Related papers: Mixing Time Bounds via the Spectral Profile
We show that the Jerrum-Sinclair Markov chain on matchings mixes in time $\widetilde{O}(\Delta^2 m)$ on any graph with $n$ vertices, $m$ edges, and maximum degree $\Delta$, for any constant edge weight $\lambda>0$. For general graphs with…
Extremes of information combining inequalities play an important role in the analysis of sparse-graph codes under message-passing decoding. We introduce new tools for the derivation of such inequalities, and show by means of a concrete…
In this work we obtain mixing (and in some cases sharp mixing rates) for a reasonable large class of invertible systems preserving an infinite measure. The examples considered here are the invertible analogue of both Markov and non Markov…
Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods,…
This study proposes a novel framework for spectral unmixing by using 1D convolution kernels and spectral uncertainty. High-level representations are computed from data, and they are further modeled with the Multinomial Mixture Model to…
The main challenge addressed in this paper is to identify individual terms in a superposition of heat kernels on a graph. We establish geometric conditions on the vertices at which these heat kernels are centered and find bounds on the time…
The paper presents efficient approaches for evaluating convergence rate in total variation for finite and general linear Markov chains. The motivation for studying convergence rate in this metric is its usefulness in various limit theorems.…
We consider the mean-field Zero-Range process in the regime where the potential function $r$ is increasing to infinity at sublinear speed, and the density of particles is bounded. We determine the mixing time of the system, and establish…
Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…
Given a mixed hyperspectral data set, linear unmixing aims at estimating the reference spectral signatures composing the data - referred to as endmembers - their abundance fractions and their number. In practice, the identified endmembers…
We consider Markov chains on general state spaces in stationary random environment which are defined by a random mapping that is contractive up to a bounded perturbation. We prove their convergence to a limiting law, providing convergence…
Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We…
We prove tight bounds on the site percolation threshold for $k$-uniform hypergraphs of maximum degree $\Delta$ and for $k$-uniform hypergraphs of maximum degree $\Delta$ in which any pair of edges overlaps in at most $r$ vertices. The…
Intensity mapping is a promising technique for surveying the large scale structure of our Universe from $z=0$ to $z \sim 150$, using the brightness temperature field of spectral lines to directly observe previously unexplored portions of…
Since 1997 a considerable effort has been spent to study the mixing time of switch Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained,…
The existing research on spectral algorithms, applied within a Reproducing Kernel Hilbert Space (RKHS), has primarily focused on general kernel functions, often neglecting the inherent structure of the input feature space. Our paper…
Given a graph $G$, the hard-core model defines a probability distribution over its independent sets, assigning to each set of size $k$ a probability of $\frac{\lambda^k}{Z}$, where $\lambda>0$ is a parameter known as the \emph{fugacity} and…
The joint detection uses Kalman filtering (KF) to estimate the prior probability of control outputs to assist channel decoding. In this paper, we regard the joint detection as maximum a posteriori (MAP) decoding and derive the lower and…
We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…
We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and…