jankoune / tripy

A package for efficient likelihood evaluation and sampling for Multivariate Normal distributions with structured covariance matrices

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. ↩

tripy's Issues

Error handling for BLAS/LAPACK calls

Scipy wrapped BLAS/LAPACK functions are used extensively in tripy.loglikelihood and tripy.utils, but no error handling is implemented. All of these functions return the info integer, which is zero on success and nonzero otherwise. A check function could be used after each call to raise an error and display the appropriate message if info != 0. This approach is used in scipy.

Input verification for space/time coordinates

Currently many of utilities and loglikelihood evaluation functions can behave unpredictably if the vector of coordinates passed to them is not ordered, (e.g. inv_cov_vec_1D). Input verification should be implemented, preferably during the problem formulation rather than during the likelihood evaluations. In the short-term, the user-facing likelihood and utility functions should be updated to make this clear in the docstrings and documentation.

Migrating to Github

Error in `kron_loglike_ND_tridiag`

kron_loglike_ND_tridiag gives incorrect results when the parameters of the correlation differ between dimensions. Temporarily disabled until the issue is fixed.

Tasks required to have an acceptable initial version of the package

Summary of tasks (to be extended):

• Add docstrings to all functions.
• Release on PyPI.
• Implement thorough testing.
• Create documentation e.g. using Sphinx, show simple usage examples and comparison with reference case.
• Cite relevant papers.
• Add testing for documentation.

Allow std_meas = None in chol_loglike_2D

Similar to what was done for chol_loglike_1D, it should be possible to obtain a solution for the 2D case with no noise by directly calculating the inverse of the covariance matrix.

Publish on Anaconda

Add chol_loglike_2D with non-Exponential covariance in space test