We present a mathematical and computational framework for learning dynamical system from noisy observations of few trajectories subject to side information. Side information is any knowledge we might have about the would like learn, besides trajectory data, typically inferred domain-specific or basic principles scientific discipline. are interested in explicitly integrating into process order c...

A source sequence is to be guessed with some fidelity based on a rate-limited description of an observed which it correlated. The tension between the rate and exponential growth power mean required number guesses quantified. This can viewed as guessing version classical indirect-rate-distortion problem Dobrushin-Tsybakov’62 Witsenhausen’80. Judicious choices correlated sequence, r...

Collaborative filtering (CF) has been one of the most important and popular recommendation methods, which aims at predicting users’ preferences (ratings) based on their past behaviors. Recently, various types side information beyond explicit ratings users give to items, such as social connections among metadata have introduced into CF shown be useful for improving performance. However, previous...

We study the problem of Private Information Retrieval (PIR) in the presence of prior side information. The problem setup includes a database of K independent messages possibly replicated on several servers, and a user that needs to retrieve one of these messages. In addition, the user has some prior side information in the form of a subset of M messages, not containing the desired message and u...