Related papers: On multidimensional record patterns
We consider the hyperuniform model of d-dimensional integer lattice perturbed by independent random variables and we investigate the large scale asymptotic fluctuations of smoothed versions of the usual counting statistics, specifically of…
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…
Chain records is a new type of multidimensional record. We discuss how often the chain records are broken when the background sampling is from the unit cube with uniform distribution (or, more generally, from an arbitrary continuous product…
A disordered medium is often constructed by $N$ points independently and identically distributed in a $d$-dimensional hyperspace. Characteristics related to the statistics of this system is known as the random point problem. As $d \to…
Generative modeling aims at producing new datapoints whose statistical properties resemble the ones in a training dataset. In recent years, there has been a burst of machine learning techniques and settings that can achieve this goal with…
Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in $\mathbb Z^d$. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of…
The distributionally robust Markov Decision Process (MDP) approach asks for a distributionally robust policy that achieves the maximal expected total reward under the most adversarial distribution of uncertain parameters. In this paper, we…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
Clustering in high-dimensional spaces is a difficult problem which is recurrent in many domains, for example in image analysis. The difficulty is due to the fact that high-dimensional data usually live in different low-dimensional subspaces…
We analyze multivariate ordered discrete response models with a lattice structure, modeling decision makers who narrowly bracket choices across multiple dimensions. These models map latent continuous processes into discrete responses using…
We construct a simple multicomponent lattice gas model in one dimension in which each site can either be empty or occupied by at most one particle of any one of $D$ species. Particles interact with a nearest neighbor interaction which…
The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is…
We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning…
For a sequence of i.i.d. $d$-dimensional random vectors with independent continuously distributed coordinates, say that the $n$th observation in the sequence sets a record if it is not dominated in every coordinate by an earlier…
High-dimensional multivariate longitudinal data, which arise when many outcome variables are measured repeatedly over time, are becoming increasingly common in social, behavioral and health sciences. We propose a latent variable model for…
We investigate the statistics of three kinds of records associated with planar random walks, namely diagonal, simultaneous and radial records. The mean numbers of these records grow as universal power laws of time, with respective exponents…
In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed…
We construct a point set in the Euclidean plane that elucidates the relationship between the fine-scale statistics of the fractional parts of $\sqrt n$ and directional statistics for a shifted lattice. We show that the randomly rotated, and…
A $d$-dimensional random array on a nonempty set $I$ is a stochastic process $\boldsymbol{X}=\langle X_s:s\in \binom{I}{d}\rangle$ indexed by the set $\binom{I}{d}$ of all $d$-element subsets of $I$. We obtain structural decompositions of…