Project: Apache Spark (App Definition and Development / Streaming & Messaging)
File: mllib-statistics.md

layout: global title: Basic Statistics - RDD-based API displayTitle: Basic Statistics - RDD-based API license: | 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. Table of contents {:toc} `\[ \newcommand{\R}{\mathbb{R}} \newcommand{\E}{\mathbb{E}} \newcommand{\x}{\mathbf{x}} \newcommand{\y}{\mathbf{y}} \newcommand{\wv}{\mathbf{w}} \newcommand{\av}{\mathbf{\alpha}} \newcommand{\bv}{\mathbf{b}} \newcommand{\N}{\mathbb{N}} \newcommand{\id}{\mathbf{I}} \newcommand{\ind}{\mathbf{1}} \newcommand{\0}{\mathbf{0}} \newcommand{\unit}{\mathbf{e}} \newcommand{\one}{\mathbf{1}} \newcommand{\zero}{\mathbf{0}} \]` We provide column summary statistics for `RDD[Vector]` through the function `colStats` available in `Statistics`. <div class="codetabs"> <div data-lang="python" markdown="1"> returns an instance of , which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the total count. Refer to the for more details on the API. {% includeexample python/mllib/summarystatistics_example.py %} </div> <div data-lang="scala" markdown="1"> returns an instance of , which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the total count. Refer to the for details on the API. {% include_example scala/org/apache/spark/examples/mllib/SummaryStatisticsExample.scala %} </div> <div data-lang="java" markdown="1"> returns an instance of , which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the total count. Refer to the for details on the API. {% include_example java/org/apache/spark/examples/mllib/JavaSummaryStatisticsExample.java %} </div> </div> 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. <div class="codetabs"> <div data-lang="python" markdown="1"> 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 for more details on the API. {% includeexample python/mllib/correlationsexample.py %} </div> <div data-lang="scala" markdown="1"> 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 for details on the API. {% include_example scala/org/apache/spark/examples/mllib/CorrelationsExample.scala %} </div> <div data-lang="java" markdown="1"> provides methods to calculate correlations between series. Depending on the type of input, two `JavaDoubleRDD`s or a `JavaRDD<Vector>`, the output will be a `Double` or the correlation `Matrix` respectively. Refer to the for details on the API. {% include_example

%} </div> </div> 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. <div class="codetabs"> <div data-lang="python" markdown="1"> allows users to sample approximately $\lceil fk \cdot nk \rceil \, \forall k \in K$ 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. {% includeexample python/mllib/stratifiedsampling_example.py %} </div> <div data-lang="scala" markdown="1"> allows users to sample exactly $\lceil fk \cdot nk \rceil \, \forall k \in K$ 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 %} </div> <div data-lang="java" markdown="1"> allows users to sample exactly $\lceil fk \cdot nk \rceil \, \forall k \in K$ 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 %} </div> </div> 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. <div class="codetabs"> <div data-lang="python" markdown="1"> provides methods to run Pearson's chi-squared tests. The following example demonstrates how to run and interpret hypothesis tests. Refer to the for more details on the API. {% includeexample

%} </div> <div data-lang="scala" markdown="1"> 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 %} </div> <div data-lang="java" markdown="1"> provides methods to run Pearson's chi-squared tests. The following example demonstrates how to run and interpret hypothesis tests. Refer to the for details on the API. {% include_example java/org/apache/spark/examples/mllib/JavaHypothesisTestingExample.java %} </div> </div> 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. <div class="codetabs"> <div data-lang="python" markdown="1"> 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 for more details on the API. {% includeexample python/mllib/hypothesistestingkolmogorovsmirnovtestexample.py %} </div> <div data-lang="scala" markdown="1"> 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 for details on the API. {% include_example scala/org/apache/spark/examples/mllib/HypothesisTestingKolmogorovSmirnovTestExample.scala %} </div> <div data-lang="java" markdown="1"> 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 for details on the API. {% include_example java/org/apache/spark/examples/mllib/JavaHypothesisTestingKolmogorovSmirnovTestExample.java %} </div> </div> `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. <div class="codetabs"> <div data-lang="scala" markdown="1"> provides streaming hypothesis testing. {% include_example scala/org/apache/spark/examples/mllib/StreamingTestExample.scala %} </div> <div data-lang="java" markdown="1"> provides streaming hypothesis testing. {% include_example java/org/apache/spark/examples/mllib/JavaStreamingTestExample.java %} </div> </div> 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. <div class="codetabs"> <div data-lang="python" markdown="1"> provides factory methods to generate random double RDDs or vector

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 for more details on the API. {% highlight python %} from pyspark.mllib.random import RandomRDDs sc = ... # SparkContext u = RandomRDDs.normalRDD(sc, 1000000L, 10) v = u.map(lambda x: 1.0 + 2.0 * x) {% endhighlight %} </div> <div data-lang="scala" markdown="1"> 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 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 %} </div> <div data-lang="java" markdown="1"> 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 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 %} </div> </div> 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. <div class="codetabs"> <div data-lang="python" markdown="1"> provides methods to compute kernel density estimates from an RDD of samples. The following example demonstrates how to do so. Refer to the for more details on the API. {% includeexample python/mllib/kerneldensityestimationexample.py %} </div> <div data-lang="scala" markdown="1"> provides methods to compute kernel density estimates from an RDD of samples. The following example demonstrates how to do so. Refer to the for details on the API. {% include_example scala/org/apache/spark/examples/mllib/KernelDensityEstimationExample.scala %} </div> <div data-lang="java" markdown="1"> provides methods to compute kernel density estimates from an RDD of samples. The following example demonstrates how to do so. Refer to the for details on the API. {% include_example java/org/apache/spark/examples/mllib/JavaKernelDensityEstimationExample.java %} </div> </div>