Random-scan Gibbs samplers possess a natural hierarchical structure. The structure connects Gibbs samplers targeting higher-dimensional distributions to those targeting lower-dimensional ones. This leads to a quasi-te...
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Random-scan Gibbs samplers possess a natural hierarchical structure. The structure connects Gibbs samplers targeting higher-dimensional distributions to those targeting lower-dimensional ones. This leads to a quasi-telescoping property of their spectral gaps. Based on this property, we derive three new bounds on the spectral gaps and convergence rates of Gibbs samplers on general domains. The three bounds relate a chain's spectral gap to, respectively, the correlation structure of the target distribution, a class of random walk chains, and a collection of influence matrices. Notably, one of our results generalizes the technique of spectral independence, which has received considerable attention for its success on finite domains, to general state spaces. We illustrate our methods through a sampler targeting the uniform distribution on a corner of an n-cube.
作者：
Flammang, VUniv Lorraine
UMR CNRS 7502 IECL Site MetzUFR MIMDept Math 3 Rue Augustin FresnelBP 45112 F-57073 Metz 03 France
We first improve the known lower bound for the absolute Zhang-Zagier measure in the general case. Then we restrict our study to totally positive algebraic integers. In this case, we are able to find six points for the...
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We first improve the known lower bound for the absolute Zhang-Zagier measure in the general case. Then we restrict our study to totally positive algebraic integers. In this case, we are able to find six points for the related spectrum. At last, we give inequalities involving the Zhang-Zagier measure, the Mahler measure and the length of such integers.
An M-estimation of the parameters in an undamped exponential signal model was proposed in Wu and Tam(IEEE Trans Signal Process 49(2):373–380,2001),and the estimation was shown to be consistent under mild *** this pap...
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An M-estimation of the parameters in an undamped exponential signal model was proposed in Wu and Tam(IEEE Trans Signal Process 49(2):373–380,2001),and the estimation was shown to be consistent under mild *** this paper,the limiting distributions of the M-estimators are *** is shown that they are asymptotically normally distributed under similar conditions as assumed in Wu and Tam(IEEE Trans Signal Process 49(2):373–380,2001).In addition,a recursive algorithm for computing the M-estimators of frequencies is proposed,and the strong consistency of these estimators is *** Carlo simulation studies using Huber’sρfunction are also provided.
Complexity of a recursive algorithm typically is related to the solution to a recurrence equation based on its recursive structure. For a broad class of recursive algorithms we model their complexity in what we call t...
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Complexity of a recursive algorithm typically is related to the solution to a recurrence equation based on its recursive structure. For a broad class of recursive algorithms we model their complexity in what we call the complexity approach space, the space of all functions in X = ]0, aaEuro parts per thousand] (Y) , where Y can be a more dimensional input space. The set X, which is a dcpo for the pointwise order, moreover carries the complexity approach structure. There is an associated selfmap I broken vertical bar on the complexity approach space X such that the problem of solving the recurrence equation is reduced to finding a fixed point for I broken vertical bar. We will prove a general fixed point theorem that relies on the presence of the limit operator of the complexity approach space X and on a given well founded relation on Y. Our fixed point theorem deals with monotone selfmaps I broken vertical bar that need not be contractive. We formulate conditions describing a class of recursive algorithms that can be treated in this way.
Suppose the X-0, ..., X-n are observations of a one-dimensional stochastic dynamic process described by autoregression equations when the autoregressive parameter is drifted with time, i.e. it is some function of time...
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Suppose the X-0, ..., X-n are observations of a one-dimensional stochastic dynamic process described by autoregression equations when the autoregressive parameter is drifted with time, i.e. it is some function of time: theta (0), ..., theta (n), with theta (k) = theta (k/n). The function theta (t) is assumed to belong a priori to a predetermined nonparametric class of functions satisfying the Lipschitz smoothness condition. At each time point t those observations are accessible which have been obtained during the preceding time interval. A recursive algorithm is proposed to estimate theta (t). Under some conditions on the model, we derive the rate of convergence of the proposed estimator when the frequency of observations n tends to infinity.
