754f820035
## What changes were proposed in this pull request? Add AL2 license to metadata of all .md files. This seemed to be the tidiest way as it will get ignored by .md renderers and other tools. Attempts to write them as markdown comments revealed that there is no such standard thing. ## How was this patch tested? Doc build Closes #24243 from srowen/SPARK-26918. Authored-by: Sean Owen <sean.owen@databricks.com> Signed-off-by: Sean Owen <sean.owen@databricks.com>
403 lines
18 KiB
Markdown
403 lines
18 KiB
Markdown
---
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layout: global
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title: Basic Statistics - RDD-based API
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displayTitle: Basic Statistics - RDD-based API
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license: |
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Licensed to the Apache Software Foundation (ASF) under one or more
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contributor license agreements. See the NOTICE file distributed with
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this work for additional information regarding copyright ownership.
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The ASF licenses this file to You under the Apache License, Version 2.0
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(the "License"); you may not use this file except in compliance with
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the License. You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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---
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* Table of contents
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{:toc}
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`\[
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\newcommand{\R}{\mathbb{R}}
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\newcommand{\E}{\mathbb{E}}
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\newcommand{\x}{\mathbf{x}}
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\newcommand{\y}{\mathbf{y}}
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\newcommand{\wv}{\mathbf{w}}
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\newcommand{\av}{\mathbf{\alpha}}
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\newcommand{\bv}{\mathbf{b}}
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\newcommand{\N}{\mathbb{N}}
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\newcommand{\id}{\mathbf{I}}
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\newcommand{\ind}{\mathbf{1}}
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\newcommand{\0}{\mathbf{0}}
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\newcommand{\unit}{\mathbf{e}}
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\newcommand{\one}{\mathbf{1}}
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\newcommand{\zero}{\mathbf{0}}
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\]`
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## Summary statistics
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We provide column summary statistics for `RDD[Vector]` through the function `colStats`
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available in `Statistics`.
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<div class="codetabs">
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<div data-lang="scala" markdown="1">
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[`colStats()`](api/scala/index.html#org.apache.spark.mllib.stat.Statistics$) returns an instance of
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[`MultivariateStatisticalSummary`](api/scala/index.html#org.apache.spark.mllib.stat.MultivariateStatisticalSummary),
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which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the
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total count.
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Refer to the [`MultivariateStatisticalSummary` Scala docs](api/scala/index.html#org.apache.spark.mllib.stat.MultivariateStatisticalSummary) for details on the API.
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{% include_example scala/org/apache/spark/examples/mllib/SummaryStatisticsExample.scala %}
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</div>
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<div data-lang="java" markdown="1">
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[`colStats()`](api/java/org/apache/spark/mllib/stat/Statistics.html) returns an instance of
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[`MultivariateStatisticalSummary`](api/java/org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html),
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which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the
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total count.
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Refer to the [`MultivariateStatisticalSummary` Java docs](api/java/org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html) for details on the API.
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{% include_example java/org/apache/spark/examples/mllib/JavaSummaryStatisticsExample.java %}
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</div>
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<div data-lang="python" markdown="1">
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[`colStats()`](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics.colStats) returns an instance of
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[`MultivariateStatisticalSummary`](api/python/pyspark.mllib.html#pyspark.mllib.stat.MultivariateStatisticalSummary),
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which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the
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total count.
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Refer to the [`MultivariateStatisticalSummary` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.MultivariateStatisticalSummary) for more details on the API.
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{% include_example python/mllib/summary_statistics_example.py %}
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</div>
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</div>
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## Correlations
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Calculating the correlation between two series of data is a common operation in Statistics. In `spark.mllib`
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we provide the flexibility to calculate pairwise correlations among many series. The supported
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correlation methods are currently Pearson's and Spearman's correlation.
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<div class="codetabs">
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<div data-lang="scala" markdown="1">
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[`Statistics`](api/scala/index.html#org.apache.spark.mllib.stat.Statistics$) provides methods to
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calculate correlations between series. Depending on the type of input, two `RDD[Double]`s or
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an `RDD[Vector]`, the output will be a `Double` or the correlation `Matrix` respectively.
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Refer to the [`Statistics` Scala docs](api/scala/index.html#org.apache.spark.mllib.stat.Statistics$) for details on the API.
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{% include_example scala/org/apache/spark/examples/mllib/CorrelationsExample.scala %}
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</div>
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<div data-lang="java" markdown="1">
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[`Statistics`](api/java/org/apache/spark/mllib/stat/Statistics.html) provides methods to
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calculate correlations between series. Depending on the type of input, two `JavaDoubleRDD`s or
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a `JavaRDD<Vector>`, the output will be a `Double` or the correlation `Matrix` respectively.
