Past Events › Stochastics and Statistics Seminar Series
The MIT Statistics and Data Science Center hosts guest lecturers from around the world in this weekly seminar.
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Stochastics and Statistics Seminar Series: Fitting a putative manifold to noisy data
Hariharan Narayanan (Tata Institute of Fundamental Research, Mumbai)
E18-304
Abstract: We give a solution to the following question from manifold learning. Suppose data belonging to a high dimensional Euclidean space is drawn independently, identically distributed from a measure supported on a low dimensional twice differentiable embedded compact manifold M, and is corrupted by a small amount of i.i.d gaussian noise. How can we produce a manifold $M_o$ whose Hausdorff distance to M is small and whose reach (normal injectivity radius) is not much smaller than the reach of M?…
Find out more »Stochastics and Statistics Seminar – Dynamic Incentive-aware Learning: Robust Pricing in Contextual Auctions
Adel Javanmard (USC)
MIT Building E18, Room 304
MIT Statistics and Data Science Center host guest lecturers from around the world in this weekly seminar.
Find out more »Stochastics and Statistics Seminar: Size-Independent Sample Complexity of Neural Networks
Ohad Shamir (Weizman Institute)
MIT Building E18, Room 304
MIT Statistics and Data Science Center host guest lecturers from around the world in this weekly seminar.
Find out more »Inference, Computation, and Visualization for Convex Clustering and Biclustering
Genevera Allen (Rice)
MIT Building E18, Room 304
Abstract: Hierarchical clustering enjoys wide popularity because of its fast computation, ease of interpretation, and appealing visualizations via the dendogram and cluster heatmap. Recently, several have proposed and studied convex clustering and biclustering which, similar in spirit to hierarchical clustering, achieve cluster merges via convex fusion penalties. While these techniques enjoy superior statistical performance, they suffer from slower computation and are not generally conducive to representation as a dendogram. In the first part of the talk, we present new convex…
Find out more »Stochastics and Statistics Seminars: Testing degree corrections in Stochastic Block Models
Subhabrata Sen (Microsoft )
MIT Building E18, Room 304
Abstract: The community detection problem has attracted signicant attention in re- cent years, and it has been studied extensively under the framework of a Stochas- tic Block Model (SBM). However, it is well-known that SBMs fit real data very poorly, and various extensions have been suggested to replicate characteristics of real data. The recovered community assignments are often sensitive to the model used, and this naturally begs the following question: Given a network with community structure, how to decide whether…
Find out more »Optimality of Spectral Methods for Ranking, Community Detections and Beyond
Jianqing Fan (Princeton University)
E18-304
Abstract: Spectral methods have been widely used for a large class of challenging problems, ranging from top-K ranking via pairwise comparisons, community detection, factor analysis, among others. Analyses of these spectral methods require super-norm perturbation analysis of top eigenvectors. This allows us to UNIFORMLY approximate elements in eigenvectors by linear functions of the observed random matrix that can be analyzed further. We first establish such an infinity-norm pertubation bound for top eigenvectors and apply the idea to several challenging problems…
Find out more »Statistical theory for deep neural networks with ReLU activation function
Johannes Schmidt-Hieber (Leiden)
Abstract: The universal approximation theorem states that neural networks are capable of approximating any continuous function up to a small error that depends on the size of the network. The expressive power of a network does, however, not guarantee that deep networks perform well on data. For that, control of the statistical estimation risk is needed. In the talk, we derive statistical theory for fitting deep neural networks to data generated from the multivariate nonparametric regression model. It is shown…
Find out more »When Inference is Tractable
David Sontag (MIT)
MIT Building E18, Room 304
Abstract: A key capability of artificial intelligence will be the ability to reason about abstract concepts and draw inferences. Where data is limited, probabilistic inference in graphical models provides a powerful framework for performing such reasoning, and can even be used as modules within deep architectures. But, when is probabilistic inference computationally tractable? I will present recent theoretical results that substantially broaden the class of provably tractable models by exploiting model stability (Lang, Sontag, Vijayaraghavan, AI Stats ’18), structure in…
Find out more »Statistical estimation under group actions: The Sample Complexity of Multi-Reference Alignment
Afonso Bandeira (NYU)
MIT Building E18, Room 304
Abstract: Many problems in signal/image processing, and computer vision amount to estimating a signal, image, or tri-dimensional structure/scene from corrupted measurements. A particularly challenging form of measurement corruption are latent transformations of the underlying signal to be recovered. Many such transformations can be described as a group acting on the object to be recovered. Examples include the Simulatenous Localization and Mapping (SLaM) problem in Robotics and Computer Vision, where pictures of a scene are obtained from different positions andorientations; Cryo-Electron…
Find out more »One and two sided composite-composite tests in Gaussian mixture models
Alexandra Carpentier (Otto von Guericke Universitaet)
MIT Building E18, Room 304
Abstract: Finding an efficient test for a testing problem is often linked to the problem of estimating a given function of the data. When this function is not smooth, it is necessary to approximate it cleverly in order to build good tests. In this talk, we will discuss two specific testing problems in Gaussian mixtures models. In both, the aim is to test the proportion of null means. The aforementioned link between sharp approximation rates of non-smooth objects and minimax testing…
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