Related papers: Expected Euler characteristic method for the large…

Spectral embedding of graphs uses the top k non-trivial eigenvectors of the random walk matrix to embed the graph into R^k. The primary use of this embedding has been for practical spectral clustering algorithms [SM00,NJW02]. Recently,…

We discuss two approaches to solving the parametric (or stochastic) eigenvalue problem. One of them uses a Taylor expansion and the other a Chebyshev expansion. The parametric eigenvalue problem assumes that the matrix $A$ depends on a…

We study the maximum of the random assignment process on rectangular matrices. We derive first-order asymptotics for the expected maximum, prove a law of large numbers under mild tail assumptions, and obtain exponential upper bounds for the…

Online variants of the Expectation Maximization (EM) algorithm have recently been proposed to perform parameter inference with large data sets or data streams, in independent latent models and in hidden Markov models. Nevertheless, the…

Consider a centered smooth Gaussian random field $\{X(t), t\in T \}$ with a general (nonconstant) variance function. In this work, we demonstrate that as $u \to \infty$, the excursion probability $\mathbb{P}\{\sup_{t\in T} X(t) \geq u\}$…

This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of…

We present a five-step method for the calculation of eigenvalue correlation functions for various ensembles of real random matrices, based upon the method of (skew-) orthogonal polynomials. This scheme systematises existing methods and also…

There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the…

We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations,…

The Matrix-Element Method (MEM) has long been a cornerstone of data analysis in high-energy physics. It leverages theoretical knowledge of parton-level processes and symmetries to evaluate the likelihood of observed events. In parallel, the…

Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…

Random sampling of large Markov matrices with a tunable spectral gap, a nonuniform stationary distribution, and a nondegenerate limiting empirical spectral distribution (ESD) is useful. Fix $c>0$ and $p>0$. Let $A_n$ be the adjacency matrix…

We consider inhomogeneous Erd\H{o}s-R\'enyi graphs. We suppose that the maximal mean degree $d$ satisfies $d \ll \log n$. We characterize the asymptotic behavior of the $n^{1 - o(1)}$ largest eigenvalues of the adjacency matrix and its…

We prove the first explicit rate of convergence to the Tracy-Widom distribution for the fluctuation of the largest eigenvalue of sample covariance matrices that are not integrable. Our primary focus is matrices of type $ X^*X $ and the…

Upper exponential inequalities for the tail probabilities of the centered and normalized number of triangles in the Erd\"{o}s-R\'{e}nyi graph are obtained, where the probability of every edge is fixed. The result is formulated in terms of…

We show that a large class of Estimation of Distribution Algorithms, including, but not limited to, Covariance Matrix Adaption, can be written as a Monte Carlo Expectation-Maximization algorithm, and as exact EM in the limit of infinite…

The Hanson-Wright inequality is an upper bound for tails of real quadratic forms in independent subgaussian random variables. In this work, we extend the Hanson-Wright inequality for the maximum eigenvalue of the quadratic sum of random…

We present a new framework for analysing the Expectation Maximization (EM) algorithm. Drawing on recent advances in the theory of gradient flows over Euclidean-Wasserstein spaces, we extend techniques from alternating minimization in…

We consider an Erd\H{o}s-R\'{e}nyi graph $\mathbb{G}(n,p)$ on $n$ vertices with edge probability $p$ such that \[ \sqrt{\frac{\log n}{\log \log n}} \ll np \le n^{1/2-o(1)}, \label{eq:abs} \tag{$\dagger$} \] and derive the upper tail large…

We develop new higher-order asymptotic techniques for the Gaussian maximum likelihood estimator in a spatial panel data model, with fixed effects, time-varying covariates, and spatially correlated errors. Our saddlepoint density and tail…