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import sys
from pyspark.rdd import RDD
from pyspark.mllib.common import callMLlibFunc, JavaModelWrapper
from pyspark.mllib.linalg import Matrix, _convert_to_vector
from pyspark.mllib.regression import LabeledPoint
from pyspark.mllib.stat.test import ChiSqTestResult, KolmogorovSmirnovTestResult
__all__ = ['MultivariateStatisticalSummary', 'Statistics']
[docs]class MultivariateStatisticalSummary(JavaModelWrapper):
"""
Trait for multivariate statistical summary of a data matrix.
"""
[docs] def mean(self):
return self.call("mean").toArray()
[docs] def variance(self):
return self.call("variance").toArray()
[docs] def count(self):
return int(self.call("count"))
[docs] def numNonzeros(self):
return self.call("numNonzeros").toArray()
[docs] def max(self):
return self.call("max").toArray()
[docs] def min(self):
return self.call("min").toArray()
[docs] def normL1(self):
return self.call("normL1").toArray()
[docs] def normL2(self):
return self.call("normL2").toArray()
[docs]class Statistics(object):
[docs] @staticmethod
def colStats(rdd):
"""
Computes column-wise summary statistics for the input RDD[Vector].
Parameters
----------
rdd : :py:class:`pyspark.RDD`
an RDD[Vector] for which column-wise summary statistics
are to be computed.
Returns
-------
:class:`MultivariateStatisticalSummary`
object containing column-wise summary statistics.
Examples
--------
>>> from pyspark.mllib.linalg import Vectors
>>> rdd = sc.parallelize([Vectors.dense([2, 0, 0, -2]),
... Vectors.dense([4, 5, 0, 3]),
... Vectors.dense([6, 7, 0, 8])])
>>> cStats = Statistics.colStats(rdd)
>>> cStats.mean()
array([ 4., 4., 0., 3.])
>>> cStats.variance()
array([ 4., 13., 0., 25.])
>>> cStats.count()
3
>>> cStats.numNonzeros()
array([ 3., 2., 0., 3.])
>>> cStats.max()
array([ 6., 7., 0., 8.])
>>> cStats.min()
array([ 2., 0., 0., -2.])
"""
cStats = callMLlibFunc("colStats", rdd.map(_convert_to_vector))
return MultivariateStatisticalSummary(cStats)
[docs] @staticmethod
def corr(x, y=None, method=None):
"""
Compute the correlation (matrix) for the input RDD(s) using the
specified method.
Methods currently supported: `pearson (default), spearman`.
If a single RDD of Vectors is passed in, a correlation matrix
comparing the columns in the input RDD is returned. Use `method`
to specify the method to be used for single RDD inout.
If two RDDs of floats are passed in, a single float is returned.
Parameters
----------
x : :py:class:`pyspark.RDD`
an RDD of vector for which the correlation matrix is to be computed,
or an RDD of float of the same cardinality as y when y is specified.
y : :py:class:`pyspark.RDD`, optional
an RDD of float of the same cardinality as x.
method : str, optional
String specifying the method to use for computing correlation.
Supported: `pearson` (default), `spearman`
Returns
-------
:py:class:`pyspark.mllib.linalg.Matrix`
Correlation matrix comparing columns in x.
