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The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…
The demand for extracting rules from high dimensional real world data is increasing in various fields. However, the possible redundancy of such data sometimes makes it difficult to obtain a good generalization ability for novel samples. To…
The 3SUM conjecture has proven to be a valuable tool for proving conditional lower bounds on dynamic data structures and graph problems. This line of work was initiated by P\v{a}tra\c{s}cu (STOC 2010) who reduced 3SUM to an offline…
The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…
Numerous practical medical problems often involve data that possess a combination of both sparse and non-sparse structures. Traditional penalized regularizations techniques, primarily designed for promoting sparsity, are inadequate to…
We present an efficient algorithm to solve semirandom planted instances of any Boolean constraint satisfaction problem (CSP). The semirandom model is a hybrid between worst-case and average-case input models, where the input is generated by…
Machine learning and statistics typically focus on building models that capture the vast majority of the data, possibly ignoring a small subset of data as "noise" or "outliers." By contrast, here we consider the problem of jointly…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
We study sparse linear regression over a network of agents, modeled as an undirected graph and no server node. The estimation of the $s$-sparse parameter is formulated as a constrained LASSO problem wherein each agent owns a subset of the…
Many regression and classification procedures fit a parameterized function $f(x;w)$ of predictor variables $x$ to data $\{x_{i},y_{i}\}_1^N$ based on some loss criterion $L(y,f)$. Often, regularization is applied to improve accuracy by…
Online sparse linear regression is an online problem where an algorithm repeatedly chooses a subset of coordinates to observe in an adversarially chosen feature vector, makes a real-valued prediction, receives the true label, and incurs the…
Many statistical inference problems correspond to recovering the values of a set of hidden variables from sparse observations on them. For instance, in a planted constraint satisfaction problem such as planted 3-SAT, the clauses are sparse…
Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
Sparse linear regression is a fundamental problem in high-dimensional statistics, but strikingly little is known about how to efficiently solve it without restrictive conditions on the design matrix. We consider the (correlated) random…
Real time application of deep learning algorithms is often hindered by high computational complexity and frequent memory accesses. Network pruning is a promising technique to solve this problem. However, pruning usually results in irregular…
Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size t is planted in a random G(n,1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best…
The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task.…
In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these…
Sparse feature selection is necessary when we fit statistical models, we have access to a large group of features, don't know which are relevant, but assume that most are not. Alternatively, when the number of features is larger than the…