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New provable techniques for learning and inference

in probabilistic graphical models

Andrej Risteski (MIT)

A common theme in machine learning is succinct modeling of distributions over large domains. Probabilistic graphical models are one of the most expressive frameworks for doing this. The two major tasks involving graphical models are learning and inference. Learning is the task of calculating the "best fit" model parameters from raw data, while inference is the task of answering probabilistic queries for a model with known parameters (e.g. what is the marginal distribution of a subset of variables, after conditioning…

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Sample complexity of population recovery

Yury Polyanskiy (MIT)

In this talk we will first consider a general question of estimating linear functional of the distribution based on the noisy samples from it. We discover that the (two-point) LeCam lower bound is in fact achievable by optimizing bias-variance tradeoff of an empirical-mean type of estimator. Next, we apply this general framework to the specific problem of population recovery. Namely, consider a random poll of sample size n conducted on a population of individuals, where each pollee is asked to…

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Optimal lower bounds for universal relation, and for samplers and finding duplicates in streams

Jelani Nelson (Harvard University)

Consider the following problem: we monitor a sequence of edgeinsertions and deletions in a graph on n vertices, so there are N = (n choose 2) possible edges (e.g. monitoring a stream of friend accepts/removals on Facebook). At any point someone may say "query()", at which point must output a random edge that exists in the graph at that time from a distribution that is statistically close to uniform. More specifically, with probability p our edge should come from a distribution close to uniform, and…

Find out more »## 2017 Charles River Lectures on Probability and Related Topics

The Charles River Lectures on Probability and Related Topics will be hosted by Harvard University on Monday, October 2, 2017 in Cambridge, MA. The lectures are jointly organized by Harvard University, Massachusetts Institute of Technology and Microsoft Research New England for the benefit of the greater Boston area mathematics community. The event features five lectures by distinguished researchers in the areas of probability and related topics. This year's lectures will be delivered by: Paul Bourgade (Courant Institute, NYU) Massimiliano Gubinelli…

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Inference in dynamical systems and the geometry of learning group actions

Sayan Mukherjee (Duke)

We examine consistency of the Gibbs posterior for dynamical systems using a classical idea in dynamical systems called the thermodynamic formalism in tracking dynamical systems. We state a variation formulation under which there is a unique posterior distribution of parameters as well as hidden states using using classic ideas from dynamical systems such as pressure and joinings. We use an example of consistency of hidden Markov with infinite lags as an application of our theory. We develop a geometric framework that characterizes…

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