spark-instrumented-optimizer/docs/mllib-statistics.md

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global	Basic Statistics - RDD-based API	Basic Statistics - RDD-based API

• Table of contents {:toc}

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Summary statistics

We provide column summary statistics for RDD[Vector] through the function colStats available in Statistics.

colStats() returns an instance of MultivariateStatisticalSummary, which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the total count.

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

{% include_example scala/org/apache/spark/examples/mllib/SummaryStatisticsExample.scala %}

colStats() returns an instance of MultivariateStatisticalSummary, which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the total count.

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

{% include_example java/org/apache/spark/examples/mllib/JavaSummaryStatisticsExample.java %}

[`colStats()`](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics.colStats) returns an instance of [`MultivariateStatisticalSummary`](api/python/pyspark.mllib.html#pyspark.mllib.stat.MultivariateStatisticalSummary), which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the total count.

Refer to the MultivariateStatisticalSummary Python docs for more details on the API.

{% include_example python/mllib/summary_statistics_example.py %}

Correlations

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

[`Statistics`](api/scala/index.html#org.apache.spark.mllib.stat.Statistics$) provides methods to calculate correlations between series. Depending on the type of input, two `RDD[Double]`s or an `RDD[Vector]`, the output will be a `Double` or the correlation `Matrix` respectively.

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

{% include_example scala/org/apache/spark/examples/mllib/CorrelationsExample.scala %}

[`Statistics`](api/java/org/apache/spark/mllib/stat/Statistics.html) provides methods to calculate correlations between series. Depending on the type of input, two `JavaDoubleRDD`s or a `JavaRDD`, the output will be a `Double` or the correlation `Matrix` respectively.

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

{% include_example java/org/apache/spark/examples/mllib/JavaCorrelationsExample.java %}

[`Statistics`](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) provides methods to calculate correlations between series. Depending on the type of input, two `RDD[Double]`s or an `RDD[Vector]`, the output will be a `Double` or the correlation `Matrix` respectively.

Refer to the Statistics Python docs for more details on the API.

{% include_example python/mllib/correlations_example.py %}

Stratified sampling

Unlike the other statistics functions, which reside in spark.mllib, stratified sampling methods, sampleByKey and sampleByKeyExact, can be performed on RDD's of key-value pairs. For stratified sampling, the keys can be thought of as a label and the value as a specific attribute. For example the key can be man or woman, or document ids, and the respective values can be the list of ages of the people in the population or the list of words in the documents. The sampleByKey method will flip a coin to decide whether an observation will be sampled or not, therefore requires one pass over the data, and provides an expected sample size. sampleByKeyExact requires significant more resources than the per-stratum simple random sampling used in sampleByKey, but will provide the exact sampling size with 99.99% confidence. sampleByKeyExact is currently not supported in python.

[`sampleByKeyExact()`](api/scala/index.html#org.apache.spark.rdd.PairRDDFunctions) allows users to sample exactly $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the desired fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the set of keys. Sampling without replacement requires one additional pass over the RDD to guarantee sample size, whereas sampling with replacement requires two additional passes.

{% include_example scala/org/apache/spark/examples/mllib/StratifiedSamplingExample.scala %}

[`sampleByKeyExact()`](api/java/org/apache/spark/api/java/JavaPairRDD.html) allows users to sample exactly $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the desired fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the set of keys. Sampling without replacement requires one additional pass over the RDD to guarantee sample size, whereas sampling with replacement requires two additional passes.

{% include_example java/org/apache/spark/examples/mllib/JavaStratifiedSamplingExample.java %}

[`sampleByKey()`](api/python/pyspark.html#pyspark.RDD.sampleByKey) allows users to sample approximately $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the desired fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the set of keys.

Note: sampleByKeyExact() is currently not supported in Python.

