Related papers: Compressibility of positive semidefinite factoriza…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…
Nondegenerate covariance, correlation and spectral density matrices are necessarily symmetric or Hermitian and positive definite. The main contribution of this paper is the development of statistical data depths for collections of Hermitian…
We explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices. These are natural matrix analogs of scalar nonnegative…
We show that any nonsingular (real or complex) square matrix can be factorized into a product of at most three normal matrices, one of which is unitary, another selfadjoint with eigenvalues in the open right half-plane, and the third one is…
Recent quantum technologies utilize complex multidimensional processes that govern the dynamics of quantum systems. We develop an adaptive diagonal-element-probing compression technique that feasibly characterizes any unknown quantum…
A real symmetric matrix $M$ is completely positive semidefinite if it admits a Gram representation by (Hermitian) positive semidefinite matrices of any size $d$. The smallest such $d$ is called the (complex) completely positive semidefinite…
A problem by Feichtinger, Heil, and Larson asks whether every infinite matrix $A$ with $\sum_{k,l}|A_{kl}| < \infty$ (an equivalent substitute for the Feichtinger algebra) that is positive-semidefinite admits a symmetric rank-one…
Entanglement in high energy and and nuclear reactions is receiving great attention. A proper description of these reactions uses density matrices, and the express of entanglement in terms of {\it separability}. Quantum tomography bypasses…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
Deep learning models have achieved tremendous success in most of the industries in recent years. The evolution of these models has also led to an increase in the model size and energy requirement, making it difficult to deploy in production…
Recent transformer language models achieve outstanding results in many natural language processing (NLP) tasks. However, their enormous size often makes them impractical on memory-constrained devices, requiring practitioners to compress…
Bounding the correlations predicted by quantum theory is an important challenge in quantum information science. Today's leading approach is semidefinite programming relaxations, but existing methods still cannot account for many relevant…
The problem of finding a $k \times k$ submatrix of maximum volume of a matrix $A$ is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of $A$. We show…
This paper establishes that every positive-definite matrix can be written as a positive linear combination of outer products of integer-valued vectors whose entries are bounded by the geometric mean of the condition number and the dimension…
Well-controlled quantum devices with their increasing system size face a new roadblock hindering further development of quantum technologies: The effort of quantum tomography---the characterization of processes and states within a quantum…
In this note, we discuss dilation-theoretic matrix parametrizations of contractions and positive matrices. These parametrizations are then applied to some problems in quantum information theory. First we establish some properties of…
The squashed entanglement is a widely used entanglement measure that has many desirable properties. However, as it is based on an optimization over extensions of arbitrary dimension, one drawback of this measure is the lack of good…
In the context of kernel machines, polynomial and Fourier features are commonly used to provide a nonlinear extension to linear models by mapping the data to a higher-dimensional space. Unless one considers the dual formulation of the…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…