Description:

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.

Changes to previous version:

Adding a write-up in written/toeblitz.pdf describing the package.

BibTeX Entry: Download

Supported Operating Systems: Platform Independent

Data Formats: Matlab, Octave

Tags: Kernel, Matrix Library, Gaussian Process, Toeplitz

Archive: download here

Other available revisons

Version	Changelog	Date
1.03	Adding a write-up in written/toeblitz.pdf describing the package.	August 13, 2014, 02:21:36
1.02	Adding tar directly instead of via link	August 25, 2013, 16:49:58
1.01	Text edits for readability	August 24, 2013, 23:45:47
1.0	Initial Announcement on mloss.org.	August 24, 2013, 23:37:43

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