Spectral Learning from a Single Trajectory under FiniteState Policies
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:361370, 2017.
Abstract
We present spectral methods of moments for learning sequential models from a single trajectory, in stark contrast with the classical literature that assumes the availability of multiple i.i.d. trajectories. Our approach leverages an efficient SVDbased learning algorithm for weighted automata and provides the first rigorous analysis for learning many important models using dependent data. We state and analyze the algorithm under three increasingly difficult scenarios: probabilistic automata, stochastic weighted automata, and reactive predictive state representations controlled by a finitestate policy. Our proofs include novel tools for studying mixing properties of stochastic weighted automata.
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