Examples
--------
>>> x = sc.parallelize([1.0, 0.0, -2.0], 2)
>>> y = sc.parallelize([4.0, 5.0, 3.0], 2)
>>> zeros = sc.parallelize([0.0, 0.0, 0.0], 2)
>>> abs(Statistics.corr(x, y) - 0.6546537) < 1e-7
True
>>> Statistics.corr(x, y) == Statistics.corr(x, y, "pearson")
True
>>> Statistics.corr(x, y, "spearman")
0.5
>>> from math import isnan
>>> isnan(Statistics.corr(x, zeros))
True
>>> from pyspark.mllib.linalg import Vectors
>>> rdd = sc.parallelize([Vectors.dense([1, 0, 0, -2]), Vectors.dense([4, 5, 0, 3]),
... Vectors.dense([6, 7, 0, 8]), Vectors.dense([9, 0, 0, 1])])
>>> pearsonCorr = Statistics.corr(rdd)
>>> print(str(pearsonCorr).replace('nan', 'NaN'))
[[ 1. 0.05564149 NaN 0.40047142]
[ 0.05564149 1. NaN 0.91359586]
[ NaN NaN 1. NaN]
[ 0.40047142 0.91359586 NaN 1. ]]
>>> spearmanCorr = Statistics.corr(rdd, method="spearman")
>>> print(str(spearmanCorr).replace('nan', 'NaN'))
[[ 1. 0.10540926 NaN 0.4 ]
[ 0.10540926 1. NaN 0.9486833 ]
[ NaN NaN 1. NaN]
[ 0.4 0.9486833 NaN 1. ]]
>>> try:
... Statistics.corr(rdd, "spearman")
... print("Method name as second argument without 'method=' shouldn't be allowed.")
... except TypeError:
... pass
"""
# Check inputs to determine whether a single value or a matrix is needed for output.
# Since it's legal for users to use the method name as the second argument, we need to
# check if y is used to specify the method name instead.
if type(y) == str:
raise TypeError("Use 'method=' to specify method name.")
if not y:
return callMLlibFunc("corr", x.map(_convert_to_vector), method).toArray()
else:
return callMLlibFunc("corr", x.map(float), y.map(float), method)
[docs] @staticmethod
def chiSqTest(observed, expected=None):
"""
If `observed` is Vector, conduct Pearson's chi-squared goodness
of fit test of the observed data against the expected distribution,
or against the uniform distribution (by default), with each category
having an expected frequency of `1 / len(observed)`.
If `observed` is matrix, conduct Pearson's independence test on the
input contingency matrix, which cannot contain negative entries or
columns or rows that sum up to 0.
If `observed` is an RDD of LabeledPoint, conduct Pearson's independence
test for every feature against the label across the input RDD.
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.
Parameters
----------
observed : :py:class:`pyspark.mllib.linalg.Vector` or \
:py:class:`pyspark.mllib.linalg.Matrix`
it could be a vector containing the observed categorical
counts/relative frequencies, or the contingency matrix
(containing either counts or relative frequencies),
or an RDD of LabeledPoint containing the labeled dataset
with categorical features. Real-valued features will be
treated as categorical for each distinct value.
expected : :py:class:`pyspark.mllib.linalg.Vector`
Vector containing the expected categorical counts/relative
frequencies. `expected` is rescaled if the `expected` sum
differs from the `observed` sum.
Returns
-------
:py:class:`pyspark.mllib.stat.ChiSqTestResult`
object containing the test statistic, degrees
of freedom, p-value, the method used, and the null hypothesis.
Notes
-----
`observed` cannot contain negative values
Examples
--------
>>> from pyspark.mllib.linalg import Vectors, Matrices
>>> observed = Vectors.dense([4, 6, 5])
>>> pearson = Statistics.chiSqTest(observed)
>>> print(pearson.statistic)
0.4
>>> pearson.degreesOfFreedom
2
>>> print(round(pearson.pValue, 4))
0.8187
>>> pearson.method
'pearson'
>>> pearson.nullHypothesis
'observed follows the same distribution as expected.'
