edu.stanford.nlp.stats

Class Distributions

java.lang.Object

edu.stanford.nlp.stats.Distributions

public class Distributions
extends java.lang.Object

Static methods for operating on Distributionss. In general, if a method is operating on a pair of Distribution objects, we imagine that the set of possible keys for each Distribution is the same. Therefore we require that d1.numberOFKeys = d2.numberOfKeys and that the number of keys in the union of the two key sets <= numKeys

Author:

Jeff Michels (jmichels@stanford.edu)

Method Summary

Modifier and Type	Method and Description
static <K> Distribution<K>	average(Distribution<K> d1, Distribution<K> d2)
protected static <K> java.util.Set<K>	getSetOfAllKeys(Distribution<K> d1, Distribution<K> d2)
static <K> double	informationRadius(Distribution<K> d1, Distribution<K> d2) Calculates the information radius (aka the Jensen-Shannon divergence) between the two Distributions.
static <K> double	jensenShannonDivergence(Distribution<K> d1, Distribution<K> d2) Calculates the Jensen-Shannon divergence between the two distributions.
static <K> double	klDivergence(Distribution<K> from, Distribution<K> to) Calculates the KL divergence between the two distributions.
static <K> double	overlap(Distribution<K> d1, Distribution<K> d2) Returns a double between 0 and 1 representing the overlap of d1 and d2.
static <K> double	skewDivergence(Distribution<K> d1, Distribution<K> d2, double skew) Calculates the skew divergence between the two distributions.
static <K> Distribution<K>	weightedAverage(Distribution<K> d1, double w1, Distribution<K> d2) Returns a new Distribution with counts averaged from the two given Distributions.

Methods inherited from class java.lang.Object

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

Method Detail

getSetOfAllKeys

protected static <K> java.util.Set<K> getSetOfAllKeys(Distribution<K> d1,
                                                      Distribution<K> d2)

overlap

public static <K> double overlap(Distribution<K> d1,
                                 Distribution<K> d2)

Returns a double between 0 and 1 representing the overlap of d1 and d2. Equals 0 if there is no overlap, equals 1 iff d1==d2

weightedAverage

public static <K> Distribution<K> weightedAverage(Distribution<K> d1,
                                                  double w1,
                                                  Distribution<K> d2)

Returns a new Distribution with counts averaged from the two given Distributions. The average Distribution will contain the union of keys in both source Distributions, and each count will be the weighted average of the two source counts for that key, a missing count in one Distribution is treated as if it has probability equal to that returned by the probabilityOf() function.

Returns:

A new distribution with counts that are the mean of the resp. counts in the given distributions with the remaining probability mass adjusted accordingly.

average

public static <K> Distribution<K> average(Distribution<K> d1,
                                          Distribution<K> d2)

klDivergence

public static <K> double klDivergence(Distribution<K> from,
                                      Distribution<K> to)

Calculates the KL divergence between the two distributions. That is, it calculates KL(from || to). In other words, how well can d1 be represented by d2. if there is some value in d1 that gets zero prob in d2, then return positive infinity.

Returns:

The KL divergence between the distributions

jensenShannonDivergence

public static <K> double jensenShannonDivergence(Distribution<K> d1,
                                                 Distribution<K> d2)

Calculates the Jensen-Shannon divergence between the two distributions. That is, it calculates 1/2 [KL(d1 || avg(d1,d2)) + KL(d2 || avg(d1,d2))] .

Returns:

The KL divergence between the distributions

skewDivergence

public static <K> double skewDivergence(Distribution<K> d1,
                                        Distribution<K> d2,
                                        double skew)

Calculates the skew divergence between the two distributions. That is, it calculates KL(d1 || (d2*skew + d1*(1-skew))) . In other words, how well can d1 be represented by a "smoothed" d2.

Returns:

The skew divergence between the distributions

informationRadius

public static <K> double informationRadius(Distribution<K> d1,
                                           Distribution<K> d2)

Calculates the information radius (aka the Jensen-Shannon divergence) between the two Distributions. This measure is defined as:

iRad(p,q) = D(p||(p+q)/2)+D(q,(p+q)/2)

where p is one Distribution, q is the other distribution, and D(p||q) is the KL divergence bewteen p and q. Note that iRad(p,q) = iRad(q,p).

Returns:

The information radius between the distributions