High dimensional Gaussian distribution

class pints.toy.HighDimensionalGaussianLogPDF(dimension=20, rho=0.5)

High-dimensional zero-mean multivariate Gaussian log pdf, with off-diagonal correlations.

Specifically, the covariance matrix Sigma is constructed so that diagonal elements are integers: Sigma_i,i = i and off-diagonal elements are Sigma_i,j = rho * sqrt(i) * sqrt(j).

Extends pints.toy.ToyLogPDF.

Parameters:

• dimension (int) – Dimensions of multivariate Gaussian distribution (which must exceed 1).
• rho (float) – The correlation between pairs of parameter dimensions. Note that this must be between `-1 / (dimension - 1) and 1 so that the covariance matrix is positive semi-definite.

distance(samples)

Returns approximate Kullback-Leibler divergence between samples and underlying distribution.

See pints.toy.ToyLogPDF.distance().

evaluateS1(x)

See pints.LogPDF.evaluateS1().

kl_divergence(samples)

Returns approximate Kullback-Leibler divergence between samples and underlying distribution.

The returned value is (near) zero for perfect sampling, and then increases as the error gets larger.

See: https://en.wikipedia.org/wiki/Kullback-Leibler_divergence

n_parameters()

See pints.LogPDF.n_parameters().

rho()

Returns rho (correlation between dimensions)

sample(n_samples)

See pints.toy.ToyLogPDF.sample().

suggested_bounds()

See pints.toy.ToyLogPDF.suggested_bounds().