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Reconstruction fidelity of sparse signals contaminated by sparse noise is considered. Statistical mechanics inspired tools are used to show that the l1-norm based convex optimization algorithm exhibits a phase transition between the…
This paper proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left…
An important problem in applications is the approximation of a function $f$ from a finite set of randomly scattered data $f(x_j)$. A common and powerful approach is to construct a trigonometric least squares approximation based on the set…
We investigate the problem of scanning and prediction ("scandiction", for short) of multidimensional data arrays. This problem arises in several aspects of image and video processing, such as predictive coding, for example, where an image…
We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…
We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community "noise" (inter-community edges) on any "community…
Part I of this paper considered optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network…
Computing accurate low rank approximations of large matrices is a fundamental data mining task. In many applications however the matrix contains sensitive information about individuals. In such case we would like to release a low rank…
A matrix algorithm is said to be superfast (that is, runs at sublinear cost) if it involves much fewer scalars and flops than the input matrix has entries. Such algorithms have been extensively studied and widely applied in modern…
Deep neural networks have been successfully applied to a broad range of problems where overparametrization yields weight matrices which are partially random. A comparison of weight matrix singular vectors to the Porter-Thomas distribution…
The Column Subset Selection Problem (CSSP) and the Nystr\"om method are among the leading tools for constructing small low-rank approximations of large datasets in machine learning and scientific computing. A fundamental question in this…
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…
We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters $p$ can be much larger than the sample size. We…
This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…
Given a single observation from a Gaussian distribution with unknown mean $\theta$, we design computationally efficient procedures that can approximately generate an observation from a different target distribution $Q_{\theta}$ uniformly…
Recently, sparse subspace clustering has been a valid tool to deal with high-dimensional data. There are two essential steps in the framework of sparse subspace clustering. One is solving the coefficient matrix of data, and the other is…
Tensor clustering, which seeks to extract underlying cluster structures from noisy tensor observations, has gained increasing attention. One extensively studied model for tensor clustering is the tensor block model, which postulates the…
In this paper we approximate high-dimensional functions $f\colon\mathbb T^d\to\mathbb C$ by sparse trigonometric polynomials based on function evaluations. Recently it was shown that a dimension-incremental sparse Fourier transform (SFT)…
Training deep neural networks (DNNs) in the presence of noisy labels is an important and challenging task. Probabilistic modeling, which consists of a classifier and a transition matrix, depicts the transformation from true labels to noisy…
A new field of research is rapidly expanding at the crossroad between statistical physics, information theory and combinatorial optimization. In particular, the use of cutting edge statistical physics concepts and methods allow one to solve…