Generative sequence modeling for infinite memory processes via predictive states

תקציר מקורי באנגליתarXiv:2609.38524v1 Announce Type: cross Abstract: 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 sufficient for predicting the future. Specifically, we s