Related papers: Cluster expansion methods in rigorous statistical …
Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. As such, the study of clusterability, which evaluates whether data possesses such structure, is an integral part of cluster analysis. Yet,…
Constrained clustering has gained significant attention in the field of machine learning as it can leverage prior information on a growing amount of only partially labeled data. Following recent advances in deep generative models, we…
Probabilistic models such as logistic regression, Bayesian classification, neural networks, and models for natural language processing, are increasingly more present in both undergraduate and graduate statistics and data science curricula…
Aiming at a comprehensive and concise tutorial survey, recap of variational inference and reinforcement learning with Probabilistic Graphical Models are given with detailed derivations. Reviews and comparisons on recent advances in deep…
In recent years, the problem of fuzzy clustering has been widely concerned. The membership iteration of existing methods is mostly considered globally, which has considerable problems in noisy environments, and iterative calculations for…
Mayer cluster expansion is an important tool in statistical physics to evaluate grand canonical partition functions. It has recently been applied to the Nekrasov instanton partition function of $\mathcal{N}=2$ 4d gauge theories. The…
The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical…
It is well known that most of the common clustering objectives are NP-hard to optimize. In practice, however, clustering is being routinely carried out. One approach for providing theoretical understanding of this seeming discrepancy is to…
This is an extensive review of recent work on the foundations of statistical mechanics. Subject matters discussed include: interpretation of probability, typicality, recurrence, reversibility, ergodicity, mixing, coarse graining, past…
To provide a survey on the existing tasks and models in Machine Reading Comprehension (MRC), this report reviews: 1) the dataset collection and performance evaluation of some representative simple-reasoning and complex-reasoning MRC tasks;…
We present a statistical system that can be used in the study of cluster populations. The basis of our approach is the construction of synthetic cluster color-magnitude-radius diagrams (CMRDs), which we compare with the observed data using…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and…
Clusters of galaxies are important laboratories for understanding both galaxy evolution and constraining cosmological quantities. Any analysis of clusters, however, is best done when one can reliably determine which galaxies are members of…
Spectral clustering requires the time-consuming decomposition of the Laplacian matrix of the similarity graph, thus limiting its applicability to large datasets. To improve the efficiency of spectral clustering, a top-down approach was…
The traditional theoretical statistics course which develops the theoretical underpinnings of the discipline (usually following a probability course) is undergoing near-continuous revision in the statistics community. In particular, recent…
The analysis of the spatial distribution and kinematics of galaxies in clusters allows one to determine the cluster internal dynamics. In this paper, I review the state of the art of this topic. In particular, I summarize what we have…
Clustering Text has been an important problem in the domain of Natural Language Processing. While there are techniques to cluster text based on using conventional clustering techniques on top of contextual or non-contextual vector space…
This paper develops power series expansions of a general class of moment functions, including transition densities and option prices, of continuous-time Markov processes, including jump--diffusions. The proposed expansions extend the ones…
Clustering is a fundamental machine learning task which has been widely studied in the literature. Classic clustering methods follow the assumption that data are represented as features in a vectorized form through various representation…