The Computational Complexity of Estimating Convergence Time

An important problem in the implementation of Markov Chain Monte Carlo algorithms is to determine the convergence time, or the number of iterations before the chain is close to stationarity. For many Markov chains used in practice this time is not known. Even in cases where the convergence time is known to be polynomial, the theoretical bounds are often too crude to be practical. Thus, practitioners like to carry out some form of statistical analysis in order to assess convergence. This has led to the development of a number of methods known as convergence diagnostics which attempt to diagnose whether the Markov chain is far from stationarity. We study the problem of testing convergence in the following settings and prove that the problem is hard in a computational sense: Given a Markov chain that mixes rapidly, it is hard for Statistical Zero Knowledge (SZK-hard) to distinguish whether starting from a given state, the chain is close to stationarity by time t or far from stationarity at time ct for a constant c. We show the problem is in AM intersect coAM. Second, given a Markov chain that mixes rapidly it is coNP-hard to distinguish whether it is close to stationarity by time t or far from stationarity at time ct for a constant c. The problem is in coAM. Finally, it is PSPACE-complete to distinguish whether the Markov chain is close to stationarity by time t or far from being mixed at time ct for c at least 1

Modeling and characterization of TES-based detectors for the Ricochet experiment

Coherent elastic neutrino-nucleus scattering (CE$\nu$NS) offers a valuable approach in searching for physics beyond the Standard Model. The Ricochet experiment aims to perform a precision measurement of the CE$\nu$NS spectrum at the Institut Laue-Langevin nuclear reactor with cryogenic solid-state detectors. The experiment plans to employ an array of cryogenic thermal detectors, each with a mass around 30 g and an energy threshold of sub-100 eV. The array includes nine detectors read out by Transition-Edge Sensors (TES). These TES based detectors will also serve as demonstrators for future neutrino experiments with thousands of detectors. In this article we present an update in the characterization and modeling of a prototype TES detector.Comment: Submitted to LTD20 proceedin

Faster Random Walks By Rewiring Online Social Networks On-The-Fly

Many online social networks feature restrictive web interfaces which only allow the query of a user's local neighborhood through the interface. To enable analytics over such an online social network through its restrictive web interface, many recent efforts reuse the existing Markov Chain Monte Carlo methods such as random walks to sample the social network and support analytics based on the samples. The problem with such an approach, however, is the large amount of queries often required (i.e., a long "mixing time") for a random walk to reach a desired (stationary) sampling distribution. In this paper, we consider a novel problem of enabling a faster random walk over online social networks by "rewiring" the social network on-the-fly. Specifically, we develop Modified TOpology (MTO)-Sampler which, by using only information exposed by the restrictive web interface, constructs a "virtual" overlay topology of the social network while performing a random walk, and ensures that the random walk follows the modified overlay topology rather than the original one. We show that MTO-Sampler not only provably enhances the efficiency of sampling, but also achieves significant savings on query cost over real-world online social networks such as Google Plus, Epinion etc.Comment: 15 pages, 14 figure, technical report for ICDE2013 paper. Appendix has all the theorems' proofs; ICDE'201

Detection of contact failures with the Markov chain Monte Carlo method by using integral transformed measurements

This work deals with the solution of an inverse heat conduction problem aiming at the detection of contact failures in layered composites through the estimation of the contact conductance between the layers. The spatially varying contact conductance is estimated using a Bayesian formulation of the problem and a Markov chain Monte Carlo method, with infrared camera measurements of the transient temperature field on the surface of the body. The inverse analysis is formulated using a data compression scheme, where the temperature measurements are integral transformed with respect to the spatial variable. The present approach is evaluated using synthetic measurements and experimental data from controlled laboratory experiments. It is shown that only few transformed modes of the data are required for solving the inverse problem, thus providing substantial reduction of the computational time in the Markov chain Monte Carlo method, as well as regularization of the ill-posed problem.Indisponível

On the Geometric Ergodicity of Metropolis-Hastings Algorithms for Lattice Gaussian Sampling

Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, the classic Metropolis-Hastings (MH) algorithm from Markov chain Monte Carlo (MCMC) methods is adapted for lattice Gaussian sampling. Two MH-based algorithms are proposed, which overcome the restriction suffered by the default Klein's algorithm. The first one, referred to as the independent Metropolis-Hastings-Klein (MHK) algorithm, tries to establish a Markov chain through an independent proposal distribution. We show that the Markov chain arising from the independent MHK algorithm is uniformly ergodic, namely, it converges to the stationary distribution exponentially fast regardless of the initial state. Moreover, the rate of convergence is explicitly calculated in terms of the theta series, leading to a predictable mixing time. In order to further exploit the convergence potential, a symmetric Metropolis-Klein (SMK) algorithm is proposed. It is proven that the Markov chain induced by the SMK algorithm is geometrically ergodic, where a reasonable selection of the initial state is capable to enhance the convergence performance.Comment: Submitted to IEEE Transactions on Information Theor