kl_div

  ↳ distance

kl_div(probs)

Given an array of probability distributions, returns a matrix of Kullback-Liebler divergences between the distributions.

The input probs has the form of a column-stochastic matrix: that is, that is, np.sum(probs,axis=1) == 1. The output is a square matrix D with length and width probs.shape[0], so that D[i,j] is the KL divergence of probs[i] over probs[j].

Mathematically, if probs[i,j] is given by the matrix \(T_{i,j}\), then D[i,j] is given by \(D_{i,j}\):

\[D_{i,j} = \sum_{k} T_{i,k} \log\left(\frac{T_{i,k}}{T_{j,k}}\right)\]