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A Constraint Generation Approach to Learning Stable Linear Dynamical Systems (2007)

Sajid Siddiqi

Byron Boots

Geoff Gordon

Abstract

Stability is a desirable characteristic for linear dynamical systems, but it is often
ignored by algorithms that learn these systems from data. We propose a novel
method for learning stable linear dynamical systems: we formulate an approximation
of the problem as a convex program, start with a solution to a relaxed version
of the program, and incrementally add constraints to improve stability. Rather
than continuing to generate constraints until we reach a feasible solution, we test
stability at each step; because the convex program is only an approximation of the
desired problem, this early stopping rule can yield a higher-quality solution. We
apply our algorithm to the task of learning dynamic textures from image sequences
as well as to modeling biosurveillance drug-sales data. The constraint generation
approach leads to noticeable improvement in the quality of simulated sequences.
We compare our method to those of Lacy and Bernstein, with positive results
in terms of accuracy, quality of simulated sequences, and efficiency.

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Approximate BibTeX Entry

@inproceedings{siddiqi_nips07,
    Month = {December},
    Year = {2007},
    Booktitle = {Advances in Neural Information Processing Systems},
    Author = { Sajid Siddiqi Byron Boots Geoff Gordon },
    Title = {A Constraint Generation Approach to Learning Stable Linear Dynamical Systems}
}

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