Related papers: Rank Minimization over Finite Fields: Fundamental …

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…

We establish non-asymptotic efficiency guarantees for tensor decomposition-based inference in count data models. Under a Poisson framework, we consider two related goals: (i) parametric inference, the estimation of the full distributional…

A quantized message passing decoding algorithm for low-density parity-check codes is presented. The algorithm relies on the min approximation at the check nodes, and on modelling the variable node inbound messages as observations of an…

In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…

Motivated by applications to the theory of rank-metric codes, we study the problem of estimating the number of common complements of a family of subspaces over a finite field in terms of the cardinality of the family and its intersection…

In this paper, we present a method to certify the approximation quality of a low rank tensor to a given third order symmetric tensor. Under mild assumptions, best low rank approximation is attained if a control parameter is zero or…

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…

In this note, we investigate how well we can reconstruct the best rank-$r$ approximation of a large matrix from a small number of its entries. We show that even if a data matrix is of full rank and cannot be approximated well by a low-rank…

Compressed Sensing decoding algorithms can efficiently recover an N dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = 2klog(N/k) measurements y = Phi x. If the sparsity or approximate…

Suppose that we observe entries or, more generally, linear combinations of entries of an unknown $m\times T$-matrix $A$ corrupted by noise. We are particularly interested in the high-dimensional setting where the number $mT$ of unknown…

Estimating the linear dimensionality of a data set in the presence of noise is a common problem. However, data may also be corrupted by monotone nonlinear distortion that preserves the ordering of matrix entries but causes linear methods…

This preprint is of a chapter to appear in {\it Combinatorics and finite fields: Difference sets, polynomials, pseudorandomness and applications. Radon Series on Computational and Applied Mathematics}, K.-U. Schmidt and A. Winterhof (eds.).…

The tensor rank decomposition problem consists of recovering the unique set of parameters representing a robustly identifiable low-rank tensor when the coordinate representation of the tensor is presented as input. A condition number for…

Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…

In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformly-distributed measurement noise and arbitrarily-distributed ``sparse'' noise. In theory, we bound the tracking error. In…

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to…

The fully connected conditional random field (CRF) with Gaussian pairwise potentials has proven popular and effective for multi-class semantic segmentation. While the energy of a dense CRF can be minimized accurately using a linear…

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…