RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC

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A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...

We propose a novel approach to evaluating the ionic Seebeck coefficient in electrolytes from relatively short equilibrium molecular dynamics simulations, based on the Green-Kubo theory of linear response and Bayesian regression analysis. By exploiting the ...

Given two jointly distributed random variables (X,Y), a functional representation of X is a random variable Z independent of Y, and a deterministic function g(⋅,⋅) such that X=g(Y,Z). The problem of finding a minimum entropy functional representation is kn ...

We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of luminous red galaxies (LRGs) data collected during the initial 2 months of operat ...

The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A. In this work, we propose a mix ...

Functional connectomes (FCs) containing pairwise estimations of functional couplings between pairs of brain regions are commonly represented by correlation matrices. As symmetric positive definite matrices, FCs can be transformed via tangent space projecti ...

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

In this paper we demonstrate ultra-high sensitivity silicon nanowires pH and protein sensing on the same Silicon nanowire array platform by using a constant current method and monitoring the drain voltage as function of analyte concentration. The injected ...

Sylvester matrix equations are ubiquitous in scientific computing. However, few solution techniques exist for their generalized multiterm version, as they now arise in an increasingly large number of applications. In this work, we consider algebraic parame ...

Context. We present a novel approach to the construction of mock galaxy catalogues for large-scale structure analysis based on the distribution of dark matter halos obtained with effective bias models at the field level. Aims. We aim to produce mock galaxy ...

Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- (PT-) and anti-PT-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian sp ...

This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...

The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...

Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address ...

In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices. In the first part, we consider algorithms for building ...

RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC

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Spectral Estimators for High-Dimensional Matrix Inference

Random matrix methods for high-dimensional machine learning models

Randomized low-rank approximation and its applications

Seebeck Coefficient of Ionic Conductors from Bayesian Regression Analysis

Information Spectrum Converse for Minimum Entropy Couplings and Functional Representations

Validation of semi-analytical, semi-empirical covariance matrices for two-point correlation function for early DESI data

A mixed precision LOBPCG algorithm

Tangent functional connectomes uncover more unique phenotypic traits

Singular quadratic eigenvalue problems: linearization and weak condition numbers

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Ultra-High Sensitivity Silicon Nanowire Array Biosensor Based on a Constant-Current Method for Continuous Real-Time pH and Protein Monitoring in Interstitial Fluid

Preconditioning techniques for generalized Sylvester matrix equations

DESI mock challenge Halo and galaxy catalogues with the bias assignment method

Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems

Positive Definite Completions and Continuous Graphical Models

Optimal denoising of rotationally invariant rectangular matrices

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

Iterative refinement of Schur decompositions

CovNet: Covariance networks for functional data on multidimensional domains

Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation