cjs_dist: Cumulative Jensen-Shannon divergence

In hyunjimoon/SBC: Simulation Based Calibration for rstan/cmdstanr models

Cumulative Jensen-Shannon divergence

Description

Computes the cumulative Jensen-Shannon distance between two samples.

Usage

cjs_dist(
  x,
  y,
  x_weights = rep(1/length(x), length(x)),
  y_weights = rep(1/length(y), length(y)),
  ...
)

Arguments

x	numeric vector of draws from first distribution
y	numeric vector of draws from second distribution
x_weights	numeric vector of weights of first distribution
y_weights	numeric vector of weights of second distribution
...	unused

Details

The Cumulative Jensen-Shannon distance is a symmetric metric based on the cumulative Jensen-Shannon divergence. The divergence CJS(P || Q) between two cumulative distribution functions P and Q is defined as:

CJS(P || Q) = \sum P(x) \log \frac{P(x)}{0.5 (P(x) + Q(x))} + \frac{1}{2 \ln 2} \sum (Q(x) - P(x))

The symmetric metric is defined as:

CJS_{dist}(P || Q) = \sqrt{CJS(P || Q) + CJS(Q || P)}

This has an upper bound of \sqrt \sum (P(x) + Q(x))

Value

distance value based on CJS computation.

References

Nguyen H-V., Vreeken J. (2015). Non-parametric Jensen-Shannon Divergence. In: Appice A., Rodrigues P., Santos Costa V., Gama J., Jorge A., Soares C. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2015. Lecture Notes in Computer Science, vol 9285. Springer, Cham. doi:10.1007/978-3-319-23525-7_11

hyunjimoon/SBC documentation built on March 15, 2024, 3:18 a.m.