5 research outputs found
Spectral learning of dynamic systems from nonequilibrium data
Observable operator models (OOMs) and related models are one of the most
important and powerful tools for modeling and analyzing stochastic systems.
They exactly describe dynamics of finite-rank systems and can be efficiently
and consistently estimated through spectral learning under the assumption of
identically distributed data. In this paper, we investigate the properties of
spectral learning without this assumption due to the requirements of analyzing
large-time scale systems, and show that the equilibrium dynamics of a system
can be extracted from nonequilibrium observation data by imposing an
equilibrium constraint. In addition, we propose a binless extension of spectral
learning for continuous data. In comparison with the other continuous-valued
spectral algorithms, the binless algorithm can achieve consistent estimation of
equilibrium dynamics with only linear complexity
Improving Predictive State Representations via Gradient Descent
Predictive state representations (PSRs) model dynamical systems using appropriately chosen predictions about future observations as a representation of the current state. In contrast to the hidden states posited by HMMs or RNNs, PSR states are directly observable in the training data; this gives rise to a moment-matching spectral algorithm for learning PSRs that is computationally efficient and statistically consistent when the model complexity matches that of the true system generating the data. In practice, however, model mismatch is inevitable and while spectral learning remains appealingly fast and simple it may fail to find optimal models. To address this problem, we investigate the use of gradient methods for improving spectrally-learned PSRs. We show that only a small amount of additional gradient optimization can lead to significant performance gains, and moreover that initializing gradient methods with the spectral learning solution yields better models in significantly less time than starting from scratch