Related papers: Dually flat structure with escort probability and …
Structured variational inference constitutes a core methodology in modern statistical applications. Unlike mean-field variational inference, the approximate posterior is assumed to have interdependent structure. We consider the natural…
Building on recent developments in models focused on the shape properties of odds ratios, this paper introduces two new models that expand the class of available distributions while preserving specific shape characteristics of an underlying…
We stress the importance of stochastic geometry as a branch of mathematical statistics particularly suited to model and investigate nontrivial spatial patterns. One of its key concepts, Voronoi tessellations, represents a versatile and…
We explore an identity between two branching graphs and propose a physical meaning in the context of the gauge-gravity correspondence. From the mathematical point of view, the identity equates probabilities associated with $\mathbb{GT}$,…
Probabilistic graphical models allow us to encode a large probability distribution as a composition of smaller ones. It is oftentimes the case that we are interested in incorporating in the model the idea that some of these smaller…
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…
Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\log n)$ time in…
We present DUAL-LOCO, a communication-efficient algorithm for distributed statistical estimation. DUAL-LOCO assumes that the data is distributed according to the features rather than the samples. It requires only a single round of…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…
Motivated by the engineering applications of uncertainty quantification, in this work we draw connections between the notions of random quantum states and operations in quantum information with probability distributions commonly encountered…
Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground…
The joint distribution of two off-diagonal Wishart matrix elements was useful in recent work on geometric probability [Finch 2010]. Not finding such formulas in the literature, we report these here.
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
In dealing with asymptotic approximation of possibly divergent nets of probability distributions, we are led to study uniform structures on the set of distributions. This paper identifies a class of such uniform structures that may be…
These expository notes are dedicated to the study of the topology of configuration spaces of manifolds. We give detailed computations of many invariants, including the fundamental group of the configuration spaces of $\mathbb{R}^2$, the…
Let $S$ be a planar $n$-point set. A triangulation for $S$ is a maximal plane straight-line graph with vertex set $S$. The Voronoi diagram for $S$ is the subdivision of the plane into cells such that all points in a cell have the same…
The paper extends Birkhoff's theorem on doubly stochastic matrices to some countable families of discrete probability spaces with nonempty intersections. We join every two elements lying in the same probability space by an edge and…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
By considering nests on a given space, we explore order-theoretical and topological properties that are closely related to the structure of a nest. In particular, we see how subbases given by two dual nests can be an indicator of how close…