Related papers: Boltzmann Samplers, P\'olya Theory, and Cycle Poin…

This paper gives a new algorithm for sampling tree-weighted partitions of a large class of planar graphs. Formally, the tree-weighted distribution on $k$-partitions of a graph weights $k$-partitions proportional to the product of the number…

Clustering is one of the most common unsupervised learning tasks in machine learning and data mining. Clustering algorithms have been used in a plethora of applications across several scientific fields. However, there has been limited…

The simple connected graphs may be classified by their cycle composition (number and lengths of cycles). This work derives the counting series of the simple connected graphs that have cycles of unrestricted number and length, but no…

Inspired by Stufler's recent probabilistic proof of Otter's asymptotic number of unlabeled trees, we revisit work of Palmer and Schwenk, and study unlabeled forests from a probabilistic point of view. We show that the number of trees in a…

Sampling from combinatorial families can be difficult. However, complicated families can often be embedded within larger, simpler ones, for which easy sampling algorithms are known. We take advantage of such a relationship to describe a…

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory…

This paper describes a process for clustering concepts into chains from data presented randomly to an evaluating system. There are a number of rules or guidelines that help the system to determine more accurately what concepts belong to a…

This paper concerns a relatively new combinatorial structure called staircase tableaux. They were introduced in the context of the asymmetric exclusion process and Askey--Wilson polynomials, however, their purely combinatorial properties…

We define and study a model of winding for non-colliding particles in finite trees. We prove that the asymptotic behavior of this statistic satisfies a central limiting theorem, analogous to similar results on winding of bounded particles…

Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…

Methods for unsupervised anomaly detection suffer from the fact that the data is unlabeled, making it difficult to assess the optimality of detection algorithms. Ensemble learning has shown exceptional results in classification and…

Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of…

Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…

We consider the problem of uniformly generating a spanning tree, of a connected undirected graph. This process is useful to compute statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle…

Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling…

With the ubiquitous availability of unstructured data, growing attention is paid as how to adjust for selection bias in such non-probability samples. The majority of the robust estimators proposed by prior literature are either fully or…

We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomized-inclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy…

We study the phase diagram of random outerplanar maps sampled according to non-negative Boltzmann weights that are assigned to each face of a map. We prove that for certain choices of weights the map looks like a rescaled version of its…

We derive the asymptotic distribution of the domination number of a new family of random digraph called proximity catch digraph (PCD), which has application to statistical testing of spatial point patterns and to pattern recognition. The…

Consider a panel data setting where repeated observations on individuals are available. Often it is reasonable to assume that there exist groups of individuals that share similar effects of observed characteristics, but the grouping is…