Related papers: A mini-review on combinatorial solutions to the Ma…
Quality assessments of models in unsupervised learning and clustering verification in particular have been a long-standing problem in the machine learning research. The lack of robust and universally applicable cluster validity scores often…
Generalized Zeckendorf decompositions are expansions of integers as sums of elements of solutions to recurrence relations. The simplest cases are base-$b$ expansions, and the standard Zeckendorf decomposition uses the Fibonacci sequence.…
There is a rich literature for modeling binary and polychotomous responses. However, existing methods are inadequate for handling combinatorial responses, where each response is an integer array under additional constraints. Such data are…
The paper addresses aggregation issues for composite (modular) solutions. A systemic view point is suggested for various aggregation problems. Several solution structures are considered: sets, set morphologies, trees, etc. Mainly, the…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…
We present a simple one-dimensional model with molecular interactions favouring the formation of clusters with a defined optimal size. Increasing the density, at low temperature, the system goes from a nearly-ideal gas of independent…
The scaling theory of irreversible aggregation is discussed in some detail. First, we review the general theory in the simplest case of binary reactions. We then extend consideration to ternary reactions, multispecies aggregation,…
Generalized linear mixed models (GLMMs) are often used for analyzing correlated non-Gaussian data. The likelihood function in a GLMM is available only as a high dimensional integral, and thus closed-form inference and prediction are not…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
While several Gaussian mixture models-based biclustering approaches currently exist in the literature for continuous data, approaches to handle discrete data have not been well researched. A multivariate Poisson-lognormal (MPLN) model-based…
We develop a systematic cluster expansion for dilute systems in the highly dilute phase. We first apply it to the calculation of the entropy of the K-satisfiability problem in the satisfiable phase. We derive a series expansion in the…
We introduce a general semiparametric clusterwise elliptical distribution to assess how latent cluster structure shapes continuous outcomes. Using a subjectwise representation, we first estimate cluster-specific mean vectors and a…
We consider the classical Smoluchowski coagulation equation with a general frequency kernel. We show that there exists a natural deterministic solution expansion in the non-associative algebra generated by the convolution product of the…
We develop a generalized hybrid iterative approach for computing solutions to large-scale Bayesian inverse problems. We consider a hybrid algorithm based on the generalized Golub-Kahan bidiagonalization for computing Tikhonov regularized…
We introduce a novel framework for uncertainty quantification in clustering that combines martingale posterior distributions with density-based clustering. Unlike classical model-based approaches, which define clusters at the latent level…
The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by…
Growth in both size and complexity of modern data challenges the applicability of traditional likelihood-based inference. Composite likelihood (CL) methods address the difficulties related to model selection and computational intractability…
Spectral clustering is a broad class of clustering procedures in which an intractable combinatorial optimization formulation of clustering is "relaxed" into a tractable eigenvector problem, and in which the relaxed solution is subsequently…
We consider the convergence of iterative solvers for problems of nonlinear magnetostatics. Using the equivalence to an underlying minimization problem, we can establish global linear convergence of a large class of methods, including the…