Related papers: An algorithm for hiding and recovering data using …
We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, signs…
Hidden Markov Models (HMMs) are one of the most fundamental and widely used statistical tools for modeling discrete time series. In general, learning HMMs from data is computationally hard (under cryptographic assumptions), and…
This is the second of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The first paper presented the original algorithm, its…
We consider the problems of Private and Secure Matrix Multiplication (PSMM) and Fully Private Matrix Multiplication (FPMM), for which matrices privately selected by a master node are multiplied at distributed worker nodes without revealing…
Motivated by orthogonal dictionary learning problems, we propose a novel method for matrix factorization, where the data matrix $\mathbf{Y}$ is a product of a Householder matrix $\mathbf{H}$ and a binary matrix $\mathbf{X}$. First, we show…
A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \in \mathbb{R}^{N\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two…
Reversible data hiding in encrypted images is an effective technology for data hiding and protecting image privacy. Although there are many high-capacity methods have been presented in recent year, most of them need a pre-processing phase…
This paper describes efficient algorithms for computing rank-revealing factorizations of matrices that are too large to fit in RAM, and must instead be stored on slow external memory devices such as solid-state or spinning disk hard drives…
Beyond its widespread application in signal and image processing, \emph{compressed sensing} principles have been greatly applied to secure information transmission (often termed 'compressive security'). In this scenario, the measurement…
We propose an information-theoretic framework for matrix completion. The theory goes beyond the low-rank structure and applies to general matrices of "low description complexity". Specifically, we consider $m\times n$ random matrices…
We present a simple randomized algorithm for approximate matrix multiplication (AMM) whose error scales with the *output* norm $\|AB\|_F$. Given any $n\times n$ matrices $A,B$ and a runtime parameter $r\leq n$, the algorithm produces in…
An interesting challenge for the cryptography community is to design authentication protocols that are so simple that a human can execute them without relying on a fully trusted computer. We propose several candidate authentication…
Low-rank matrix recovery problems are inverse problems which naturally arise in various fields like signal processing, imaging and machine learning. They are non-convex and NP-hard in full generality. It is therefore a delicate problem to…
We consider a variant of matrix completion where entries are revealed in a biased manner. We wish to understand the extent to which such bias can be exploited in improving predictions. Towards that, we propose a natural model where the…
Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical…
In this report, a novel efficient algorithm for recovery of jointly sparse signals (sparse matrix) from multiple incomplete measurements has been presented, in particular, the NESTA-based MMV optimization method. In a nutshell, the jointly…
We study the problem of private function retrieval (PFR) in a distributed storage system. In PFR the user wishes to retrieve a linear combination of $M$ messages stored in non-colluding $(N,K)$ MDS coded databases while revealing no…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…
We present a very fast algorithm for general matrix factorization of a data matrix for use in the statistical analysis of high-dimensional data via latent factors. Such data are prevalent across many application areas and generate an…
A Euclidean Distance Matrix (EDM) is a table of distance-square between points on a k- dimensional Euclidean space, with applications in many fields (e.g. engineering, geodesy, economics, genetics, biochemistry, psychology). A problem that…