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经验风险最小化与动力系统模型的复杂度AI 解读

A dynamical model consists of a continuous self-map $T:\mathcal{X}\to \mathcal{X}$ of a compact state space $\mathcal{X}$ and a continuous observation function $f:\mathcal{X}\to \mathbb{R}$. This paper considers the fitting of a parametrized family of dynamical models to an observed real-valued stochastic process using empirical risk minimization. The limiting behavior of the minimum risk parameters is studied in a general setting. We establish a general convergence theorem…

遍历过程下分类与回归估计的局限AI 解读

We answer two open questions concerning the existence of universal schemes for classification and regression estimation from stationary ergodic processes. It is shown that no measurable procedure can produce weakly consistent regression estimates from every bivariate stationary ergodic process, even if the covariate and response variables are restricted to take values in the unit interval. It is further shown that no measurable procedure can produce weakly consistent…