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Refer to the [`Statistics` Java docs](api/java/org/apache/spark/mllib/stat/Statistics.html) for details on the API.
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{% include_example java/org/apache/spark/examples/mllib/JavaCorrelationsExample.java %}
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</div>
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<div data-lang="python" markdown="1">
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[`Statistics`](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) provides methods to
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calculate correlations between series. Depending on the type of input, two `RDD[Double]`s or
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an `RDD[Vector]`, the output will be a `Double` or the correlation `Matrix` respectively.
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Refer to the [`Statistics` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) for more details on the API.
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{% include_example python/mllib/correlations_example.py %}
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</div>
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</div>
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## Stratified sampling
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Unlike the other statistics functions, which reside in `spark.mllib`, stratified sampling methods,
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`sampleByKey` and `sampleByKeyExact`, can be performed on RDD's of key-value pairs. For stratified
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sampling, the keys can be thought of as a label and the value as a specific attribute. For example
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the key can be man or woman, or document ids, and the respective values can be the list of ages
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of the people in the population or the list of words in the documents. The `sampleByKey` method
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will flip a coin to decide whether an observation will be sampled or not, therefore requires one
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pass over the data, and provides an *expected* sample size. `sampleByKeyExact` requires significant
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more resources than the per-stratum simple random sampling used in `sampleByKey`, but will provide
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the exact sampling size with 99.99% confidence. `sampleByKeyExact` is currently not supported in
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python.
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<div class="codetabs">
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<div data-lang="scala" markdown="1">
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[`sampleByKeyExact()`](api/scala/index.html#org.apache.spark.rdd.PairRDDFunctions) allows users to
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sample exactly $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the desired
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fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the set of
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keys. Sampling without replacement requires one additional pass over the RDD to guarantee sample
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size, whereas sampling with replacement requires two additional passes.
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{% include_example scala/org/apache/spark/examples/mllib/StratifiedSamplingExample.scala %}
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</div>
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<div data-lang="java" markdown="1">
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[`sampleByKeyExact()`](api/java/org/apache/spark/api/java/JavaPairRDD.html) allows users to
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sample exactly $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the desired
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fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the set of
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keys. Sampling without replacement requires one additional pass over the RDD to guarantee sample
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size, whereas sampling with replacement requires two additional passes.
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{% include_example java/org/apache/spark/examples/mllib/JavaStratifiedSamplingExample.java %}
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</div>
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<div data-lang="python" markdown="1">
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[`sampleByKey()`](api/python/pyspark.html#pyspark.RDD.sampleByKey) allows users to
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sample approximately $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the
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desired fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the
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set of keys.
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*Note:* `sampleByKeyExact()` is currently not supported in Python.
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{% include_example python/mllib/stratified_sampling_example.py %}
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</div>
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</div>
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## Hypothesis testing
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Hypothesis testing is a powerful tool in statistics to determine whether a result is statistically
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significant, whether this result occurred by chance or not. `spark.mllib` currently supports Pearson's
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chi-squared ( $\chi^2$) tests for goodness of fit and independence. The input data types determine
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whether the goodness of fit or the independence test is conducted. The goodness of fit test requires
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an input type of `Vector`, whereas the independence test requires a `Matrix` as input.
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`spark.mllib` also supports the input type `RDD[LabeledPoint]` to enable feature selection via chi-squared
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independence tests.
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<div class="codetabs">
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<div data-lang="scala" markdown="1">
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[`Statistics`](api/scala/index.html#org.apache.spark.mllib.stat.Statistics$) provides methods to
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run Pearson's chi-squared tests. The following example demonstrates how to run and interpret
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hypothesis tests.
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{% include_example scala/org/apache/spark/examples/mllib/HypothesisTestingExample.scala %}
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</div>
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<div data-lang="java" markdown="1">
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[`Statistics`](api/java/org/apache/spark/mllib/stat/Statistics.html) provides methods to
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run Pearson's chi-squared tests. The following example demonstrates how to run and interpret
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hypothesis tests.
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Refer to the [`ChiSqTestResult` Java docs](api/java/org/apache/spark/mllib/stat/test/ChiSqTestResult.html) for details on the API.
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{% include_example java/org/apache/spark/examples/mllib/JavaHypothesisTestingExample.java %}
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</div>
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<div data-lang="python" markdown="1">
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[`Statistics`](api/python/index.html#pyspark.mllib.stat.Statistics$) provides methods to
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run Pearson's chi-squared tests. The following example demonstrates how to run and interpret
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hypothesis tests.
