Discreet
Discreet is a small opinionated toolbox to estimate entropy and mutual information from discrete samples. It contains methods to adjust results and correct over- or under-estimations.
Estimating entropy
Discreet uses StatsBase's FrequencyWeights and ProbabilityWeights types.
using StatsBase: FrequencyWeights, ProbabilityWeights
using Discreet
dist = FrequencyWeights([1, 1, 1, 1, 1, 1])
entropy(dist) # Naive method: log(6) ≈ 1.792
entropy(dist; method=:CS) # Chao-Shen correction: ≈ 3.840
entropy(dist; method=:Shrink) # Shrinkage correction: ≈ 1.792
dist = ProbabilityWeights([.5, .5])
entropy(dist) # log(2) ≈ 0.693Discreet can also estimate the entropy of a sample:
using Discreet
data = ["tomato", "apple", "apple", "banana", "tomato"]
estimate_entropy(data) # == entropy(FrequencyWeights([2, 2, 1]))Estimate mutual information
Discrete provides similar routines to estimate mutual information.
using Discreet
labels_a = [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3]
labels_b = [1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 1, 3, 3, 3, 2, 2]
mutual_information(labels_a, labels_b) # Naive method: ≈ 0.410
mutual_information(labels_a, labels_b; method=:CS) # Chao-Shen correction: ≈ 0.148
mutual_information(labels_a, labels_b; normalize=true) # Normalized score (between 0 and 1): ≈ 0.382