head()
print("pValues: " + str(r.pValues))
print("degreesOfFreedom: " + str(r.degreesOfFreedom))
print("statistics: " + str(r.statistics))

Find full example code at "examples/src/main/python/ml/chi_square_test_example.py" in the Spark repo.

Summarizer

We provide vector column summary statistics for Dataframe through Summarizer. Available metrics are the column-wise max, min, mean, sum, variance, std, and number of nonzeros, as well as the total count.

The following example demonstrates using Summarizer to compute the mean and variance for a vector column of the input dataframe, with and without a weight column.

import org.apache.spark.ml.linalg.{Vector, Vectors}
import org.apache.spark.ml.stat.Summarizer

val data = Seq(
  (Vectors.dense(2.0, 3.0, 5.0), 1.0),
  (Vectors.dense(4.0, 6.0, 7.0), 2.0)
)

val df = data.toDF("features", "weight")

val (meanVal, varianceVal) = df.select(metrics("mean", "variance")
  .summary($"features", $"weight").as("summary"))
  .select("summary.mean", "summary.variance")
  .as[(Vector, Vector)].first()

println(s"with weight: mean = ${meanVal}, variance = ${varianceVal}")

val (meanVal2, varianceVal2) = df.select(mean($"features"), variance($"features"))
  .as[(Vector, Vector)].first()

println(s"without weight: mean = ${meanVal2}, sum = ${varianceVal2}")

Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/SummarizerExample.scala" in the Spark repo.

The following example demonstrates using Summarizer to compute the mean and variance for a vector column of the input dataframe, with and without a weight column.

import java.util.Arrays;
import java.util.List;

import org.apache.spark.ml.linalg.Vector;
import org.apache.spark.ml.linalg.Vectors;
import org.apache.spark.ml.linalg.VectorUDT;
import org.apache.spark.ml.stat.Summarizer;
import org.apache.spark.sql.types.DataTypes;
import org.apache.spark.sql.types.Metadata;
import org.apache.spark.sql.types.StructField;
import org.apache.spark.sql.types.StructType;

List<Row> data = Arrays.asList(
  RowFactory.create(Vectors.dense(2.0, 3.0, 5.0), 1.0),
  RowFactory.create(Vectors.dense(4.0, 6.0, 7.0), 2.0)
);

StructType schema = new StructType(new StructField[]{
  new StructField("features", new VectorUDT(), false, Metadata.empty()),
  new StructField("weight", DataTypes.DoubleType, false, Metadata.empty())
});

Dataset<Row> df = spark.createDataFrame(data, schema);

Row result1 = df.select(Summarizer.metrics("mean", "variance")
  .summary(new Column("features"), new Column("weight")).as("summary"))
  .select("summary.mean", "summary.variance").first();
System.out.println("with weight: mean = " + result1.<Vector>getAs(0).toString() +
  ", variance = " + result1.<Vector>getAs(1).toString());

Row result2 = df.select(
  Summarizer.mean(new Column("features")),
  Summarizer.variance(new Column("features"))
).first();
System.out.println("without weight: mean = " + result2.<Vector>getAs(0).toString() +
  ", variance = " + result2.<Vector>getAs(1).toString());

Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaSummarizerExample.java" in the Spark repo.

Refer to the Summarizer Python docs for details on the API.

from pyspark.ml.stat import Summarizer
from pyspark.sql import Row
from pyspark.ml.linalg import Vectors

df = sc.parallelize([Row(weight=1.0, features=Vectors.dense(1.0, 1.0, 1.0)),
                     Row(weight=0.0, features=Vectors.dense(1.0, 2.0, 3.0))]).toDF()

# create summarizer for multiple metrics "mean" and "count"
summarizer = Summarizer.metrics("mean", "count")

# compute statistics for multiple metrics with weight
df.select(summarizer.summary(df.features, df.weight)).show(truncate=False)

# compute statistics for multiple metrics without weight
df.select(summarizer.summary(df.features)).show(truncate=False)

# compute statistics for single metric "mean" with weight
df.select(Summarizer.mean(df.features, df.weight)).show(truncate=False)

# compute statistics for single metric "mean" without weight
df.select(Summarizer.mean(df.features)).show(truncate=False)

Find full example code at "examples/src/main/python/ml/summarizer_example.py" in the Spark repo.

MLlib: Main Guide

MLlib: RDD-based API Guide

Basic Statistics

Correlation

Hypothesis testing

Summarizer