Brummer & Partners MathDataLab
Welcome to the home page of the Brummer & Partners MathDataLab. Here you can find information about the Lab and its activities.
Seminar with Jeffrey Herschel Giansiracusa
Room F11, Friday Feb 16, 9:00-10:00.
Title: A tour of some applications of persistent homology
Abstract: I will give an overview of persistent homology - how it is constructed and how we use it as a tool in data analysis. Originally it was popularised as a way of producing a description of the shape of a data set, but more recently it has taken on an alternative role as a component in functional data analysis pipelines where each element in a data set represents a complicated geometric object and persistent homology provides a way of comparing the topology and geometry of different elements, and potentially feeding the topology directly into statistical learning methods. I will describe how this works in some examples.
Seminar with Caroline Uhler, MIT
Room F11, Wednesday Feb 7, 13.15-14.15
Title: Your dreams may come true with MTP2
Abstract: We study probability distributions that are multivariate totally positive of order two (MTP2). Such distributions appear in various applications from ferromagnetism to Brownian tree models used in phylogenetics. We first describe some of the intriguing properties of such distributions with respect to conditional independence and graphical models. In the Gaussian setting, these translate into new statements about M-matrices that may be of independent interest to algebraists. We then consider the problem of nonparametric density estimation under MTP2. This requires us to develop new results in geometric combinatorics. In particular, we introduce bimonotone subdivisions of polytopes and show that the maximum likelihood estimator under MTP2 is a piecewise linear function that induces bimonotone subdivisions. In summary, MTP2 distributions not only have broad applications for data analysis, but also leads to interesting new problems in combinatorics, geometry, and algebra.
Carolone Uhler joined the MIT faculty ni 2015 as the Henry L. and Grace Doherty assistant professor in EECS and IDSS. She is a member of the LIDS, the Center for Statistics, Machine Learning at MIT, and the ORC. She holds a PhD in statistics from UC Berkely.
Her research focuses on mathematical statistics and computational biology, in particular on graphical models, causal inference and algebraic statistics, and on applications to learning gene regulatory networks and the development of geometric models for the organization of chromosomes.
Opening workshop on Nov 17, 2017.
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