Spectral gap markov chain
WebMar 26, 2024 · We consider the problem of estimating from sample paths the absolute spectral gap 1 - λ of a reversible, irreducible and aperiodic Markov chain (X_t)_t∈N over a … WebNov 7, 2024 · For example, the spectral gap of a transition matrix is closely related to the mixing time of the corresponding Markov chain, which can be useful in one of the topics …
Spectral gap markov chain
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WebThe Markov chain can be considered as a random walk on this weighted graph, and the edge weights represent theergodic ow q(x;y) which travels along the edge at each step if the chain is in the stationary distribution. WebSpectral gap, which is the area between the radius with length equal to the second largest eigenvalue magnitude (SLEM) and the radius with a length of 1. The spectral gap determines the mixing time of the Markov chain. Large gaps indicate faster mixing, whereas thin gaps indicate slower mixing.
WebWell-known inequalities for the spectral gap of a discrete-time Markov chain, such as Poincaré's and Cheeger's inequalities, do not perform well if the transition graph of the Markov chain is strongly connected. WebThe spectral gapγof a finite, ergodic and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In ap- plications, the transition matrixPmay be unknown, yet one sample of the chainuptoafixedtimenmay be observed. We consider here the problem of estimatingγfrom this data.
WebJul 14, 2016 · On spectral gap estimates of a Markov chain via hitting times and coupling - Volume 36 Issue 2 Skip to main content Accessibility help We use cookies to distinguish … WebDec 16, 2016 · The spectral gap of an ergodic and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix may be unknown, yet one sample of the chain up to a fixed time may be observed. Hsu, Kontorovich, and Szepesvari (2015) considered the problem of estimating from this …
Webspectral gap. The following theorem resolves the optimal risk for k-state Markov chains: Theorem 1 (Optimal rates without spectral gap). There exists a universal constant C>0 such that for all 3 ≤k≤ √ n/C, k2 Cn log n k2 ≤Risk k,n≤ Ck2 n log n k2 . (3) Furthermore, the lower bound continues to hold even if the Markov chain is ...
Webon the spectral gap (Theorem 4.4) and log–Sobolev con-stant (Theorem 5.4) of π–recursive Markov chains. Our approach yields a tight bound on spectral gap for the ran-dom walk … breathable mouth guard footballWebspectral gap of the weight matrix [17], [18]. More precisely, the mixing time of a Markov chain with transition probability matrix W quantifies the convergence time of a discrete-time consensus algorithm with weight matrix W to the average. Thus, in this paper we only state our results in terms of the terminology of Markov chain theory. III. cosy club bristol menuWeb1 Approximate spectral gaps for Markov chains mixing times in high dimensions 2 Yves F. Atchad ey 3 4 Abstract. This paper introduces a concept of approximate spectral gap to … breathable mouthguardWebJul 15, 2024 · where \(\mathbbm {1}_k(\cdot )\) is the indicator function, which is 1 only if the regime is \(s_t = k\) and 0 otherwise.. In the case of an ergodic Markov chain, there exists a positive probability of being at any of the states. Furthermore, and according to the Perron–Frobenius theorem (Levin and Peres 2024), the corresponding transition P will … breathable motorcycle pantsWebThe development of new symmetrization inequalities in high-dimensional probability for Markov chains is a key element in our extension, where the spectral gap of the infinitesimal generator of the Markov chain plays a key parameter in these inequalities. We also propose a simple method to convert these bounds and other similar ones in ... breathable motorcycle rain suitWebJul 14, 2016 · The spectral gap and perturbation bounds for reversible continuous-time Markov chains - Volume 41 Issue 4. Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. ... We show that, for reversible continuous-time Markov chains, the closeness … breathable muck bootsWebHowever, calculating (and even approximating) the spectral gaps of practical Monte Carlo Markov chains in statistics has proven to be an extremely difficult and often … cosy club private hire