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KullbackLeibler.jl

💫 Fast Julia implementation of various Kullback-Leibler divergences for 1D parametric distributions. 🏋 Also provides optimized code for kl-UCB indexes

Julia implementation of Kullback-Leibler divergences and kl-UCB indexes

This repository contains a small, simple and efficient module, implementing various Kullback-Leibler divergences for parametric 1D continuous or discrete distributions.

References

Garivier & Cappé & Kaufmann, 2012, for the pymaBandits project on which this implementation is based,
Besson, 2018, SMPyBandits project for improvements on the initial implementation,
Filippi & Cappé & Garivier, 2011,
Garivier & Cappé, 2011,
Kullback & Leibler, 1951 for the first article introducing the so-called Kullback & Leibler divergences.

Examples

Simple usage

If the KullbackLeibler.jl file is accessible in your PATH or in Python’s path:

julia> using KullbackLeibler
julia> KullbackLeibler.klBern(0.5, 0.5)
0.0
julia> KullbackLeibler.klBern(0.1, 0.9)
1.757779...
julia> KullbackLeibler.klBern(0.9, 0.1)  # And this KL is symmetric
1.757779...
julia> KullbackLeibler.klBern(0.4, 0.5)
0.020135...
julia> KullbackLeibler.klBern(0.01, 0.99)
4.503217...

You can also use the common function that supports different distributions using the Distributions module.

julia> using Distributions
julia> Bern1 = Distributions.Bernoulli(0.33)
Distributions.Bernoulli{Float64}(p=0.33)
julia> Bern2 = Distributions.Bernoulli(0.42)
Distributions.Bernoulli{Float64}(p=0.42)
julia> ex_kl_1 = KL( Bern1, Bern2 )  # Calc KL divergence for Bernoulli R.V
0.017063...
julia> klBern(0.33, 0.42)  # same!
0.017063...

Vectorized version?

All functions are not vectorized, and assume only one value for each argument. If you want vectorized function, please ask and we will try to add them.