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Consider a noisy linear observation model with an unknown permutation, based on observing y = &#x03A0;*Ax* + w, where x* &#x2208; &#x211D;<sup>d</sup> is an unknown vector, &#x03A0;* is an unknown n &#x00D7; n permutation matrix, and w &#x2208; &#x211D;<sup>n</sup> is additive Gaussian noise. We analyze the problem of permutation recovery in a random design(More)
We consider the problem of a social group of users trying to obtain a " universe " of files, first from a server and then via exchange amongst themselves. We consider the selfish file-exchange paradigm of give-and-take, whereby two users can exchange files only if each has something unique to offer the other. We are interested in maximizing the number of(More)
We establish quantitative stability results for the entropy power inequality (EPI). Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they must be close to Gaussian densities in the quadratic Wasserstein distance. Further, if one of the densities is log-concave and the other is Gaussian, then the deficit in the EPI(More)
The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the minimax error rate that is sharp up to logarithmic factors. We also analyze the performance of two versions of a(More)
We address a classical problem concerning energy efficiency in sensor networks. In particular, we consider the problem of maximizing the lifetime of coverage of targets in a wireless sensor network with battery-limited sensors. We first show that the problem cannot be approximated within a factor less than <inline-formula> <tex-math notation="LaTeX">$\ln n$(More)
We consider a variable-length source coding problem subject to local decodability constraints. In particular, we investigate the blocklength scaling behavior attainable by encodings of r-sparse binary sequences, under the constraint that any source bit can be correctly decoded upon probing at most d codeword bits. We consider both adaptive and non-adaptive(More)
In this paper, we investigate the approximability of two node deletion problems. Given a vertex weighted graph G = (V, E) and a specified, or " distinguished " vertex p ∈ V , MDD(min) is the problem of finding a minimum weight vertex set S ⊆ V \ {p} such that p becomes the minimum degree vertex in G[V \ S]; and MDD(max) is the problem of finding a minimum(More)
It has been experimentally observed that distributed implementations of mini-batch stochastic gradient descent (SGD) algorithms exhibit speedup saturation and decaying generalization ability beyond a particular batch-size. In this work, we present an analysis hinting that high similarity between concurrently processed gradients may be a cause of this(More)
Given a universe U of n elements and a collection of subsets S of U, the maximum disjoint set cover problem (DSCP) is to partition S into as many set covers as possible, where a set cover is defined as a collection of subsets whose union is U. We consider the online DSCP, in which the subsets arrive one by one (possibly in an order chosen by an adversary),(More)