mahalanobis_bound: Upper Bound of the Bayes Error Rate given by the Mahalanobis...

In ryanholbrook/bayeserror: Estimating Bayes Error in Classification Tasks

Description

Provides an upper bound for the Bayes error rate of a dataset on binary classes. This bound requires no assumptions of the distribution of the data.

Usage

mahalanobis_bound(x, y)

Arguments

x	a data matrix with numeric values
y	a binary vector

Details

The Mahalanobis distance between class 0 and class 1 is given by

M_d = (mu_0 - mu_1)' Sigma^-1 (mu_0 - mu_1)

where μ_0 and μ_1 are the class means in x for class 0 and 1, respectively. This provides an upper bound on the Bayes error ε_bayes by

ε_bayes <= (2 Pr(0) Pr(1)) / (1 + Pr(0) Pr(1) M_d)

where Pr(0) and Pr(1) are the class probabilities of 0 and 1.

Value

an estimate of the Bayes error rate of x w.r.t. y

ryanholbrook/bayeserror documentation built on Jan. 12, 2020, 6:25 p.m.