Related papers: Matchings on trees and the adjacency matrix: A det…
Inferring a decision tree from a given dataset is one of the classic problems in machine learning. This problem consists of buildings, from a labelled dataset, a tree such that each node corresponds to a class and a path between the tree…
Metabolites, small molecules that are involved in cellular reactions, provide a direct functional signature of cellular state. Untargeted metabolomics experiments usually relies on tandem mass spectrometry to identify the thousands of…
Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…
We estimate the size of a labelled tree by comparing the amount of (labelled) nodes with the size of the set of labels. Roughly speaking, a exponentially big labelled tree, is any labelled tree that has an exponential gap between its size,…
A graph $G=(V,E)$ is geometrically embeddable into a normed space $X$ when there is a mapping $\zeta: V\to X$ such that $\|\zeta(v)-\zeta(w)\|_X\leqslant 1$ if and only if $\{v,w\}\in E$, for all distinct $v,w\in V$. Our result is the…
We consider two classes of natural stochastic processes on finite unlabeled graphs. These are Euclidean stochastic optimization algorithms on the adjacency matrix of weighted graphs and a modified version of the Metropolis MCMC algorithm on…
Comparing observed behavior (event data generated during process executions) with modeled behavior (process models), is an essential step in process mining analyses. Alignments are the de-facto standard technique for calculating conformance…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
Uniform laws of large numbers form a cornerstone of Vapnik--Chervonenkis theory, where they are characterized by the finiteness of the VC dimension. In this work, we study uniform convergence phenomena in cartesian product spaces, under…
In this article, Temperley's bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on the other, is extended to the setting of general planar directed…
The Expectation-Maximization (EM) algorithm for mixture models often results in slow or invalid convergence. The popular convergence proof affirms that the likelihood increases with Q; Q is increasing in the M -step and non-decreasing in…
We review the uniform electron gas (UEG) at finite temperature and over a broad density range relevant for warm dense matter (WDM) applications. We provide an overview of different simulation techniques, focusing on recent developments in…
We study the minimal spanning arborescence which is the directed analogue of the minimal spanning tree, with a particular focus on its infinite volume limit and its geometric properties. We prove that in a certain large class of transient…
We show that for every $n$-point metric space $M$ there exists a spanning tree $T$ with unweighted diameter $O(\log n)$ and weight $\omega(T) = O(\log n) \cdot \omega(MST(M))$. Moreover, there is a designated point $rt$ such that for every…
We present a new and surprisingly simple analysis of random-shift decompositions -- originally proposed by Miller, Peng, and Xu [SPAA'13]: We show that decompositions for exponentially growing scales $D = 2^0, 2^1, \ldots,…
The Learnable Tree Filter presents a remarkable approach to model structure-preserving relations for semantic segmentation. Nevertheless, the intrinsic geometric constraint forces it to focus on the regions with close spatial distance,…
Computing a Euclidean minimum spanning tree of a set of points is a seminal problem in computational geometry and geometric graph theory. We combine it with another classical problem in graph drawing, namely computing a monotone geometric…
We present an integrated approach for structure and parameter estimation in latent tree graphical models. Our overall approach follows a "divide-and-conquer" strategy that learns models over small groups of variables and iteratively merges…
In this article we investigate the Uniform Spanning Forest ($\mathsf{USF}$) in the nearest-neighbour integer lattice $\mathbf{Z}^{d+1} = \mathbf{Z}\times \mathbf{Z}^d$ with an assignment of conductances that makes the underlying (Network)…
Understanding the dynamic properties of the uniform electron gas (UEG) is important for numerous applications ranging from semiconductor physics to exotic warm dense matter. In this work, we apply the maximum entropy method (MEM), as…