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<K> 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<K> with counts averaged from the two given Distributions. The average Distribution<K> 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