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Refer to the [`Statistics` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) for more details on the API.
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{% include_example python/mllib/hypothesis_testing_example.py %}
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</div>
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</div>
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Additionally, `spark.mllib` provides a 1-sample, 2-sided implementation of the Kolmogorov-Smirnov (KS) test
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for equality of probability distributions. By providing the name of a theoretical distribution
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(currently solely supported for the normal distribution) and its parameters, or a function to
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calculate the cumulative distribution according to a given theoretical distribution, the user can
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test the null hypothesis that their sample is drawn from that distribution. In the case that the
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user tests against the normal distribution (`distName="norm"`), but does not provide distribution
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parameters, the test initializes to the standard normal distribution and logs an appropriate
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message.
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<div class="codetabs">
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<div data-lang="scala" markdown="1">
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[`Statistics`](api/scala/index.html#org.apache.spark.mllib.stat.Statistics$) provides methods to
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run a 1-sample, 2-sided Kolmogorov-Smirnov test. The following example demonstrates how to run
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and interpret the hypothesis tests.
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Refer to the [`Statistics` Scala docs](api/scala/index.html#org.apache.spark.mllib.stat.Statistics$) for details on the API.
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{% include_example scala/org/apache/spark/examples/mllib/HypothesisTestingKolmogorovSmirnovTestExample.scala %}
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</div>
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<div data-lang="java" markdown="1">
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[`Statistics`](api/java/org/apache/spark/mllib/stat/Statistics.html) provides methods to
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run a 1-sample, 2-sided Kolmogorov-Smirnov test. The following example demonstrates how to run
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and interpret the hypothesis tests.
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Refer to the [`Statistics` Java docs](api/java/org/apache/spark/mllib/stat/Statistics.html) for details on the API.
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{% include_example java/org/apache/spark/examples/mllib/JavaHypothesisTestingKolmogorovSmirnovTestExample.java %}
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</div>
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<div data-lang="python" markdown="1">
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[`Statistics`](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) provides methods to
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run a 1-sample, 2-sided Kolmogorov-Smirnov test. The following example demonstrates how to run
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and interpret the hypothesis tests.
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Refer to the [`Statistics` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) for more details on the API.
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{% include_example python/mllib/hypothesis_testing_kolmogorov_smirnov_test_example.py %}
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</div>
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</div>
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### Streaming Significance Testing
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`spark.mllib` provides online implementations of some tests to support use cases
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like A/B testing. These tests may be performed on a Spark Streaming
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`DStream[(Boolean, Double)]` where the first element of each tuple
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indicates control group (`false`) or treatment group (`true`) and the
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second element is the value of an observation.
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Streaming significance testing supports the following parameters:
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* `peacePeriod` - The number of initial data points from the stream to
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ignore, used to mitigate novelty effects.
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* `windowSize` - The number of past batches to perform hypothesis
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testing over. Setting to `0` will perform cumulative processing using
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all prior batches.
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<div class="codetabs">
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<div data-lang="scala" markdown="1">
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[`StreamingTest`](api/scala/index.html#org.apache.spark.mllib.stat.test.StreamingTest)
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provides streaming hypothesis testing.
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{% include_example scala/org/apache/spark/examples/mllib/StreamingTestExample.scala %}
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</div>
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<div data-lang="java" markdown="1">
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[`StreamingTest`](api/java/index.html#org.apache.spark.mllib.stat.test.StreamingTest)
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provides streaming hypothesis testing.
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{% include_example java/org/apache/spark/examples/mllib/JavaStreamingTestExample.java %}
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</div>
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</div>
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## Random data generation
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Random data generation is useful for randomized algorithms, prototyping, and performance testing.
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`spark.mllib` supports generating random RDDs with i.i.d. values drawn from a given distribution:
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uniform, standard normal, or Poisson.
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<div class="codetabs">
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<div data-lang="scala" markdown="1">
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[`RandomRDDs`](api/scala/index.html#org.apache.spark.mllib.random.RandomRDDs$) provides factory
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methods to generate random double RDDs or vector RDDs.
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The following example generates a random double RDD, whose values follows the standard normal
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distribution `N(0, 1)`, and then map it to `N(1, 4)`.
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Refer to the [`RandomRDDs` Scala docs](api/scala/index.html#org.apache.spark.mllib.random.RandomRDDs$) for details on the API.
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{% highlight scala %}
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import org.apache.spark.SparkContext
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import org.apache.spark.mllib.random.RandomRDDs._
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val sc: SparkContext = ...
