tripy

A package for efficient¹ likelihood evaluation and sampling for Multivariate Normal distributions where the covariance matrix:

• Is Separable, i.e. can be expressed as the Kronecker product of the covariance over different dimensions (e.g. space and time);
• May have Exponential correlation (i.e. (block-) tridiagonal precision matrix) in one or more dimensions;
• Is polluted with uncorrelated scalar or vector noise.

Structure

base: Base class for problem formulation, taken from taralli. Likely to be removed in a future update.

utils: Utility functions for efficient linear algebra invovling tridiagonal and Kronecker product matrices.

loglikelihood: Functions for efficient loglikelihood evaluation.

kernels: Formulation of commonly used kernels.

sampling: Functions for efficient sampling.

Usage

TODOs

• Validation of all functions against reference implementations.
• Documentation, including examples and timing tests.
• Unit and integration testing.
• Improve this README by including mathematical notation and references.

Footnotes

1. In the general case, exact likelihood evaluation has O(N³) computational complexity and O(N²) memory requirements. The term "efficient" is used here to refer to the reduction of complexity and memory usage by utilizing the sparsity and Kronecker product structure of the covariance matrix. ↩