Learning Structure from Data: Applications, Algorithms, Statistical Efficiency and General Frameworks

Abstract:

In machine learning, many inference problems require a known structure which is unobserved in the real world. This structure is usually expressed as a graphical model which provides a way to represent entities along with their dependencies. Structure learning refers to the problem of learning the topology (and parameters) of the graphical model from observed data. My research in this area focus on developing computationally and statistically efficient algorithms, understanding their behavior using concepts such as convergence and sample complexity, and designing new modeling paradigms such as models rooted in game theory.

This talk will first focus on the problem of learning probabilistic and game-theoretical structures from data. Motivated by these goals, this talk introduces recent techniques for the approximate optimization of a discontinuous and NP-hard objective function, as well as convergence rates for a class of objective functions for which only biased estimates of the gradient are available. On the applied side, we will discuss issues of interpretability and regularization, and show interesting findings in political science (U.S. congressional voting records), neuroscience (cocaine addiction) and genetics (cancer).

The above learning problems are instances of a more general problem: regularized loss minimization (RLM). Understanding the behavior of this general problem is of great importance, given that RLM is a common approach to solving many machine learning problems. This talk introduces novel results of loss consistency, norm consistency, sparsistency and sign consistency for RLM. These results pertain to several problems in the literature, such as the estimation of exponential family distributions (e.g. learning the graph structure of Gaussian or discrete MRFs), generalized linear models (e.g. linear regression, compressed sensing), matrix factorization problems (e.g. exponential-family PCA, max-margin matrix factorization), nonparametric linear regression (with an infinite set of basis functions), nonparametric clustering with exponential families (where the number of clusters is not fixed and possibly infinite), PAC-Bayes learning (e.g. classification, structured prediction) as well as several regularization techniques.

Bio:

Jean Honorio is a postdoctoral associate at MIT CSAIL. He received his PhD in Computer Science from Stony Brook University in 2012. His research focuses on developing computationally and statistically efficient algorithms for high dimensional problems (big data), and designing new modeling paradigms such as models rooted in game theory. His theoretical and algorithmic work is directly motivated by, and contributes to, applications in political science, neuroscience and genetics.