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October 2017

Transport maps for Bayesian computation

Youssef Marzouk (MIT)

October 6, 2017 @ 11:00 am - 12:00 pm

Abstract: Integration against an intractable probability measure is among the fundamental challenges of Bayesian inference. A useful approach to this problem seeks a deterministic coupling of the measure of interest with a tractable "reference" measure (e.g., a standard Gaussian). This coupling is induced by a transport map, and enables direct simulation from the desired measure simply by evaluating the transport map at samples from the reference. Approximate transports can also be used to "precondition" standard Monte Carlo schemes. Yet characterizing a…

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Additivity of Information in Deep Generative Networks: The I-MMSE Transform Method

Galen Reeves (Duke University)

October 13, 2017 @ 11:00 am - 12:00 pm

Abstract:  Deep generative networks are powerful probabilistic models that consist of multiple stages of linear transformations (described by matrices) and non-linear, possibly random, functions (described generally by information channels). These models have gained great popularity due to their ability to characterize complex probabilistic relationships arising in a wide variety of inference problems. In this talk, we introduce a new method for analyzing the fundamental limits of statistical inference in settings where the model is known. The validity of our method can…

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Structure in multi-index tensor data: a trivial byproduct of simpler phenomena?

John Cunningham (Columbia)

October 19, 2017 @ 4:30 pm - 5:30 pm

Abstract:  As large tensor-variate data become increasingly common across applied machine learning and statistics, complex analysis methods for these data similarly increase in prevalence.  Such a trend offers the opportunity to understand subtler and more meaningful features of the data that, ostensibly, could not be studied with simpler datasets or simpler methodologies.  While promising, these advances are also perilous: novel analysis techniques do not always consider the possibility that their results are in fact an expected consequence of some simpler, already-known…

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Inference in dynamical systems and the geometry of learning group actions

Sayan Mukherjee (Duke)

October 20, 2017 @ 11:00 am - 12:00 pm

Abstract: 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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On Learning Theory and Neural Networks

Amit Daniely (Google)

October 27, 2017 @ 11:00 am - 12:00 pm

Abstract:  Can learning theory, as we know it today, form a theoretical basis for neural networks. I will try to discuss this question in light of two new results -- one positive and one negative. Based on joint work with Roy Frostig, Vineet Gupta and Yoram Singer, and with Vitaly Feldman Biography: Amit Daniely is an Assistant Professor at the Hebrew University in Jerusalem, and a research scientist at Google Research, Tel-Aviv. Prior to that, he was a research scientist at Google Research, Mountain-View. Even…

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November 2017

Unbiased Markov chain Monte Carlo with couplings

Pierre Jacob (Harvard)

November 1, 2017 @ 11:00 am - 12:00 pm

Abstract: Markov chain Monte Carlo methods provide consistent approximations of integrals as the number of iterations goes to infinity. However, these estimators are generally biased after any fixed number of iterations, which complicates both parallel computation. In this talk I will explain how to remove this burn-in  bias by using couplings of Markov chains and a telescopic sum argument, inspired by Glynn & Rhee (2014). The resulting unbiased estimators can be computed independently in parallel, and averaged. I will present…

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Statistics, Computation and Learning with Graph Neural Networks

Joan Bruna Estrach (NYU)

November 3, 2017 @ 11:00 am - 12:00 pm

Abstract:  Deep Learning, thanks mostly to Convolutional architectures, has recently transformed computer vision and speech recognition. Their ability to encode geometric stability priors, while offering enough expressive power, is at the core of their success. In such settings, geometric stability is expressed in terms of local deformations, and it is enforced thanks to localized convolutional operators that separate the estimation into scales. Many problems across applied sciences, from particle physics to recommender systems, are formulated in terms of signals defined over…

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Generative Models and Compressed Sensing

Alex Dimakis (University of Texas at Austin)

November 17, 2017 @ 11:00 am - 12:00 pm

Abstract:   The goal of compressed sensing is to estimate a vector from an under-determined system of noisy linear measurements, by making use of prior knowledge in the relevant domain. For most results in the literature, the structure is represented by sparsity in a well-chosen basis. We show how to achieve guarantees similar to standard compressed sensing but without employing sparsity at all. Instead, we assume that the unknown vectors lie near the range of a generative model, e.g. a GAN…

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December 2017

Challenges in Developing Learning Algorithms to Personalize Treatment in Real Time

Susan Murphy (Harvard)

December 1, 2017 @ 11:00 am - 12:00 pm

Abstract:  A formidable challenge in designing sequential treatments is to  determine when and in which context it is best to deliver treatments.  Consider treatment for individuals struggling with chronic health conditions.  Operationally designing the sequential treatments involves the construction of decision rules that input current context of an individual and output a recommended treatment.   That is, the treatment is adapted to the individual's context; the context may include  current health status, current level of social support and current level of adherence…

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Stochastics and Statistics Seminar

Alex Bloemendal (Broad Institute)

December 8, 2017 @ 11:00 am - 12:00 pm

Biography: Alex Bloemendal is a computational scientist at the Broad Institute of MIT and Harvard and at the Analytic and Translational Genetics Unit of Massachusetts General Hospital. As a member of Broad institute member Ben Neale’s lab, Bloemendal leads a group in developing new methods to analyze genetic data, harnessing its unprecedented scope and scale to discover the genetic causes of disease. He also co-founded and directs the Models, Inference & Algorithms initiative at the Broad, bridging computational biology, mathematical…

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