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We analyze a simple prefiltered variation of the least squares estimator forthe problem of estimation with biased, semi-parametric noise, an error modelstudied more broadly in causal statistics and active learning. We prove anoracle inequality which demonstrates that this procedure provably mitigates thevariance introduced by long-term dependencies. We then demonstrate thatprefiltered least squares yields, to our knowledge, the first algorithm thatprovably estimates the parameters of partially-observed linear systems thatattains rates which do not not incur a worst-case dependence on the rate atwhich these dependencies decay. The algorithm is provably consistent even forsystems which satisfy the weaker marginal stability condition obeyed by manyclassical models based on Newtonian mechanics. In this context, oursemi-parametric framework yields guarantees for both stochastic and worst-casenoise.

Learning Linear Dynamical Systems with Semi-Parametric Least Squares