de.jstacs.utils

Class StatisticalModelTester

java.lang.Object

de.jstacs.utils.StatisticalModelTester

public class StatisticalModelTester
extends Object

This class is useful for some test for any (discrete) models. It implements several statistics (log-likelihood, Shannon entropy, AIC, BIC, ...) to compare models.

Author:

Jens Keilwagen

See Also:

StatisticalModel

Constructor Summary

Constructors

Constructor and Description
StatisticalModelTester()

Method Summary

Modifier and Type	Method and Description
static double	getKLDivergence(StatisticalModel m1, StatisticalModel m2, int length) Returns the Kullback-Leibler-divergence D(p_m1||p_m2).
static double	getLogLikelihood(StatisticalModel m, DataSet data) Returns the log-likelihood of a DataSet data for a given model m.
static double	getLogLikelihood(StatisticalModel m, DataSet data, double[] weights) Returns the log-likelihood of a DataSet data for a given model m.
static double[]	getMarginalDistribution(StatisticalModel m, int[]... constraint) This method computes the marginal distribution for any discrete model m and all sequences that fulfill the constraint , if possible.
static double	getMaxOfDeviation(StatisticalModel m1, StatisticalModel m2, int length) This method computes the maximum deviation between the probabilities for all sequences of length for discrete models m1 and m2.
static Sequence	getMostProbableSequence(SequenceScore m, int length) Returns one most probable sequence for the discrete model m.
static double	getShannonEntropy(StatisticalModel m, int length) This method computes the Shannon entropy for any discrete model m and all sequences of length, if possible.
static double	getShannonEntropyInBits(StatisticalModel m, int length) This method computes the Shannon entropy in bits for any discrete model m and all sequences of length, if possible.
static double	getSumOfDeviation(StatisticalModel m1, StatisticalModel m2, int length) This method computes the sum of deviations between the probabilities for all sequences of length for discrete models m1 and m2.
static double	getSumOfDistribution(StatisticalModel m, int length) This method computes the marginal distribution for any discrete model m and all sequences of length, if possible.
static double	getSymKLDivergence(StatisticalModel m1, StatisticalModel m2, int length) Returns the difference of the Kullback-Leibler-divergences, i.e.
static double	getValueOfAIC(StatisticalModel m, DataSet s, int k) This method computes the value of Akaikes Information Criterion (AIC).
static double	getValueOfBIC(StatisticalModel m, DataSet s, int k) This method computes the value of the Bayesian Information Criterion (BIC).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

StatisticalModelTester

public StatisticalModelTester()

Method Detail

getKLDivergence

public static double getKLDivergence(StatisticalModel m1,
                                     StatisticalModel m2,
                                     int length)
                              throws Exception

Returns the Kullback-Leibler-divergence D(p_m1||p_m2).

Computes \sum_x p(x|m1) * \log \frac{p(x|m1)}{p(x|m2)}.

Parameters:

m1 - one discrete model

m2 - another discrete model

length - the length of the sequence (for inhomogeneous models length has to be SequenceScore.getLength())

Returns:

the Kullback-Leibler-divergence

Throws:

Exception - if something went wrong

getSymKLDivergence

public static double getSymKLDivergence(StatisticalModel m1,
                                        StatisticalModel m2,
                                        int length)
                                 throws Exception

Returns the difference of the Kullback-Leibler-divergences, i.e. D(p_m1||p_m2) - D(p_m2||p_m1).

Computes \sum_x (p(x|m1)-p(x|m2)) * \log \frac{p(x|m1)}{p(x|m2)}.

Parameters:

m1 - one discrete model

m2 - another discrete model

length - the length of the sequence (for inhomogeneous models length has to be SequenceScore.getLength())

Returns:

the difference of the Kullback-Leibler-divergence

Throws:

Exception - if something went wrong

getLogLikelihood

public static double getLogLikelihood(StatisticalModel m,
                                      DataSet data)
                               throws Exception

Returns the log-likelihood of a DataSet data for a given model m.

Parameters:

m - the given model

data - the DataSet

Returns:

the log-likelihood of data

Throws:

Exception - if something went wrong

getLogLikelihood

public static double getLogLikelihood(StatisticalModel m,
                                      DataSet data,
                                      double[] weights)
                               throws Exception

Returns the log-likelihood of a DataSet data for a given model m.

Parameters:

m - the given model

data - the DataSet

weights - the weight for each element of the DataSet

Returns:

the log-likelihood of data

Throws:

Exception - if something went wrong

getMarginalDistribution

public static double[] getMarginalDistribution(StatisticalModel m,
                                               int[]... constraint)
                                        throws Exception

This method computes the marginal distribution for any discrete model m and all sequences that fulfill the constraint , if possible.

