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The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is…
Sorting is one of the most basic primitives in many algorithms and data analysis tasks. Comparison-based sorting algorithms, like quick-sort and merge-sort, are known to be optimal when the outcome of each comparison is error-free. However,…
In robust statistics, the breakdown point of an estimator is the percentage of outliers with which an estimator still generates reliable estimation. The upper bound of breakdown point is 50%, which means it is not possible to generate…
Universality, namely distributional invariance, is a well-known property for many random structures. For example, it is known to hold for a broad range of variational problems with random input. Much less is known about the algorithmic…
Consider robot swarm wireless networks where mobile robots offload their computing tasks to a computing server located at the mobile edge. Our aim is to maximize the swarm lifetime through efficient exploitation of the correlation between…
Given a stream with frequencies $f_d$, for $d\in[n]$, we characterize the space necessary for approximating the frequency negative moments $F_p=\sum |f_d|^p$, where $p<0$ and the sum is taken over all items $d\in[n]$ with nonzero frequency,…
For many distributed algorithms, neighborhood size is an important parameter. In radio networks, however, obtaining this information can be difficult due to ad hoc deployments and communication that occurs on a collision-prone shared…
We propose a multi-hop diffusion strategy for a sensor network to perform distributed least mean-squares (LMS) estimation under local and network-wide energy constraints. At each iteration of the strategy, each node can combine intermediate…
Despite significant advances on distributed continuous-time optimization of multi-agent networks, there is still lack of an efficient algorithm to achieve the goal of distributed optimization at a pre-specified time. Herein, we design a…
In recent years, video analysis tools for automatically extracting meaningful information from videos are widely studied and deployed. Because most of them use deep neural networks which are computationally expensive, feeding only a subset…
We consider the problem of maximizing the lifetime of coverage (MLCP) of targets in a wireless sensor network with battery-limited sensors. We first show that the MLCP cannot be approximated within a factor less than $\ln n$ by any…
Federated learning (FL) algorithms usually sample a fraction of clients in each round (partial participation) when the number of participants is large and the server's communication bandwidth is limited. Recent works on the convergence…
This paper aims to propose and theoretically analyze a new distributed scheme for sparse linear regression and feature selection. The primary goal is to learn the few causal features of a high-dimensional dataset based on noisy observations…
We study high-dimensional robust statistics tasks in the streaming model. A recent line of work obtained computationally efficient algorithms for a range of high-dimensional robust estimation tasks. Unfortunately, all previous algorithms…
We study the problem of estimating the value of sums of the form $S_p \triangleq \sum \binom{x_i}{p}$ when one has the ability to sample $x_i \geq 0$ with probability proportional to its magnitude. When $p=2$, this problem is equivalent to…
We investigate the vulnerabilities of consensus-based distributed optimization protocols to nodes that deviate from the prescribed update rule (e.g., due to failures or adversarial attacks). We first characterize certain fundamental…
We consider message-efficient continuous random sampling from a distributed stream, where the probability of inclusion of an item in the sample is proportional to a weight associated with the item. The unweighted version, where all weights…
We study linear programming and general LP-type problems in several big data (streaming and distributed) models. We mainly focus on low dimensional problems in which the number of constraints is much larger than the number of variables. Low…
In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…
We study the {\em robust proper learning} of univariate log-concave distributions (over continuous and discrete domains). Given a set of samples drawn from an unknown target distribution, we want to compute a log-concave hypothesis…