A recursive algorithm for the construction of the generalized form of the interpolating rational function is derived. This generalization of the Neville-Aitken algorithm constructs a table of all possible rational int...
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A recursive algorithm for the construction of the generalized form of the interpolating rational function is derived. This generalization of the Neville-Aitken algorithm constructs a table of all possible rational interpolants in implicit form. The algorithm may be simply modified so that it does not break down when a singularity occasionally appears. The coefficients of the interpolant and the evaluation of the interpolant at an arbitrary point may be easily calculated.
作者：
Flammang, VUniv Lorraine
IECL Site Metz UFR MIMDept Math 3 Rue Augustin FresnelBP 45112 F-57073 Metz 3 France
We give upper and lower bounds for the trace of a Salem number whose Mahler measure is less than 1.3. We use the method of explicit auxiliary functions, combined with a recursive algorithm developed by the author.
We give upper and lower bounds for the trace of a Salem number whose Mahler measure is less than 1.3. We use the method of explicit auxiliary functions, combined with a recursive algorithm developed by the author.
Sampling from probability distributions in high dimensional spaces is generally impractical. Diffusion processes with invariant equilibrium distributions can be used as a means to generate approximations. An important...
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Sampling from probability distributions in high dimensional spaces is generally impractical. Diffusion processes with invariant equilibrium distributions can be used as a means to generate approximations. An important task in such an endeavor is to design an equilibrium-preserving drift to accelerate the convergence. Starting from a reversible diffusion, it is desirable to depart for non-reversible dynamics via a perturbed drift so that the convergence rate is maximized with the common equilibrium. In the Gaussian diffusion acceleration, this problem can be cast as perturbing the inverse of a given covariance matrix by skew-symmetric matrices so that all resulting eigenvalues have identical real part. This paper describes two approaches to obtain the optimal rate of Gaussian diffusion. The asymptotical approach works universally for arbitrary Ornstein-Uhlenbeck processes, whereas the direct approach can be implemented as a fast divide-and-conquer algorithm. A comparison with recently proposed LeliSvre-Nier-Pavliotis algorithm is made.
This work proposes a causal and recursive algorithm for solving the "robust" principal components' analysis problem. We primarily focus on robustness to correlated outliers. In recent work, we proposed a...
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ISBN:
(纸本)9781457705953
This work proposes a causal and recursive algorithm for solving the "robust" principal components' analysis problem. We primarily focus on robustness to correlated outliers. In recent work, we proposed a new way to look at this problem and showed how a key part of its solution strategy involves solving a noisy compressive sensing (CS) problem. However, if the support size of the outliers becomes too large, for a given dimension of the current principal components' space, then the number of "measurements" available for CS may become too small. In this work, we show how to address this issue by utilizing the correlation of the outliers to predict their support at the current time;and using this as "partial support knowledge" for solving Modified-CS instead of CS.
In recent years, many industrialfacilities have been required to install sensing system to monitor the health status of the equipment. Although the PC-based diagnosis system is a good alternative, it undoubtedly incre...
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In recent years, many industrialfacilities have been required to install sensing system to monitor the health status of the equipment. Although the PC-based diagnosis system is a good alternative, it undoubtedly increases the hardware cost greatly, and also causes restrictions on system assembly. In some critical environments, installation of the PC-based system is not suitable because of high temperature, dust, and humidity. On the contrary, a high mobility portable smart sensor will be relatively adequate for onsite inspections. To solve this problem, we developed a low-cost embedded handheld smart sensor. Instead of using sophisticated algorithms, certain frequently used statistic indicators are considered. Nevertheless, due to the resource limitations of the embedded systems, it causes difficulty for real-time realization and therefore, the recursive architecture of the statistic indicators is derived. These statistical factors are then fed into a Gaussian classifier for online defect detection, which gives a great contribution to field operators for onsite inspections. The highly integrated hardware/software co-design of the developed device provides user-friendly and high mobility for field inspections. Finally, a practical industrial application regarding the online diagnosis of a solenoid valve actuator defect is presented to demonstrate the effectiveness of the developed embedded smart sensor.
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