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通过随机游走转移耦合对齐与比较有向网络AI 解读

Abstract We describe and study a transport-based procedure called network optimal transition coupling (NetOTC) for the comparison and alignment of two networks. The networks of interest may be directed or undirected, weighted or unweighted, and may have distinct vertex sets of different sizes. Given two networks and a cost function relating their vertices, NetOTC finds a transition coupling of their associated random walks having minimum expected cost. The minimizing cost…

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…

若干动力系统中最大似然估计的一致性AI 解读

We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Our proof involves ideas from both information theory and dynamical systems. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum…