Related papers: Half-Wormholes and Ensemble Averages

In this paper we investigate \textit{pigeonhole statistics} for the fractional parts of the sequence $\sqrt{n}$. Namely, we partition the unit circle $ \mathbb{T} = \mathbb{R}/\mathbb{Z}$ into $N$ intervals and show that the proportion of…

Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three…

We discuss recently discovered links of the statistical models of normal random matrices to some important physical problems of pattern formation and to the quantum Hall effect. Specifically, the large $N$ limit of the normal matrix model…

Organoids, sophisticated in vitro models of human tissues, are crucial for medical research due to their ability to simulate organ functions and assess drug responses accurately. Accurate organoid instance segmentation is critical for…

Model averaging (MA) and ensembling play a crucial role in statistical and machine learning practice. When multiple candidate models are considered, MA techniques can be used to weight and combine them, often resulting in improved…

We establish asymptotic normality results for estimation of the block probability matrix $\mathbf{B}$ in stochastic blockmodel graphs using spectral embedding when the average degrees grows at the rate of $\omega(\sqrt{n})$ in $n$, the…

Field observations form the basis of many scientific studies, especially in ecological and social sciences. Despite efforts to conduct such surveys in a standardized way, observations can be prone to systematic measurement errors. The…

This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. Under a generalised random dot product graph, the embedding provides uniformly…

Machine learning offers potential solutions to current issues in industrial systems in areas such as quality control and predictive maintenance, but also faces unique barriers in industrial applications. An ongoing challenge is extreme…

It is usual to rely on the quasi-likelihood methods for deriving statistical methods applied to clustered multinomial data with no underlying distribution. Even though extensive literature can be encountered for these kind of data sets,…

Global sensitivity analysis is a set of methods aiming at quantifying the contribution of an uncertain input parameter of the model (or combination of parameters) on the variability of the response. We consider here the estimation of the…

This paper proves joint convergence of the approximation error for several stochastic integrals with respect to local Brownian semimartingales, for nonequidistant and random grids. The conditions needed for convergence are that the Lebesgue…

We introduce a novel varying-weight dependent Dirichlet process (DDP) model that extends a recently developed semi-parametric generalized linear model (SPGLM) by adding a nonparametric Bayesian prior on the baseline distribution of the GLM.…

This paper provides a selective review of the statistical network analysis literature focused on clustering and inference problems for stochastic blockmodels and their variants. We survey asymptotic normality results for stochastic…

Semisupervised methods inevitably invoke some assumption that links the marginal distribution of the features to the regression function of the label. Most commonly, the cluster or manifold assumptions are used which imply that the…

In this paper, we propose a unified framework for sampling, clustering and embedding data points in semi-metric spaces. For a set of data points $\Omega=\{x_1, x_2, \ldots, x_n\}$ in a semi-metric space, we consider a complete graph with…

The Nested Dirichlet Distribution (NDD) provides a flexible alternative to the Dirichlet distribution for modeling compositional data, relaxing constraints on component variances and correlations through a hierarchical tree structure. While…

We calculate connected correlators in time dependent Gaussian orthogonal and symplectic random matrix ensembles by a diagrammatic method. We obtain averaged one-point Green's functions in the leading order O(1) and wide two-level and…

In a recent letter [Phys. Rev. Lett. {\bf 100}, 164101 (2008)] and within the context of quantized chaotic billiards, random plane wave and semiclassical theoretical approaches were applied to an example of a relatively new class of…

We study asymmetric rank-one spiked tensor models in the high-dimensional regime, where the noise entries are independent and identically distributed with zero mean, unit variance, and finite fourth moment. This extends the classical…