Parameters:

m - a discrete model

constraint - constraint[j][i] < 0 stands for an irrelevant position, constraint[j][i] = c with 0 <= c < m.getAlphabets()[(m.getLength==0)?0:i].getAlphabetLength() is the encoded character of position i

Returns:

the marginal distributions of the given constraints for the discrete model

Throws:

Exception - if something went wrong

getMaxOfDeviation

public static double getMaxOfDeviation(StatisticalModel m1,
                                       StatisticalModel m2,
                                       int length)
                                throws Exception

This method computes the maximum deviation between the probabilities for all sequences of length for discrete models m1 and m2.

Parameters:

m1 - one discrete model

m2 - another discrete model

length - the length of the sequence (for inhomogeneous models length has to be SequenceScore.getLength())

Returns:

the maximum deviation between the probabilities

Throws:

Exception - if something went wrong

getMostProbableSequence

public static Sequence getMostProbableSequence(SequenceScore m,
                                               int length)
                                        throws Exception

Returns one most probable sequence for the discrete model m. (Maybe there are more than one most probable sequences. In this case only one of them is returned.)

This is only a standard implementation. For some special models like Markov models it is possible to compute the probabilities of the sequences much faster by using a dynamic-programming-algorithm.

Parameters:

m - the discrete model

length - the length of the sequence (for inhomogeneous models length has to be SequenceScore.getLength())

Returns:

one most probable sequence

Throws:

Exception - if something went wrong

getShannonEntropy

public static double getShannonEntropy(StatisticalModel m,
                                       int length)
                                throws Exception

This method computes the Shannon entropy for any discrete model m and all sequences of length, if possible.

Parameters:

m - the discrete model

length - the length of the sequence (for inhomogeneous models length has to be SequenceScore.getLength())

Returns:

the Shannon entropy for a discrete model

Throws:

Exception - if something went wrong

getShannonEntropyInBits

public static double getShannonEntropyInBits(StatisticalModel m,
                                             int length)
                                      throws Exception

This method computes the Shannon entropy in bits for any discrete model m and all sequences of length, if possible.

Parameters:

m - the discrete model

length - the length of the sequence (for inhomogeneous models length has to be SequenceScore.getLength())

Returns:

the Shannon entropy in bits for a discrete model

Throws:

Exception - if something went wrong

getSumOfDeviation

public static double getSumOfDeviation(StatisticalModel m1,
                                       StatisticalModel m2,
                                       int length)
                                throws Exception

This method computes the sum of deviations between the probabilities for all sequences of length for discrete models m1 and m2.

Parameters:

m1 - one discrete model

m2 - another discrete model

length - the length of the sequence (for inhomogeneous models length has to be SequenceScore.getLength())

Returns:

the sum of deviations between the probabilities

Throws:

Exception - if something went wrong

getSumOfDistribution

public static double getSumOfDistribution(StatisticalModel m,
                                          int length)
                                   throws Exception

This method computes the marginal distribution for any discrete model m and all sequences of length, if possible. So this method can be used to give a hint whether a model is a distribution or if some mistakes are in the implementation.

It is expected that this method delivers the value 1.0, but because of the limited precision in Java the value 1.0 is unrealistic.

Math.abs( 1.0d - getSumOfDistribution( m, length ) should be smaller than 1E-10.

Parameters:

m - the discrete model

length - the length of the sequence (for inhomogeneous models length has to be SequenceScore.getLength())

Returns:

the marginal distribution for a discrete model

Throws:

Exception - if something went wrong

getValueOfAIC

public static double getValueOfAIC(StatisticalModel m,
                                   DataSet s,
                                   int k)
                            throws Exception

This method computes the value of Akaikes Information Criterion (AIC). It uses the formula: AIC = 2 * log L(t,x) - 2*k, where L(t,x) is the likelihood of the DataSet and k is the number of parameters in the model.

The value of the AIC can be used for model selection.

Parameters:

m - a trained model

s - the DataSet for the test

k - the number of parameters of the model m

Returns:

the value of AIC

Throws:

Exception - if something went wrong

getValueOfBIC

public static double getValueOfBIC(StatisticalModel m,
                                   DataSet s,
                                   int k)
                            throws Exception

This method computes the value of the Bayesian Information Criterion (BIC). It uses the formula: BIC = 2 * log L(t,x) - k * log n, where L(t,x) is the likelihood of the DataSet, k is the number of parameters in the model and n is the number of sequences in the DataSet.

The value of the BIC can be used for model selection.

Parameters:

m - a trained model

s - the DataSet for the test

k - the number of parameters of the model m

Returns:

value of AIC

Throws:

Exception - if something went wrong