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We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other…
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…
The goal of a denoising algorithm is to reconstruct a signal from its noise-corrupted observations. Perfect reconstruction is seldom possible and performance is measured under a given fidelity criterion. In a recent work, the authors…
We present a new method for online prediction and learning of tensors ($N$-way arrays, $N >2$) from sequential measurements. We focus on the specific case of 3-D tensors and exploit a recently developed framework of structured tensor…
We consider the problem of finding the smallest or largest entry of a tensor of order N that is specified via its rank decomposition. Stated in a different way, we are given N sets of R-dimensional vectors and we wish to select one vector…
Factorization of matrices where the rank of the two factors diverges linearly with their sizes has many applications in diverse areas such as unsupervised representation learning, dictionary learning or sparse coding. We consider a setting…
A new unbiased Monte Carlo technique called Tensor Network Monte Carlo (TNMC) is introduced based on sampling all possible renormalizations (or course-grainings) of tensor networks, in this case matrix-product states. Tensor networks are a…
We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…
We study the fundamental problem of learning an unknown, smooth probability function via pointwise Bernoulli tests. We provide a scalable algorithm for efficiently solving this problem with rigorous guarantees. In particular, we prove the…
Motivated by a flurry of recent work on efficient tensor decomposition algorithms, we show that the celebrated moment matrix extension algorithm of Brachat, Comon, Mourrain, and Tsigaridas for symmetric tensor canonical polyadic (CP)…
With the advancement of neural networks, there has been a notable increase, both in terms of quantity and variety, in research publications concerning the application of autoencoders to reduced-order models. We propose a polytopic…
We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data…
In this work, we consider the optimization formulation for symmetric tensor decomposition recently introduced in the Subspace Power Method (SPM) of Kileel and Pereira. Unlike popular alternative functionals for tensor decomposition, the SPM…
Anomaly detection in spatiotemporal data is a challenging problem encountered in a variety of applications, including video surveillance, medical imaging data, and urban traffic monitoring. Existing anomaly detection methods focus mainly on…
We introduce a tensor network algorithm for the solution of $p$-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system…
We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm…
We consider the problem of recovering a low-rank tensor from its noisy observation. Previous work has shown a recovery guarantee with signal to noise ratio $O(n^{\lceil K/2 \rceil /2})$ for recovering a $K$th order rank one tensor of size…
We study the learnability of linear separators in $\Re^d$ in the presence of bounded (a.k.a Massart) noise. This is a realistic generalization of the random classification noise model, where the adversary can flip each example $x$ with…
We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…
An important building block in all current asymptotically fast algorithms for matrix multiplication are tensors with low border rank, that is, tensors whose border rank is equal or very close to their size. To find new asymptotically fast…