Related papers: Worst-Case Source for Distributed Compression with…
An energy-limited source trying to transmit multiple packets to a destination with possibly different sizes is considered. With limited energy, the source cannot potentially transmit all bits of all packets. In addition, there is a delay…
We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…
We consider the problem of estimating the parameters a Gaussian Mixture Model with K components of known weights, all with an identity covariance matrix. We make two contributions. First, at the population level, we present a sharper…
The goal of this thesis is to study the compression problems arising in distributed computing systematically. In the first part of the thesis, we study gradient compression for distributed first-order optimization. We begin by establishing…
We formulate quantum rate-distortion theory in the most general setting where classical side information is included in the tradeoff. Using a natural distortion measure based on entanglement fidelity and specializing to the case of an…
One of the most popular algorithms for clustering in Euclidean space is the $k$-means algorithm; $k$-means is difficult to analyze mathematically, and few theoretical guarantees are known about it, particularly when the data is {\em…
This work considers the problem of transmitting multiple compressible sources over a network at minimum cost. The aim is to find the optimal rates at which the sources should be compressed and the network flows using which they should be…
This paper derives fundamental limits on the performance of compressive classification when the source is a mixture of Gaussians. It provides an asymptotic analysis of a Bhattacharya based upper bound on the misclassification probability…
The mixture of Gaussian distributions, a soft version of k-means , is considered a state-of-the-art clustering algorithm. It is widely used in computer vision for selecting classes, e.g., color, texture, and shapes. In this algorithm, each…
This paper is concerned with quantum data compression of asymptotically many independent and identically distributed copies of ensembles of mixed quantum states. The encoder has access to a side information system. The figure of merit is…
The weighted MAX k-CUT problem involves partitioning a weighted undirected graph into k subsets, or colors, to maximize the sum of the weights of edges between vertices in different subsets. This problem has significant applications across…
The problem of optimal real-time transmission of a Markov source under constraints on the expected number of transmissions is considered, both for the discounted and long term average cases. This setup is motivated by applications where…
We consider the problem of determining the top-$k$ largest measurements from a dataset distributed among a network of $n$ agents with noisy communication links. We show that this scenario can be cast as a distributed convex optimization…
This paper examines the theory pertaining to lossless compression of correlated sources located at the edge of a network. Importantly, communication between nodes is prohibited. In particular, a method that combines correlated source coding…
This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal…
The distributed remote source coding (so-called CEO) problem is studied in the case where the underlying source, not necessarily Gaussian, has finite differential entropy and the observation noise is Gaussian. The main result is a new lower…
We investigate the optimal performance of dense sensor networks by studying the joint source-channel coding problem. The overall goal of the sensor network is to take measurements from an underlying random process, code and transmit those…
We propose and study the problem of distribution-preserving lossy compression. Motivated by recent advances in extreme image compression which allow to maintain artifact-free reconstructions even at very low bitrates, we propose to optimize…
The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…
This paper derives fundamental limits associated with compressive classification of Gaussian mixture source models. In particular, we offer an asymptotic characterization of the behavior of the (upper bound to the) misclassification…