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We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…
Modeling of growth (or decay) curves arises in many fields such as microbiology, epidemiology, marketing, and econometrics. Parametric forms like Logistic and Gompertz are often used for modeling such monotonic patterns. While useful for…
This paper studies parametric bootstrap methods for network data, with the goal of quantifying the uncertainty of network statistics of interest. While existing network resampling methods primarily focus on count statistics under…
We develop the mathematical theory of a model, constructed by C. Gu, I. Downes, O. Gnawali, and L. Guibas, of networks that diffuse continuously acquired information from mobile sensor nodes. We prove new results on the maximum, minimum,…
We consider the problem of enumeration of planar maps and revisit its one-matrix model solution in the light of recent combinatorial techniques involving conjugated trees. We adapt and generalize these techniques so as to give an…
The paper introduces the Hidden Tree Markov Network (HTN), a neuro-probabilistic hybrid fusing the representation power of generative models for trees with the incremental and discriminative learning capabilities of neural networks. We put…
We consider Robinson-Schensted-Knuth algorithm applied to a random input and study the growth of the bottom rows of the corresponding Young diagrams. We prove multidimensional Poisson limit theorem for the resulting Plancherel growth…
Generative network models are extremely useful for understanding the mechanisms that operate in network formation and are widely used across several areas of knowledge. However, when it comes to bipartite networks -- a class of network…
Convolution trees, loopy belief propagation, and fast numerical p-convolution are combined for the first time to efficiently solve networks with several additive constraints between random variables. An implementation of this "convolution…
In this work we focus on modeling a little studied type of traffic, namely the network traffic generated from endhosts. We introduce a parsimonious parametric model of the marginal distribution for connection arrivals. We employ mixture…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
Mixture models are probabilistic models aimed at uncovering and representing latent subgroups within a population. In the realm of network data analysis, the latent subgroups of nodes are typically identified by their connectivity…
Tree-child networks are an important class of phylogenetic network used to model reticulate evolutionary processes. These networks have attracted increasing attention from researchers with interests in both combinatorics and algorithms. A…
Given an $\mathbb{N}$-weighted tree automaton, we give a decision procedure for exponential vs polynomial growth (with respect to the input size) in quadratic time, and an algorithm that computes the exact polynomial degree of growth in…
The standard procedures for analysing hierarquical or grouped data are by (non)linear mixed models or generalized mixed models. However, the generalized additive models for location, scale and shape (GAMLSSs) also allow different types of…
Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a…
This paper demonstrates the advantages of sharing information about unknown features of covariates across multiple model components in various nonparametric regression problems including multivariate, heteroscedastic, and semi-continuous…
Many networked systems involve multiple modes of transport. Such systems are called multimodal, and examples include logistic networks, biomedical phenomena, manufacturing process and telecommunication networks. Existing techniques for…
We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…
The relative importance of the intrinsic and extrinsic factors determining the variety of geometric shapes exhibited by dendritic trees remains unclear. This question was addressed by developing a model of the growth of dendritic trees…