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Basic Statistics - spark.mllib |
Basic Statistics - spark.mllib |
- Table of contents {:toc}
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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.
{% highlight scala %} import org.apache.spark.mllib.linalg.Vector import org.apache.spark.mllib.stat.{MultivariateStatisticalSummary, Statistics}
val observations: RDD[Vector] = ... // an RDD of Vectors
// Compute column summary statistics. val summary: MultivariateStatisticalSummary = Statistics.colStats(observations) println(summary.mean) // a dense vector containing the mean value for each column println(summary.variance) // column-wise variance println(summary.numNonzeros) // number of nonzeros in each column
{% endhighlight %}
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.
{% highlight java %} import org.apache.spark.api.java.JavaRDD; import org.apache.spark.api.java.JavaSparkContext; import org.apache.spark.mllib.linalg.Vector; import org.apache.spark.mllib.stat.MultivariateStatisticalSummary; import org.apache.spark.mllib.stat.Statistics;
JavaSparkContext jsc = ...
JavaRDD mat = ... // an RDD of Vectors
// Compute column summary statistics. MultivariateStatisticalSummary summary = Statistics.colStats(mat.rdd()); System.out.println(summary.mean()); // a dense vector containing the mean value for each column System.out.println(summary.variance()); // column-wise variance System.out.println(summary.numNonzeros()); // number of nonzeros in each column
{% endhighlight %}
Refer to the MultivariateStatisticalSummary Python docs for more details on the API.
{% highlight python %} from pyspark.mllib.stat import Statistics
sc = ... # SparkContext
mat = ... # an RDD of Vectors
summary = Statistics.colStats(mat) print(summary.mean()) print(summary.variance()) print(summary.numNonzeros())
{% endhighlight %}
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.
Refer to the Statistics Scala docs for details on the API.
{% highlight scala %} import org.apache.spark.SparkContext import org.apache.spark.mllib.linalg._ import org.apache.spark.mllib.stat.Statistics
val sc: SparkContext = ...
val seriesX: RDD[Double] = ... // a series val seriesY: RDD[Double] = ... // must have the same number of partitions and cardinality as seriesX
// compute the correlation using Pearson's method. Enter "spearman" for Spearman's method. If a // method is not specified, Pearson's method will be used by default. val correlation: Double = Statistics.corr(seriesX, seriesY, "pearson")
val data: RDD[Vector] = ... // note that each Vector is a row and not a column
// calculate the correlation matrix using Pearson's method. Use "spearman" for Spearman's method. // If a method is not specified, Pearson's method will be used by default. val correlMatrix: Matrix = Statistics.corr(data, "pearson")
{% endhighlight %}
Refer to the Statistics Java docs for details on the API.
{% highlight java %} import org.apache.spark.api.java.JavaDoubleRDD; import org.apache.spark.api.java.JavaSparkContext; import org.apache.spark.mllib.linalg.*; import org.apache.spark.mllib.stat.Statistics;
JavaSparkContext jsc = ...
JavaDoubleRDD seriesX = ... // a series JavaDoubleRDD seriesY = ... // must have the same number of partitions and cardinality as seriesX
// compute the correlation using Pearson's method. Enter "spearman" for Spearman's method. If a // method is not specified, Pearson's method will be used by default. Double correlation = Statistics.corr(seriesX.srdd(), seriesY.srdd(), "pearson");
JavaRDD data = ... // note that each Vector is a row and not a column
// calculate the correlation matrix using Pearson's method. Use "spearman" for Spearman's method. // If a method is not specified, Pearson's method will be used by default. Matrix correlMatrix = Statistics.corr(data.rdd(), "pearson");
{% endhighlight %}
Refer to the Statistics Python docs for more details on the API.
{% highlight python %} from pyspark.mllib.stat import Statistics
sc = ... # SparkContext
seriesX = ... # a series seriesY = ... # must have the same number of partitions and cardinality as seriesX
print(Statistics.corr(seriesX, seriesY, method="pearson"))
data = ... # an RDD of Vectors
print(Statistics.corr(data, method="pearson"))
{% endhighlight %}
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.
