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Predictive rate-distortion analysis suffers from the curse of dimensionality:clustering arbitrarily long pasts to retain information about arbitrarily longfutures requires resources that typically grow exponentially with length. Thechallenge is compounded for infinite-order Markov processes, since conditioningon finite sequences cannot capture all of their past dependencies. Spectralarguments show that algorithms which cluster finite-length sequences faildramatically when the underlying process has long-range temporal correlationsand can fail even for processes generated by finite-memory hidden Markovmodels. We circumvent the curse of dimensionality in rate-distortion analysisof infinite-order processes by casting predictive rate-distortion objectivefunctions in terms of the forward- and reverse-time causal states ofcomputational mechanics. Examples demonstrate that the resulting causalrate-distortion theory substantially improves current predictiverate-distortion analyses.

Circumventing the Curse of Dimensionality in Prediction: Causal Rate-Distortion for Infinite-Order Markov Processes