{% include_example python/mllib/stratified_sampling_example.py %}

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.mllib currently supports Pearson's chi-squared ( $\chi^2$) tests for goodness of fit and independence. The input data types determine whether the goodness of fit or the independence test is conducted. The goodness of fit test requires an input type of Vector, whereas the independence test requires a Matrix as input.

spark.mllib also supports the input type RDD[LabeledPoint] to enable feature selection via chi-squared independence tests.

[`Statistics`](api/scala/index.html#org.apache.spark.mllib.stat.Statistics$) provides methods to run Pearson's chi-squared tests. The following example demonstrates how to run and interpret hypothesis tests.

{% include_example scala/org/apache/spark/examples/mllib/HypothesisTestingExample.scala %}

[`Statistics`](api/java/org/apache/spark/mllib/stat/Statistics.html) provides methods to run Pearson's chi-squared tests. The following example demonstrates how to run and interpret hypothesis tests.

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

{% include_example java/org/apache/spark/examples/mllib/JavaHypothesisTestingExample.java %}

[`Statistics`](api/python/index.html#pyspark.mllib.stat.Statistics$) provides methods to run Pearson's chi-squared tests. The following example demonstrates how to run and interpret hypothesis tests.

Refer to the Statistics Python docs for more details on the API.

{% include_example python/mllib/hypothesis_testing_example.py %}

Additionally, spark.mllib provides a 1-sample, 2-sided implementation of the Kolmogorov-Smirnov (KS) test for equality of probability distributions. By providing the name of a theoretical distribution (currently solely supported for the normal distribution) and its parameters, or a function to calculate the cumulative distribution according to a given theoretical distribution, the user can test the null hypothesis that their sample is drawn from that distribution. In the case that the user tests against the normal distribution (distName="norm"), but does not provide distribution parameters, the test initializes to the standard normal distribution and logs an appropriate message.

[`Statistics`](api/scala/index.html#org.apache.spark.mllib.stat.Statistics$) provides methods to run a 1-sample, 2-sided Kolmogorov-Smirnov test. The following example demonstrates how to run and interpret the hypothesis tests.

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

{% include_example scala/org/apache/spark/examples/mllib/HypothesisTestingKolmogorovSmirnovTestExample.scala %}

[`Statistics`](api/java/org/apache/spark/mllib/stat/Statistics.html) provides methods to run a 1-sample, 2-sided Kolmogorov-Smirnov test. The following example demonstrates how to run and interpret the hypothesis tests.

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

{% include_example java/org/apache/spark/examples/mllib/JavaHypothesisTestingKolmogorovSmirnovTestExample.java %}

[`Statistics`](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) provides methods to run a 1-sample, 2-sided Kolmogorov-Smirnov test. The following example demonstrates how to run and interpret the hypothesis tests.

Refer to the Statistics Python docs for more details on the API.

{% include_example python/mllib/hypothesis_testing_kolmogorov_smirnov_test_example.py %}

Streaming Significance Testing

spark.mllib provides online implementations of some tests to support use cases like A/B testing. These tests may be performed on a Spark Streaming DStream[(Boolean,Double)] where the first element of each tuple indicates control group (false) or treatment group (true) and the second element is the value of an observation.

Streaming significance testing supports the following parameters:

• peacePeriod - The number of initial data points from the stream to ignore, used to mitigate novelty effects.
• windowSize - The number of past batches to perform hypothesis testing over. Setting to 0 will perform cumulative processing using all prior batches.

[`StreamingTest`](api/scala/index.html#org.apache.spark.mllib.stat.test.StreamingTest) provides streaming hypothesis testing.

{% include_example scala/org/apache/spark/examples/mllib/StreamingTestExample.scala %}

[`StreamingTest`](api/java/index.html#org.apache.spark.mllib.stat.test.StreamingTest) provides streaming hypothesis testing.

{% include_example java/org/apache/spark/examples/mllib/JavaStreamingTestExample.java %}

Random data generation

Random data generation is useful for randomized algorithms, prototyping, and performance testing. spark.mllib supports generating random RDDs with i.i.d. values drawn from a given distribution: uniform, standard normal, or Poisson.

