Related papers: Bootstraps Regularize Singular Correlation Matrice…

Interpolation models are critical for a wide range of applications, from numerical optimization to artificial intelligence. The reliability of the provided interpolated value is of utmost importance, and it is crucial to avoid the…

We investigate bootstrap percolation with infection threshold $r> 1$ on the binomial $k$-uniform random hypergraph $H_k(n,p)$ in the regime $n^{-1}\ll n^{k-2}p \ll n^{-1/r}$, when the initial set of infected vertices is chosen uniformly at…

Intelligent systems possess a crucial characteristic of breaking complicated problems into smaller reusable components or parts and adjusting to new tasks using these part representations. However, current part-learners encounter…

We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson…

The tensorial principal component analysis is a generalization of ordinary principal component analysis, focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative…

A $n$-by-$n$ matrix is called totally positive ($TP$) if all its minors are positive and $TP_k$ if all of its $k$-by-$k$ submatrices are $TP$. For an arbitrary totally positive matrix or $TP_k$ matrix, we investigate if the $r$th compound…

We show that the last few components in principal component analysis of the correlation matrix of a group of stocks may contain useful financial information by identifying highly correlated pairs or larger groups of stocks. The results of…

We perturb a real matrix $A$ of full column rank, and derive lower bounds for the smallest singular values of the perturbed matrix, in terms of normwise absolute perturbations. Our bounds, which extend existing lower-order expressions,…

We continue our investigation of correlation functions of the large-N (planar) limit of the (1+1)-dimensional principal chiral sigma model, whose bare field U(x) lies in the fundamental matrix representation of SU(N). We find all the form…

Starting from the Pearson Correlation Matrix of stock returns and from the desire to obtain a reduced number of parameters relevant for the dynamics of a financial market, we propose to take the idea of a sectorial matrix, which would have…

The general correlation function for the eigenvalues of $p$ complex hermitian matrices coupled in a chain is given as a single determinant. For this we use a slight generalization of a theorem of Dyson.

It is widely believed that engineering a model to be invariant/equivariant improves generalisation. Despite the growing popularity of this approach, a precise characterisation of the generalisation benefit is lacking. By considering the…

We consider the class of non-negative rank-one convex isotropic integrands on $\mathbb{R}^{n\times n}$ which are also positively $p$-homogeneous. If $p \leq n = 2$ we prove, conditional on the quasiconvexity of the Burkholder integrand,…

Dependent rounding is a useful technique for optimization problems with hard budget constraints. This framework naturally leads to \emph{negative correlation} properties. However, what if an application naturally calls for dependent…

This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any…

A matrix $A\in\mathbb{C}^{n\times n}$ is diagonalizable if it has a basis of linearly independent eigenvectors. Since the set of nondiagonalizable matrices has measure zero, every $A\in \mathbb{C}^{n\times n}$ is the limit of diagonalizable…

Let $\mathcal B=\mathcal B_{k,n,p}$ be a random collection of $k$-subsets of $[n]$ where each possible set is present independently with probability $p$. Let $\cal E_{\mathcal B}$ be the event that $\mathcal B$ defines the set of bases of a…

We revisit the large $N$ two-matrix model with $\text{tr}[A,B]^2$ interaction and quartic potentials by the analytic trajectory bootstrap, where $A$ and $B$ represent the two matrices. In the large $N$ limit, we can focus on the single…

We consider the $r$-neighbor bootstrap percolation process on the graph with vertex set $V=\{0,1\}^n$ and edges connecting the pairs at Hamming distance $1,2,\dots,k$, where $k\ge 2$. We find asymptotics of the critical probability of…

In this paper, we show that the largest and smallest eigenvalues of a sample correlation matrix stemming from $n$ independent observations of a $p$-dimensional time series with iid components converge almost surely to $(1+\sqrt{\gamma})^2$…