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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 multivariate linear regression model with shuffled data and additive noise, which arises in various correspondence estimation and matching problems. We focus on the denoising problem and characterize the minimax error rate up to logarithmic factors. We also analyze the performance of two versions of a computationally efficient estimator that(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)
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)
Pairwise comparison data arises in many domains, including tournament rankings, web search, and preference elicitation. Given noisy comparisons of a fixed subset of pairs of items, we study the problem of estimating the underlying comparison probabilities under the assumption of strong stochastic transitivity (SST). We also consider the noisy sorting(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)
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)
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)
We establish quantitative stability results for the entropy power inequality (EPI) in arbitrary dimension. 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(More)