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// Generate a random double RDD that contains 1 million i.i.d. values drawn from the
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// standard normal distribution `N(0, 1)`, evenly distributed in 10 partitions.
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val u = normalRDD(sc, 1000000L, 10)
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// Apply a transform to get a random double RDD following `N(1, 4)`.
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val v = u.map(x => 1.0 + 2.0 * x)
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{% endhighlight %}
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</div>
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<div data-lang="java" markdown="1">
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[`RandomRDDs`](api/java/index.html#org.apache.spark.mllib.random.RandomRDDs) provides factory
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methods to generate random double RDDs or vector RDDs.
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The following example generates a random double RDD, whose values follows the standard normal
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distribution `N(0, 1)`, and then map it to `N(1, 4)`.
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Refer to the [`RandomRDDs` Java docs](api/java/org/apache/spark/mllib/random/RandomRDDs) for details on the API.
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{% highlight java %}
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import org.apache.spark.SparkContext;
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import org.apache.spark.api.JavaDoubleRDD;
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import static org.apache.spark.mllib.random.RandomRDDs.*;
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JavaSparkContext jsc = ...
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// Generate a random double RDD that contains 1 million i.i.d. values drawn from the
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// standard normal distribution `N(0, 1)`, evenly distributed in 10 partitions.
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JavaDoubleRDD u = normalJavaRDD(jsc, 1000000L, 10);
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// Apply a transform to get a random double RDD following `N(1, 4)`.
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JavaDoubleRDD v = u.mapToDouble(x -> 1.0 + 2.0 * x);
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{% endhighlight %}
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</div>
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<div data-lang="python" markdown="1">
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[`RandomRDDs`](api/python/pyspark.mllib.html#pyspark.mllib.random.RandomRDDs) provides factory
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methods to generate random double RDDs or vector RDDs.
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The following example generates a random double RDD, whose values follows the standard normal
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distribution `N(0, 1)`, and then map it to `N(1, 4)`.
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Refer to the [`RandomRDDs` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.random.RandomRDDs) for more details on the API.
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{% highlight python %}
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from pyspark.mllib.random import RandomRDDs
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sc = ... # SparkContext
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# Generate a random double RDD that contains 1 million i.i.d. values drawn from the
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# standard normal distribution `N(0, 1)`, evenly distributed in 10 partitions.
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u = RandomRDDs.normalRDD(sc, 1000000L, 10)
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# Apply a transform to get a random double RDD following `N(1, 4)`.
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v = u.map(lambda x: 1.0 + 2.0 * x)
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{% endhighlight %}
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</div>
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</div>
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## Kernel density estimation
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[Kernel density estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation) is a technique
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useful for visualizing empirical probability distributions without requiring assumptions about the
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particular distribution that the observed samples are drawn from. It computes an estimate of the
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probability density function of a random variables, evaluated at a given set of points. It achieves
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this estimate by expressing the PDF of the empirical distribution at a particular point as the
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mean of PDFs of normal distributions centered around each of the samples.
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<div class="codetabs">
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<div data-lang="scala" markdown="1">
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[`KernelDensity`](api/scala/index.html#org.apache.spark.mllib.stat.KernelDensity) provides methods
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to compute kernel density estimates from an RDD of samples. The following example demonstrates how
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to do so.
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Refer to the [`KernelDensity` Scala docs](api/scala/index.html#org.apache.spark.mllib.stat.KernelDensity) for details on the API.
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{% include_example scala/org/apache/spark/examples/mllib/KernelDensityEstimationExample.scala %}
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</div>
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<div data-lang="java" markdown="1">
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[`KernelDensity`](api/java/index.html#org.apache.spark.mllib.stat.KernelDensity) provides methods
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to compute kernel density estimates from an RDD of samples. The following example demonstrates how
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to do so.
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Refer to the [`KernelDensity` Java docs](api/java/org/apache/spark/mllib/stat/KernelDensity.html) for details on the API.
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{% include_example java/org/apache/spark/examples/mllib/JavaKernelDensityEstimationExample.java %}
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</div>
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<div data-lang="python" markdown="1">
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[`KernelDensity`](api/python/pyspark.mllib.html#pyspark.mllib.stat.KernelDensity) provides methods
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to compute kernel density estimates from an RDD of samples. The following example demonstrates how
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to do so.
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Refer to the [`KernelDensity` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.KernelDensity) for more details on the API.
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{% include_example python/mllib/kernel_density_estimation_example.py %}
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</div>
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</div>
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