priorsense (version 1.1.0)

cjs_dist: Cumulative Jensen-Shannon divergence

Description

Computes the cumulative Jensen-Shannon distance between two samples.

Usage

cjs_dist(
  x,
  y,
  x_weights = NULL,
  y_weights = NULL,
  metric = TRUE,
  unsigned = TRUE,
  ...
)

Value

distance value based on CJS computation.

Arguments

x

numeric vector of draws from first distribution

y

numeric vector of draws from second distribution

x_weights

numeric vector (same length as x) of weights for the draws of the first distribution

y_weights

numeric vector (same length as y) of weights for the draws of the second distribution

metric

Logical; if TRUE, return square-root of CJS. Default is TRUE

unsigned

Logical; if TRUE then return max of CJS(P(x) || Q(x)) and CJS(P(-x) || Q(-x)). This ensures invariance to transformations such as PCA. Default is TRUE

...

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 \(\sqrt{ \sum (P(x) + Q(x))}\)

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

Examples

x <- rnorm(100)
y <- rnorm(100, 2, 2)
cjs_dist(x, y, x_weights = NULL, y_weights = NULL)