Learning Ergodic Dynamical Systems from a Finite Trajectory
The paper gives high-probability learning guarantees from one dependent trajectory, rather than assuming independent samples.
Kachaiev, Villa, and Rosasco study discrete-time stochastic systems modeled as time-homogeneous Markov processes. They analyze nonlinear least squares for one-step prediction, with error measured against the process’s invariant measure. The result spells out how trajectory dependence changes standard statistical learning bounds, then extends the setup to higher-order systems, finite-state spaces, and Koopman operator learning. ArXiv · AI/CL/LG's note
Kachaiev, Villa, and Rosasco study discrete-time stochastic systems modeled as time-homogeneous Markov processes. They analyze nonlinear least squares for one-step prediction, with error measured against the process’s invariant measure. The result spells out how trajectory dependence changes standard statistical learning bounds, then extends the setup to higher-order systems, finite-state spaces, and Koopman operator learning. ArXiv · AI/CL/LG's note
score 4