Developed by 10 MIT faculty members at IDSS, this seven-week course is specially designed for data scientists, business analysts, engineers and technical managers looking to learn strategies to harness data. Offered by MIT xPRO. Course begins Sept 10, 2018.
Abstract: We consider the problem of data feature selection prior to inference task specification, which is central to high-dimensional learning. Introducing natural notions of universality for such problems, we show a local equivalence among them. Our analysis is naturally expressed via information geometry, and represents a conceptually and practically useful learning methodology. The development reveals the key roles of the singular value decomposition, Hirschfeld-Gebelein-Renyi maximal correlation, canonical correlation and principle component analyses, Tishby's information bottleneck, Wyner's common information, Ky Fan…
Title: Strong data processing inequalities and information percolation Abstract: The data-processing inequality, that is, $I(U;Y) \le I(U;X)$ for a Markov chain $U \to X \to Y$, has been the method of choice for proving impossibility (converse) results in information theory and many other disciplines. A channel-dependent improvement is called the strong data-processing inequality (or SDPI). In this talk we will: a) review SDPIs; b) show how point-to-point SDPIs can be combined into an SDPI for a network; c) show recent…
Title: Graphical models under total positivity Abstract: We discuss properties of distributions that are multivariate totally positive of order two (MTP2). Such distributions appear in the context of positive dependence, ferromagnetism in the Ising model, and various latent models. While such distributions have a long history in probability theory and statistical physics, in this talk I will discuss such distributions in the context of high dimensional statistics and graphical models. In particular, I will show that MTP2 in the Gaussian…
Abstract: Concentration of measure refers to a collection of tools and results from analysis and probability theory that have been used in many areas of pure and applied mathematics. Arguably, the first data science application of measure concentration (under the name ‘‘blowing-up lemma’’) is the proof of strong converses in multiuser information theory by Ahlswede, G'acs and K"orner in 1976. Since then, measure concentration has found applications in many other information theoretic problems, most notably the converse (impossibility) results in…
Abstract: The Graph Matching problem is a robust version of the Graph Isomorphism problem: given two not-necessarily-isomorphic graphs, the goal is to find a permutation of the vertices which maximizes the number of common edges. We study a popular average-case variant; we deviate from the common heuristic strategy and give the first quasi-polynomial time algorithm, where previously only sub-exponential time algorithms were known. Based on joint work with Boaz Barak, Chi-Ning Chou, Zhixian Lei, and Yueqi Sheng. Biography: Tselil Schramm is a postdoc in theoretical…
Abstract: Local geometric analysis is a method to define a coordinate system in a small neighborhood in the space of distributions over a given alphabet. It is a powerful technique since the notions of distance, projection, and inner product defined this way are useful in the optimization problems involving distributions, such as regressions. It has been used in many places in the literature such as correlation analysis, correspondence analysis. In this talk, we will go through some of the basic…
Abstract: In this talk, we investigate statistical learning and estimation under local privacy constraints, where data providers do not trust the collector of the data and so privatize their data before it is even collected. We identify fundamental tradeoffs between statistical utility and privacy in such local models of privacy, providing instance-specific bounds for private estimation and learning problems by developing local minimax risks. In contrast to approaches based on worst-case (minimax) error, which are conservative, this allows us to…
Developed by 10 MIT faculty members at IDSS, this seven-week course is specially designed for data scientists, business analysts, engineers and technical managers looking to learn strategies to harness data. Offered by MIT xPRO. Course begins Oct. 15, 2018.
This seminar consists of a series of lectures each followed by a period of informal discussion and social. The topics are at the nexus of information theory, inference, causality, estimation, and non-convex optimization. The lectures are intended to be tutorial in nature with the goal of learning about interesting and exciting topics rather than merely hearing about the most recent results. The topics are driven by the interests of the speakers, and with the exception of the two lectures on…
