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Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
The partition function of the finite $1+\epsilon$ state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are…
We present a global optimization algorithm for clustering data given the ratio of likelihoods that each pair of data points is in the same cluster or in different clusters. To define a clustering solution in terms of pairwise relationships,…
We examine the structure of the percolating cluster (PC) formed by site percolation on a random clustered network (RCN) model. Using the generating functions, we formulate the clustering coefficient and assortative coefficient of the PC. We…
A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of $[n]=\{1,...,n\}$ at time $\theta \ge 0$ is governed by the Ewens sampling formula with parameter $\theta$. These…
Algorithms for community detection are usually stochastic, leading to different partitions for different choices of random seeds. Consensus clustering has proven to be an effective technique to derive more stable and accurate partitions…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…
We present a novel framework for concomitant dimension reduction and clustering. This framework is based on a novel class of Bayesian clustering factor models. These models assume a factor model structure where the vectors of common factors…
We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over…
This paper proposes a new linearized mixed data sampling (MIDAS) model and develops a framework to infer clusters in a panel regression with mixed frequency data. The linearized MIDAS estimation method is more flexible and substantially…
We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…
A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…
Colloidal clusters consist of small numbers of colloidal particles bound by weak, short-range attractions. The equilibrium probability of observing a cluster in a particular geometry is well-described by a statistical mechanical model…
Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of…
Bayesian clustering typically relies on mixture models, with each component interpreted as a different cluster. After defining a prior for the component parameters and weights, Markov chain Monte Carlo (MCMC) algorithms are commonly used to…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
We describe and analyze a simple random feature scheme (RFS) from prescribed compositional kernels. The compositional kernels we use are inspired by the structure of convolutional neural networks and kernels. The resulting scheme yields…
The repeated presentation of an identical visual stimulus in the receptive field of a neuron may evoke different spiking patterns at each trial. Probabilistic methods are essential to understand the functional role of this variance within…