Related papers: Path Coupling and Aggregate Path Coupling
We propose a new method for clustering multivariate time-series data based on Dynamic Linear Models. Whereas usual time-series clustering methods obtain static membership parameters, our proposal allows each time-series to dynamically…
The Coupled-Cluster theory is one of the most successful high precision methods used to solve the stationary Schr\"odinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in…
Predictive distributions need to be aggregated when probabilistic forecasts are merged, or when expert opinions expressed in terms of probability distributions are fused. We take a prediction space approach that applies to discrete, mixed…
An analysis using a composition of currently-accepted theories is given. Starting with a synthesis of what may be generically termed ``paths'', analysis of representations for these ``paths'' is developed. Foreground and background…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
The random-cluster model with parameters $(p,q)$ is a random graph model that generalizes bond percolation ($q=1$) and the Ising and Potts models ($q\geq 2$). We study its Glauber dynamics on $n\times n$ boxes $\Lambda_{n}$ of the integer…
Given the adjacency matrix of an undirected graph, we define a coupling of the spectral measures at the vertices, whose moments count the rooted closed paths in the graph. The resulting joint spectral measure verifies numerous interesting…
Detecting anomalous edges in dynamic graphs is an important task in many applications over evolving triple-based data, such as social networks, transaction management, and epidemiology. A major challenge with this task is the absence of…
Gauge coupling unification is studied within the framework where there are extra Higgs doublets and $E_6$ exotic fields. Supersymmetric models and nonsupersymmetric models are investigated, and a catalog of models with gauge coupling…
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
A diagrammatic method is presented for averaging over the circular ensemble of random-matrix theory. The method is applied to phase-coherent conduction through a chaotic cavity (a ``quantum dot'') and through the interface between a normal…
We describe a new family of coupling designs, extending the basic principle of stratified randomization to experiments with continuous, constrained multivariate, text/image and other irregular treatment spaces. Our approach is to first…
We describe computationally efficient methods for learning mixtures in which each component is a directed acyclic graphical model (mixtures of DAGs or MDAGs). We argue that simple search-and-score algorithms are infeasible for a variety of…
We consider the simulation of distributions that are a mixture of discrete and continuous components. We extend a Metropolis-Hastings-based perfect sampling algorithm of Corcoran and Tweedie to allow for a broader class of transition…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…
Facing the congestion challenges of mixed road networks comprising expressways and arterial road networks, traditional control solutions fall short. To effectively alleviate traffic congestion in mixed road networks, it is crucial to clear…
The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this paper we analyze the Glauber dynamics of the…
In this article, we present some specific aspects of symmetric Gamma process mixtures for use in regression models. We propose a new Gibbs sampler for simulating the posterior and we establish adaptive posterior rates of convergence related…
Generalized mode-coupling theory (GMCT) has recently emerged as a promising first-principles theory to study the poorly understood dynamics of glass-forming materials. Formulated as a hierarchical extension of standard mode-coupling theory…