pyspark.mllib.stat.
Statistics
Methods
chiSqTest(observed[, expected])
chiSqTest
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).
colStats(rdd)
colStats
Computes column-wise summary statistics for the input RDD[Vector].
corr(x[, y, method])
corr
Compute the correlation (matrix) for the input RDD(s) using the specified method.
kolmogorovSmirnovTest(data[, distName])
kolmogorovSmirnovTest
Performs the Kolmogorov-Smirnov (KS) test for data sampled from a continuous distribution.
Methods Documentation
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.
pyspark.mllib.linalg.Vector
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.
Vector containing the expected categorical counts/relative frequencies. expected is rescaled if the expected sum differs from the observed sum.
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
pyspark.RDD
an RDD[Vector] for which column-wise summary statistics are to be computed.
MultivariateStatisticalSummary
object containing column-wise summary statistics.
>>> 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.])
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.
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.
an RDD of float of the same cardinality as x.
String specifying the method to use for computing correlation. Supported: pearson (default), spearman
Correlation matrix comparing columns in x.
>>> 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
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.
RDD, samples from the data
string, currently only “norm” is supported. (Normal distribution) to calculate the theoretical distribution of the data.
additional values which need to be provided for a certain distribution. If not provided, the default values are used.
pyspark.mllib.stat.KolmogorovSmirnovTestResult
>>> 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