>>> observed = Vectors.dense([21, 38, 43, 80])
>>> expected = Vectors.dense([3, 5, 7, 20])
>>> pearson = Statistics.chiSqTest(observed, expected)
>>> print(round(pearson.pValue, 4))
0.0027
>>> data = [40.0, 24.0, 29.0, 56.0, 32.0, 42.0, 31.0, 10.0, 0.0, 30.0, 15.0, 12.0]
>>> chi = Statistics.chiSqTest(Matrices.dense(3, 4, data))
>>> print(round(chi.statistic, 4))
21.9958
>>> data = [LabeledPoint(0.0, Vectors.dense([0.5, 10.0])),
... LabeledPoint(0.0, Vectors.dense([1.5, 20.0])),
... LabeledPoint(1.0, Vectors.dense([1.5, 30.0])),
... LabeledPoint(0.0, Vectors.dense([3.5, 30.0])),
... LabeledPoint(0.0, Vectors.dense([3.5, 40.0])),
... LabeledPoint(1.0, Vectors.dense([3.5, 40.0])),]
>>> rdd = sc.parallelize(data, 4)
>>> chi = Statistics.chiSqTest(rdd)
>>> print(chi[0].statistic)
0.75
>>> print(chi[1].statistic)
1.5
"""
if isinstance(observed, RDD):
if not isinstance(observed.first(), LabeledPoint):
raise ValueError("observed should be an RDD of LabeledPoint")
jmodels = callMLlibFunc("chiSqTest", observed)
return [ChiSqTestResult(m) for m in jmodels]
if isinstance(observed, Matrix):
jmodel = callMLlibFunc("chiSqTest", observed)
else:
if expected and len(expected) != len(observed):
raise ValueError("`expected` should have same length with `observed`")
jmodel = callMLlibFunc("chiSqTest", _convert_to_vector(observed), expected)
return ChiSqTestResult(jmodel)
[docs] @staticmethod
def kolmogorovSmirnovTest(data, distName="norm", *params):
"""
Performs the Kolmogorov-Smirnov (KS) test for data sampled from
a continuous distribution. It tests the null hypothesis that
the data is generated from a particular distribution.
The given data is sorted and the Empirical Cumulative
Distribution Function (ECDF) is calculated
which for a given point is the number of points having a CDF
value lesser than it divided by the total number of points.
Since the data is sorted, this is a step function
that rises by (1 / length of data) for every ordered point.
The KS statistic gives us the maximum distance between the
ECDF and the CDF. Intuitively if this statistic is large, the
probability that the null hypothesis is true becomes small.
For specific details of the implementation, please have a look
at the Scala documentation.
Parameters
----------
data : :py:class:`pyspark.RDD`
RDD, samples from the data
distName : str, optional
string, currently only "norm" is supported.
(Normal distribution) to calculate the
theoretical distribution of the data.
params
additional values which need to be provided for
a certain distribution.
If not provided, the default values are used.
Returns
-------
:py:class:`pyspark.mllib.stat.KolmogorovSmirnovTestResult`
object containing the test statistic, degrees of freedom, p-value,
the method used, and the null hypothesis.
Examples
--------
>>> kstest = Statistics.kolmogorovSmirnovTest
>>> data = sc.parallelize([-1.0, 0.0, 1.0])
>>> ksmodel = kstest(data, "norm")
>>> print(round(ksmodel.pValue, 3))
1.0
>>> print(round(ksmodel.statistic, 3))
0.175
>>> ksmodel.nullHypothesis
'Sample follows theoretical distribution'
>>> data = sc.parallelize([2.0, 3.0, 4.0])
>>> ksmodel = kstest(data, "norm", 3.0, 1.0)
>>> print(round(ksmodel.pValue, 3))
1.0
>>> print(round(ksmodel.statistic, 3))
0.175
"""
if not isinstance(data, RDD):
raise TypeError("data should be an RDD, got %s." % type(data))
if not isinstance(distName, str):
raise TypeError("distName should be a string, got %s." % type(distName))
params = [float(param) for param in params]
return KolmogorovSmirnovTestResult(
callMLlibFunc("kolmogorovSmirnovTest", data, distName, params))
def _test():
import doctest
import numpy
from pyspark.sql import SparkSession
try:
# Numpy 1.14+ changed it's string format.
numpy.set_printoptions(legacy='1.13')
except TypeError:
pass
globs = globals().copy()
spark = SparkSession.builder\
.master("local[4]")\
.appName("mllib.stat.statistics tests")\
.getOrCreate()
globs['sc'] = spark.sparkContext
(failure_count, test_count) = doctest.testmod(globs=globs, optionflags=doctest.ELLIPSIS)
spark.stop()
if failure_count:
sys.exit(-1)
if __name__ == "__main__":
_test()