Related papers: Neighborhood radius estimation in Variable-neighbo…
Let random vectors $R^c=\{R_p^c:p\in P_c\}$ represent joint measurements of certain subsets $P_c$ of properties $p\in P$ in different contexts $c\in C$. Such a system is traditionally called noncontextual if there exists a jointly…
Many modern methods for prediction leverage nearest neighbor search to find past training examples most similar to a test example, an idea that dates back in text to at least the 11th century and has stood the test of time. This monograph…
This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the…
Many physical and mathematical models involve random fields in their input data. Examples are ordinary differential equations, partial differential equations and integro--differential equations with uncertainties in the coefficient…
The availability of high-throughput parallel methods for sequencing microbial communities is increasing our knowledge of the microbial world at an unprecedented rate. Though most attention has focused on determining lower-bounds on the…
Mossel and Ross (2019) introduce the shotgun assembly problem for random graphs: what radius $R$ ensures that the random graph $G$ can be uniquely recovered from its list of rooted $R$-neighborhoods, with high probability? Here we consider…
Recent years have seen new general notions of contextuality emerge. Most of these employ context-independent symbols to represent random variables in different contexts. As an example, the operational theory of Spekkens [1] treats an…
Motivated by recent results on radial projections and applications to the celebrated Falconer distance problem, we study radial projections in the setting of finite fields. More precisely, we extend results due to Mattila and Orponen…
Random fields have remained a topic of great interest over past decades for the purpose of structured inference, especially for problems such as image segmentation. The local nodal interactions commonly used in such models often suffer the…
Stochastic parameterisations deployed in models of the Earth system frequently invoke locality assumptions such as Markovianity or spatial locality. This work highlights the impact of such assumptions on predictive performance. Both in…
Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…
The notion of the Urysohn $d$-width measures to what extent a metric space can be approximated by a $d$-dimensional simplicial complex. We investigate how local Urysohn width bounds on a riemannian manifold affect its global width. We bound…
We propose a novel method for determining the radius of a spherical surface based on the distances measured between points on this surface. We consider the most general case of determining the radius when the distances are measured with…
Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th…
We consider detecting objects in an image by iteratively selecting from a set of arbitrarily shaped candidate regions. Our generic approach, which we term visual chunking, reasons about the locations of multiple object instances in an image…
We introduce and initiate the study of new parameters associated with any norm and any log-concave measure on $\mathbb R^n$, which provide sharp distributional inequalities. In the Gaussian context this investigation sheds light to the…
A major public health concern in the United States (US) is gun-related deaths. The number of gun injuries largely varies spatially because of county-wise heterogeneity of race, sex, age, and income distributions. But still, a major…
Let $G_n$ be a random geometric graph with vertex set $[n]$ based on $n$ i.i.d.\ random vectors $X_1,\ldots,X_n$ drawn from an unknown density $f$ on $\R^d$. An edge $(i,j)$ is present when $\|X_i -X_j\| \le r_n$, for a given threshold…
In this paper, we present a method for computing the marginal likelihood, also known as the model likelihood or Bayesian evidence, from Markov Chain Monte Carlo (MCMC), or other sampled posterior distributions. In order to do this, one…
The radiological characterization of contaminated elements (walls, grounds, objects) from nuclear facilities often suffers from a too small number of measurements. In order to determine risk prediction bounds on the level of contamination,…