Learning Linear Dynamical Systems with SemiParametric Least Squares
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Proceedings of the ThirtySecond Conference on Learning Theory, PMLR 99:27142802, 2019.
Abstract
We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, \emph{semiparametric} noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle inequality which demonstrates that this procedure provably mitigates the variance introduced by longterm dependencies. % We then demonstrate that prefiltered least squares yields, to our knowledge, the first algorithm that provably estimates the parameters of partiallyobserved linear systems that attains rates which do not not incur a worstcase dependence on the rate at which these dependencies decay. % The algorithm is provably consistent even for systems which satisfy the weaker \emph{marginal stability} condition obeyed by many classical models based on Newtonian mechanics. In this context, our semiparametric framework yields guarantees for both stochastic and worstcase noise.
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