Generative sequence modeling for infinite memory processes via predictive states
We consider estimating the one-step-ahead conditional distribution of a multivariate stochastic process. Many existing approaches rely on assumptions such as finite-range memory, sparsity, or additivity, which can be poorly suited to processes with long-range nonlinear interactions. However, without such structural assumptions, nonparametric estimation is challenging due to the curse of dimensionality. To address this challenge, we introduce a new estimation approach based on the predictive states of a process, possibly with infinite-range memory. We show that our estimator achieves fast convergence rates when the past history can be compressed into a low-dimensional statistic that is suf...
| Authors | Michael Wieck-Sosa, Cosma Rohilla Shalizi |
|---|---|
| Primary category | stat.ML |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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