{% highlight scala %} import org.apache.spark.SparkContext import org.apache.spark.SparkContext._ import org.apache.spark.rdd.PairRDDFunctions
val sc: SparkContext = ...
val data = ... // an RDD[(K, V)] of any key value pairs val fractions: Map[K, Double] = ... // specify the exact fraction desired from each key
// Get an exact sample from each stratum val approxSample = data.sampleByKey(withReplacement = false, fractions) val exactSample = data.sampleByKeyExact(withReplacement = false, fractions)
{% endhighlight %}
{% highlight java %} import java.util.Map;
import org.apache.spark.api.java.JavaPairRDD; import org.apache.spark.api.java.JavaSparkContext;
JavaSparkContext jsc = ...
JavaPairRDD<K, V> data = ... // an RDD of any key value pairs Map<K, Object> fractions = ... // specify the exact fraction desired from each key
// Get an exact sample from each stratum JavaPairRDD<K, V> approxSample = data.sampleByKey(false, fractions); JavaPairRDD<K, V> exactSample = data.sampleByKeyExact(false, fractions);
{% endhighlight %}
Note: sampleByKeyExact() is currently not supported in Python.
{% highlight python %}
sc = ... # SparkContext
data = ... # an RDD of any key value pairs fractions = ... # specify the exact fraction desired from each key as a dictionary
approxSample = data.sampleByKey(False, fractions);
{% endhighlight %}
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 ( 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.
{% highlight scala %} import org.apache.spark.SparkContext import org.apache.spark.mllib.linalg._ import org.apache.spark.mllib.regression.LabeledPoint import org.apache.spark.mllib.stat.Statistics._
val sc: SparkContext = ...
val vec: Vector = ... // a vector composed of the frequencies of events
// compute the goodness of fit. If a second vector to test against is not supplied as a parameter,
// the test runs against a uniform distribution.
val goodnessOfFitTestResult = Statistics.chiSqTest(vec)
println(goodnessOfFitTestResult) // summary of the test including the p-value, degrees of freedom,
// test statistic, the method used, and the null hypothesis.
val mat: Matrix = ... // a contingency matrix
// conduct Pearson's independence test on the input contingency matrix val independenceTestResult = Statistics.chiSqTest(mat) println(independenceTestResult) // summary of the test including the p-value, degrees of freedom...
val obs: RDD[LabeledPoint] = ... // (feature, label) pairs.
// 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. val featureTestResults: Array[ChiSqTestResult] = Statistics.chiSqTest(obs) var i = 1 featureTestResults.foreach { result => println(s"Column $i:\n$result") i += 1 } // summary of the test
{% endhighlight %}
Refer to the ChiSqTestResult Java docs for details on the API.
{% highlight java %} import org.apache.spark.api.java.JavaRDD; import org.apache.spark.api.java.JavaSparkContext; import org.apache.spark.mllib.linalg.*; import org.apache.spark.mllib.regression.LabeledPoint; import org.apache.spark.mllib.stat.Statistics; import org.apache.spark.mllib.stat.test.ChiSqTestResult;
JavaSparkContext jsc = ...
Vector vec = ... // a vector composed of the frequencies of events
// compute the goodness of fit. If a second vector to test against is not supplied as a parameter,
// the test runs against a uniform distribution.
ChiSqTestResult goodnessOfFitTestResult = Statistics.chiSqTest(vec);
// summary of the test including the p-value, degrees of freedom, test statistic, the method used,
// and the null hypothesis.
System.out.println(goodnessOfFitTestResult);
Matrix mat = ... // a contingency matrix
// conduct Pearson's independence test on the input contingency matrix ChiSqTestResult independenceTestResult = Statistics.chiSqTest(mat); // summary of the test including the p-value, degrees of freedom... System.out.println(independenceTestResult);
JavaRDD obs = ... // an RDD of labeled points
// 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. ChiSqTestResult[] featureTestResults = Statistics.chiSqTest(obs.rdd()); int i = 1; for (ChiSqTestResult result : featureTestResults) { System.out.println("Column " + i + ":"); System.out.println(result); // summary of the test i++; }
{% endhighlight %}
Refer to the Statistics Python docs for more details on the API.