[`RandomRDDs`](api/scala/index.html#org.apache.spark.mllib.random.RandomRDDs$) provides factory methods to generate random double RDDs or vector RDDs. The following example generates a random double RDD, whose values follows the standard normal distribution `N(0, 1)`, and then map it to `N(1, 4)`.

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

{% highlight scala %} import org.apache.spark.SparkContext import org.apache.spark.mllib.random.RandomRDDs._

val sc: SparkContext = ...

// Generate a random double RDD that contains 1 million i.i.d. values drawn from the // standard normal distribution N(0, 1), evenly distributed in 10 partitions. val u = normalRDD(sc, 1000000L, 10) // Apply a transform to get a random double RDD following N(1, 4). val v = u.map(x => 1.0 + 2.0 * x) {% endhighlight %}

[`RandomRDDs`](api/java/index.html#org.apache.spark.mllib.random.RandomRDDs) provides factory methods to generate random double RDDs or vector RDDs. The following example generates a random double RDD, whose values follows the standard normal distribution `N(0, 1)`, and then map it to `N(1, 4)`.

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

{% highlight java %} import org.apache.spark.SparkContext; import org.apache.spark.api.JavaDoubleRDD; import static org.apache.spark.mllib.random.RandomRDDs.*;

JavaSparkContext jsc = ...

// Generate a random double RDD that contains 1 million i.i.d. values drawn from the // standard normal distribution N(0, 1), evenly distributed in 10 partitions. JavaDoubleRDD u = normalJavaRDD(jsc, 1000000L, 10); // Apply a transform to get a random double RDD following N(1, 4). JavaDoubleRDD v = u.mapToDouble(x -> 1.0 + 2.0 * x); {% endhighlight %}

[`RandomRDDs`](api/python/pyspark.mllib.html#pyspark.mllib.random.RandomRDDs) provides factory methods to generate random double RDDs or vector RDDs. The following example generates a random double RDD, whose values follows the standard normal distribution `N(0, 1)`, and then map it to `N(1, 4)`.

Refer to the RandomRDDs Python docs for more details on the API.

{% highlight python %} from pyspark.mllib.random import RandomRDDs

sc = ... # SparkContext

Generate a random double RDD that contains 1 million i.i.d. values drawn from the

standard normal distribution N(0, 1), evenly distributed in 10 partitions.

u = RandomRDDs.normalRDD(sc, 1000000L, 10)

Apply a transform to get a random double RDD following N(1, 4).

v = u.map(lambda x: 1.0 + 2.0 * x) {% endhighlight %}

Kernel density estimation

Kernel density estimation is a technique useful for visualizing empirical probability distributions without requiring assumptions about the particular distribution that the observed samples are drawn from. It computes an estimate of the probability density function of a random variables, evaluated at a given set of points. It achieves this estimate by expressing the PDF of the empirical distribution at a particular point as the mean of PDFs of normal distributions centered around each of the samples.

[`KernelDensity`](api/scala/index.html#org.apache.spark.mllib.stat.KernelDensity) provides methods to compute kernel density estimates from an RDD of samples. The following example demonstrates how to do so.

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

{% include_example scala/org/apache/spark/examples/mllib/KernelDensityEstimationExample.scala %}

[`KernelDensity`](api/java/index.html#org.apache.spark.mllib.stat.KernelDensity) provides methods to compute kernel density estimates from an RDD of samples. The following example demonstrates how to do so.

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

{% include_example java/org/apache/spark/examples/mllib/JavaKernelDensityEstimationExample.java %}

[`KernelDensity`](api/python/pyspark.mllib.html#pyspark.mllib.stat.KernelDensity) provides methods to compute kernel density estimates from an RDD of samples. The following example demonstrates how to do so.

Refer to the KernelDensity Python docs for more details on the API.

{% include_example python/mllib/kernel_density_estimation_example.py %}