Related papers: Neighborhood radius estimation in Variable-neighbo…
In this paper, we establish a local limit theorem for linear fields of random variables constructed from independent and identically distributed innovations each with finite second moment. When the coefficients are absolutely summable we do…
Motivated by change point problems in time series and the detection of textured objects in images, we consider the problem of detecting a piece of a Gaussian Markov random field hidden in white Gaussian noise. We derive minimax lower bounds…
We first review the derivation of the exact expression for the average distance $<r_n>$ of the n-th neighbour of a reference point among a set of N random points distributed uniformly in a unit volume of a D-dimensional geometric space.…
Nearest-neighbor methods are fundamental to classical and modern machine learning, yet their geometric properties are typically analyzed under independent sampling. In this paper, we study the nearest-neighbor radii under dependent…
We study different ways of determining the mean distance $ < r_n >$ between a reference point and its $n$-th neighbour among random points distributed with uniform density in a $D$-dimensional Euclidean space. First we present a heuristic…
A local projection model is defined by a set of linear regressions that account for the associations between exogenous variables and an endogenous variable observed at different time points. While it is standard practice to separately…
Construction of tight confidence regions and intervals is central to statistical inference and decision making. This paper develops new theory showing minimum average volume confidence regions for categorical data. More precisely, consider…
The pseudo likelihood method of Besag(1974), has remained a popular method for estimating Markov random field on a very large lattice, despite various documented deficiencies. This is partly because it remains the only computationally…
We study the problem of detecting local geometry in random graphs. We introduce a model $\mathcal{G}(n, p, d, k)$, where a hidden community of average size $k$ has edges drawn as a random geometric graph on $\mathbb{S}^{d-1}$, while all…
Models of a phenomenon are often developed by examining it under different experimental conditions, or measurement contexts. The resultant probabilistic models assume that the underlying random variables, which define a measurable set of…
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…
Developing and deploying machine learning models safely depends on the ability to characterize and compare their abilities to generalize to new environments. Although recent work has proposed a variety of methods that can directly predict…
Given an $n$-sample of random vectors $(X_i,Y_i)_{1 \leq i \leq n}$ whose joint law is unknown, the long-standing problem of supervised classification aims to \textit{optimally} predict the label $Y$ of a given a new observation $X$. In…
The SNPs (Single Nucleotide Polymorphisms) genotyping platforms are of great value for gene mapping of complex diseases. Nowadays, the high-density of these molecular markers enables studies of dependence patterns between loci over the…
In this article, we prove that a small random perturbation of dynamical system with multiple stable equilibria converges to a Markov chain whose states are neighborhoods of the deepest stable equilibria, under a suitable time-rescaling,…
Many prediction problems can be phrased as inferences over local neighborhoods of graphs. The graph represents the interaction between entities, and the neighborhood of each entity contains information that allows the inferences or…
For many distributed algorithms, neighborhood size is an important parameter. In radio networks, however, obtaining this information can be difficult due to ad hoc deployments and communication that occurs on a collision-prone shared…
In this work, we propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector based on a finite sample. By global criterion, we mean optimizing a function over the entire set of possible…
This paper introduces the concept of random context representations for the transition probabilities of a finite-alphabet stochastic process. Processes with these representations generalize context tree processes (a.k.a. variable length…
We consider the problem of estimating the interacting neighborhood of a Markov Random Field model with finite support and homogeneous pairwise interactions based on relative positions of a two-dimensional lattice. Using a Bayesian…