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March 2018

One and two sided composite-composite tests in Gaussian mixture models

Alexandra Carpentier (Otto von Guericke Universitaet)

March 2 @ 11:00 am - 12:00 pm
E18-304

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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Statistical estimation under group actions: The Sample Complexity of Multi-Reference Alignment

Afonso Bandeira (NYU)

March 9 @ 11:00 am - 12:00 pm
E18-304

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;…

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When Inference is tractable

David Sontag (MIT)

March 16 @ 11:00 am - 12:00 pm
E18-304

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…

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Statistical theory for deep neural networks with ReLU activation function

Johannes Schmidt-Hieber (Leiden)

March 23 @ 11:00 am - 12:00 pm
E18-304

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…

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April 2018

Optimality of Spectral Methods for Ranking, Community Detections and Beyond

Jianqing Fan (Princeton University)

April 6 @ 11:00 am - 12:00 pm
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…

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Testing degree corrections in Stochastic Block Models

Subhabrata Sen (Microsoft)

April 13 @ 11:00 am - 12:00 pm
E18-304

Abstract: The community detection problem has attracted significant 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 t 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…

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Inference, Computation, and Visualization for Convex Clustering and Biclustering

Genevera Allen (Rice)

April 27 @ 11:00 am - 12:00 pm
E18-304

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…

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May 2018

Size-Independent Sample Complexity of Neural Networks

Ohad Shamir (Weizman Institute)

May 4 @ 11:00 am - 12:00 pm
E18-304

Abstract: I'll describe new bounds on the sample complexity of deep neural networks, based on the norms of the parameter matrices at each layer. In particular, we show how certain norms lead to the first explicit bounds which are fully independent of the network size (both depth and width), and are therefore applicable to arbitrarily large neural networks. These results are derived using some novel techniques, which may be of independent interest. Joint work with Noah Golowich (Harvard) and Alexander…

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Dynamic Incentive-aware Learning: Robust Pricing in Contextual Auctions

Adel Javanmard (USC)

May 11 @ 11:00 am - 12:00 pm
E18-304

Abstract: Motivated by pricing in ad exchange markets, we consider the problem of robust learning of reserve prices against strategic buyers in repeated contextual second-price auctions. Buyers’ valuations for an item depend on the context that describes the item. However, the seller is not aware of the relationship between the context and buyers’ valuations, i.e., buyers’ preferences. The seller’s goal is to design a learning policy to set reserve prices via observing the past sales data, and her objective is…

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Fitting a putative manifold to noisy data

Hariharan Narayanan (Tata Institute of Fundamental Research, Mumbai)

May 25 @ 11:00 am - 12:00 pm
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 whose Hausdorff distance to M is small and whose reach (normal injectivity radius) is not much smaller than the reach of M? This…

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