Related papers: Cluster expansion methods in rigorous statistical …
A new depth-based clustering procedure for directional data is proposed. Such method is fully non-parametric and has the advantages to be flexible and applicable even in high dimensions when a suitable notion of depth is adopted. The…
We investigate two examples of node-based cluster summation rules that have been proposed for the quasicontinuum method: a force-based approach (Knap & Ortiz, J. Mech. Phys. Solids 49, 2001), and an energy-based approach which is a…
Inference in clustering is paramount to uncovering inherent group structure in data. Clustering methods which assess statistical significance have recently drawn attention owing to their importance for the identification of patterns in high…
The one-dimensional contact process is analyzed by a cluster approximation. In this approach, the hierarchy of rate equations for the densities of finite length empty intervals are truncated under the assumption that adjacent intervals are…
Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of such graphs. Some of the most useful graph metrics are based on triangles, such as those measuring social…
It has become standard for empirical studies to conduct inference robust to cluster dependence and heterogeneity. With a small number of clusters, the normal approximation for the $t$-statistics of regression coefficients may be poor. This…
Clustering is a crucial tool for analyzing data in virtually every scientific and engineering discipline. There are more scalable solutions framed to enable time and space clustering for the future large-scale data analyses. As a result,…
A scalable graphical method is presented for selecting, and partitioning datasets for the training phase of a classification task. For the heuristic, a clustering algorithm is required to get its computation cost in a reasonable proportion…
The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating…
An approach to improve neural network interpretability is via clusterability, i.e., splitting a model into disjoint clusters that can be studied independently. We define a measure for clusterability and show that pre-trained models form…
In this work we present a coupled-cluster theory for the propagation of multireference electronic systems initiating at general quantum mechanical states. Our formalism is based on the infinitesimal analysis of modified cluster operators,…
Continuous-time Bayesian networks (CTBNs) constitute a general and powerful framework for modeling continuous-time stochastic processes on networks. This makes them particularly attractive for learning the directed structures among…
Several issues related to the gravitational clustering of collisionless dark matter in an expanding universe is discussed. The discussion is pedagogical but the emphasis is on semianalytic methods and open questions - rather than on well…
Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).
Expanded lecture notes. Preliminary version, comments are welcome.
These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author…
Clustering is one of the most fundamental tasks in data analysis and machine learning. It is central to many data-driven applications that aim to separate the data into groups with similar patterns. Moreover, clustering is a complex…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…
A quantitative first-principles description of complex substitutional materials like alloys is challenging due to the vast number of configurations and the high computational cost of solving the quantum-mechanical problem. Therefore,…
This is a supplement to the article "Markov Chain Monte Carlo Based on Deterministic Transformations" available at http://arxiv.org/abs/1106.5850