Related papers: Rank Resilience of Pattern Matrices against Struct…

When we speak about parametric programming, sensitivity analysis, or related topics, we usually mean the problem of studying specified perturbations of the data such that for a given optimization problem some optimality criterion remains…

This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…

We present an analysis of sets of matrices with rank less than or equal to a specified number $s$. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank…

We study the structural complexity of bimatrix games, formalized via rank, from an empirical perspective. We consider a setting where we have data on player behavior in diverse strategic situations, but where we do not observe the relevant…

Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-rank matrix completion (Recht et al., 2010) are extensions of PCA to allow for outliers and missing entries respectively. It is well-known that solving these problems…

The use of available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a persistent disturbance is…

A central question in random matrix theory is universality. When an emergent phenomena is observed from a large collection of chosen random variables it is natural to ask if this behavior is specific to the chosen random variable or if the…

We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use…

Recently, we have witnessed the bloom of neural ranking models in the information retrieval (IR) field. So far, much effort has been devoted to developing effective neural ranking models that can generalize well on new data. There has been…

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…

The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…

We investigate how the response of coupled dynamical systems is modified due to a structural alteration of the interaction. The majority of the literature focuses on additive perturbations and symmetrical interaction networks. Here, we…

Low-rank training methods reduce the number of trainable parameters by re-parameterizing the weights with matrix decompositions (e.g., singular value decomposition). However, enforcing a fixed low-rank structure caps the rank of the weight…

We derive a sufficient condition for a sparse random matrix with given numbers of non-zero entries in the rows and columns having full row rank. The result covers both matrices over finite fields with independent non-zero entries and…

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…

The ability to achieve coordinated behavior -- engineered or emergent -- on networked systems has attracted widespread interest over several fields. This interest has led to remarkable advances in developing a theoretical understanding of…

Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…

We study an ensemble of random matrices (the Rosenzweig-Porter model) which, in contrast to the standard Gaussian ensemble, is not invariant under changes of basis. We show that a rather complete understanding of its level correlations can…

The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…

We study the problem of resilient strategies in the presence of uncertainty. Resilient strategies enable an agent to make decisions that are robust against disturbances. In particular, we are interested in those disturbances that are able…