Toeblitz Toolkit for Fast Toeplitz Matrix Operations 1.03

john cunningham, william zhang — Wed, 13 Aug 2014 02:21:36 -0000

Toeplitz matrices arise naturally in machine learning whenever a stationary kernel is evaluated on equally spaced indices; one common example is the use of Gaussian processes to model time series data. Unfortunately, the usefulness of kernel methods involving Toeplitz matrices is limited by both the O(n^2) memory requirements and the O(n^3) runtime complexity of key matrix operations such as determinants and linear solves.

Toeblitz is a MATLAB/Octave package for operations on positive definite Toeplitz matrices. It uses existing findings from linear algebra to perform the following for any positive definite Toeplitz matrix T:

(i) solve Toeplitz systems Tx = b in O(n*log(n)) time and O(n) memory

(ii) compute Toeplitz matrix inverses T^(-1) (with free log determinant) in O(n^2) time and memory

(iii) compute Toeplitz log determinants (without inverses) in O(n^2) time and O(n) memory

(iv) compute traces of products A*T for any matrix A and a Toeplitz matrix T, in minimal O(n^2) time and memory.

mloss.org Toeblitz Toolkit for Fast Toeplitz Matrix Operations

Toeblitz Toolkit for Fast Toeplitz Matrix Operations 1.03