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- W4299441796 abstract "We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate distortion theory to use causal shielding---a natural principle of learning. We study two distinct cases of causal inference: optimal causal filtering and optimal causal estimation. Filtering corresponds to the ideal case in which the probability distribution of measurement sequences is known, giving a principled method to approximate a system's causal structure at a desired level of representation. We show that, in the limit in which a model complexity constraint is relaxed, filtering finds the exact causal architecture of a stochastic dynamical system, known as the causal-state partition. From this, one can estimate the amount of historical information the process stores. More generally, causal filtering finds a graded model-complexity hierarchy of approximations to the causal architecture. Abrupt changes in the hierarchy, as a function of approximation, capture distinct scales of structural organization. For nonideal cases with finite data, we show how the correct number of underlying causal states can be found by optimal causal estimation. A previously derived model complexity control term allows us to correct for the effect of statistical fluctuations in probability estimates and thereby avoid over-fitting." @default.
- W4299441796 created "2022-10-02" @default.
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- W4299441796 date "2007-08-11" @default.
- W4299441796 modified "2023-09-23" @default.
- W4299441796 title "Optimal Causal Inference: Estimating Stored Information and Approximating Causal Architecture" @default.
- W4299441796 doi "https://doi.org/10.48550/arxiv.0708.1580" @default.
- W4299441796 hasPublicationYear "2007" @default.
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