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Poster

Long-Context Linear System Identification

Oğuz Kaan Yüksel · Mathieu Even · Nicolas Flammarion

Hall 3 + Hall 2B #493
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Fri 25 Apr midnight PDT — 2:30 a.m. PDT

Abstract: This paper addresses the problem of long-context linear system identification, where the state xt of the system at time t depends linearly on previous states xs over a fixed context window of length p. We establish a sample complexity bound that matches the _i.i.d._ parametric rate, up to logarithmic factors for a broad class of systems, extending previous work that considered only first-order dependencies. Our findings reveal a learning-without-mixing'' phenomenon, indicating that learning long-context linear autoregressive models is not hindered by slow mixing properties potentially associated with extended context windows. Additionally, we extend these results to _(i)_ shared low-rank feature representations, where rank-regularized estimators improve rates with respect to dimensionality, and _(ii)_ misspecified context lengths in strictly stable systems, where shorter contexts offer statistical advantages.

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