{% highlight python %} from pyspark import SparkContext from pyspark.mllib.linalg import Vectors, Matrices from pyspark.mllib.regresssion import LabeledPoint from pyspark.mllib.stat import Statistics
sc = SparkContext()
vec = Vectors.dense(...) # a vector composed of the frequencies of events
goodnessOfFitTestResult = Statistics.chiSqTest(vec) print(goodnessOfFitTestResult) # summary of the test including the p-value, degrees of freedom, # test statistic, the method used, and the null hypothesis.
mat = Matrices.dense(...) # a contingency matrix
independenceTestResult = Statistics.chiSqTest(mat) print(independenceTestResult) # summary of the test including the p-value, degrees of freedom...
obs = sc.parallelize(...) # LabeledPoint(feature, label) .
featureTestResults = Statistics.chiSqTest(obs)
for i, result in enumerate(featureTestResults): print("Column $d:" % (i + 1)) print(result) {% endhighlight %}
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.
Refer to the Statistics Scala docs for details on the API.
{% highlight scala %} import org.apache.spark.mllib.stat.Statistics
val data: RDD[Double] = ... // an RDD of sample data
// run a KS test for the sample versus a standard normal distribution val testResult = Statistics.kolmogorovSmirnovTest(data, "norm", 0, 1) println(testResult) // summary of the test including the p-value, test statistic, // and null hypothesis // if our p-value indicates significance, we can reject the null hypothesis
// perform a KS test using a cumulative distribution function of our making val myCDF: Double => Double = ... val testResult2 = Statistics.kolmogorovSmirnovTest(data, myCDF) {% endhighlight %}
Refer to the Statistics Java docs for details on the API.
{% highlight java %} import java.util.Arrays;
import org.apache.spark.api.java.JavaDoubleRDD; import org.apache.spark.api.java.JavaSparkContext;
import org.apache.spark.mllib.stat.Statistics; import org.apache.spark.mllib.stat.test.KolmogorovSmirnovTestResult;
JavaSparkContext jsc = ... JavaDoubleRDD data = jsc.parallelizeDoubles(Arrays.asList(0.2, 1.0, ...)); KolmogorovSmirnovTestResult testResult = Statistics.kolmogorovSmirnovTest(data, "norm", 0.0, 1.0); // summary of the test including the p-value, test statistic, // and null hypothesis // if our p-value indicates significance, we can reject the null hypothesis System.out.println(testResult); {% endhighlight %}
Refer to the Statistics Python docs for more details on the API.
{% highlight python %} from pyspark.mllib.stat import Statistics
parallelData = sc.parallelize([1.0, 2.0, ... ])
testResult = Statistics.kolmogorovSmirnovTest(parallelData, "norm", 0, 1) print(testResult) # summary of the test including the p-value, test statistic, # and null hypothesis # if our p-value indicates significance, we can reject the null hypothesis
{% endhighlight %}
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 to0will perform cumulative processing using all prior batches.
{% include_example scala/org/apache/spark/examples/mllib/StreamingTestExample.scala %}
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.
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 %}
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.map(
new Function<Double, Double>() {
public Double call(Double x) {
return 1.0 + 2.0 * x;
}
});
{% endhighlight %}
Refer to the RandomRDDs Python docs 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 %}
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 the mean of PDFs of normal distributions centered around each of the samples.
Refer to the KernelDensity Scala docs for details on the API.
{% highlight scala %} import org.apache.spark.mllib.stat.KernelDensity import org.apache.spark.rdd.RDD
val data: RDD[Double] = ... // an RDD of sample data
// Construct the density estimator with the sample data and a standard deviation for the Gaussian // kernels val kd = new KernelDensity() .setSample(data) .setBandwidth(3.0)
// Find density estimates for the given values val densities = kd.estimate(Array(-1.0, 2.0, 5.0)) {% endhighlight %}
Refer to the KernelDensity Java docs for details on the API.
{% highlight java %} import org.apache.spark.mllib.stat.KernelDensity; import org.apache.spark.rdd.RDD;
RDD data = ... // an RDD of sample data
// Construct the density estimator with the sample data and a standard deviation for the Gaussian // kernels KernelDensity kd = new KernelDensity() .setSample(data) .setBandwidth(3.0);
// Find density estimates for the given values double[] densities = kd.estimate(new double[] {-1.0, 2.0, 5.0}); {% endhighlight %}
Refer to the KernelDensity Python docs for more details on the API.
{% highlight python %} from pyspark.mllib.stat import KernelDensity
data = ... # an RDD of sample data
kd = KernelDensity() kd.setSample(data) kd.setBandwidth(3.0)
densities = kd.estimate([-1.0, 2.0, 5.0]) {% endhighlight %}