Related papers: The probability of drawing intersections: extendin…
The rules of a game of dice are extended to a "hyper-die" with $n\in\mathbb{N}$ equally probable faces, numbered from 1 to $n$. We derive recursive and explicit expressions for the probability mass function and the cumulative distribution…
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…
Background: We study the statistical properties of fragment coverage in genome sequencing experiments. In an extension of the classic Lander-Waterman model, we consider the effect of the length distribution of fragments. We also introduce…
One of the main questions that arise when studying random and quasi-random structures is which properties P are such that any object that satisfies P "behaves" like a truly random one. In the context of graphs, Chung, Graham, and Wilson…
We determine to within a constant factor the threshold for the property that two random k-uniform hypergraphs with edge probability p have an edge-disjoint packing into the same vertex set. More generally, we allow the hypergraphs to have…
Real-life data are often non-IID due to complex distributions and interactions, and the sensitivity to the distribution of samples can differ among learning models. Accordingly, a key question for any supervised or unsupervised model is…
We study the distribution of the set of copies of some given graph $H$ in the random graph $G(n,p)$, focusing on the case when $H = K_r$. Our main results capture the 'leading term' in the difference between this distribution and the…
Interpreting graph neural networks (GNNs) is difficult because message passing mixes signals and internal channels rarely align with human concepts. We study superposition, the sharing of directions by multiple features, directly in the…
Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…
The superposition hypothesis states that single neurons may participate in representing multiple features in order for the neural network to represent more features than it has neurons. In neuroscience and AI, representational alignment…
Dimensionality Reduction (DR) methods are widely used to visualize high-dimensional data. One key task in DR-based analysis is discovering neighborhoods, which relies on analyzing the fine-grained local structure of a projection. However,…
Though widely used in applications, reinforced random walk on graphs have never been the subject of a valid statistical inference. We develop in this paper a statistical framework for a general two-colored urn model. The probability to draw…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
Modeling the distribution of natural images is a landmark problem in unsupervised learning. This task requires an image model that is at once expressive, tractable and scalable. We present a deep neural network that sequentially predicts…
This work was motivated by a twin study with the goal of assessing the genetic control of immune traits. We propose a mixture bivariate distribution to model twin data where the underlying order within a pair is unclear. Though estimation…
Pedigrees are directed acyclic graphs that represent ancestral relationships between individuals in a population. Based on a schematic recombination process, we describe two simple Markov models for sequences evolving on pedigrees - Model R…
A partial differential equation governing the global evolution of the joint probability distribution of an arbitrary number of local flow observations, drawn randomly from a control volume, is derived and applied to examples involving…
This note describes a method for detecting dense random texture using fully connected points sampled on image edges. An edge image is randomly sampled with points, the standard L2 distance is calculated between all connected points in a…
Partitioning a set of elements into subsets of a priori unknown sizes is essential in many applications. These subset sizes are rarely explicitly learned - be it the cluster sizes in clustering applications or the number of shared versus…
This article discusses random hypergraphs with varying hyperedge sizes, admitting large hyperedges with size tending to infinity, and heavy-tailed limiting hyperedge size distributions. The main result describes a threshold for the random…