In the traditional formulation of Gaussian Process Regression (GPR), the input data is assumed to be noise-free. However, this assumption is not always realistic in many practical problems. A new robust GPR model is i...
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In the traditional formulation of Gaussian Process Regression (GPR), the input data is assumed to be noise-free. However, this assumption is not always realistic in many practical problems. A new robust GPR model is introduced in this paper where the input and output are both corrupted by noise. To address this problem, the output noise is modelled using a mixture of two Gaussian distributions to account for both regular and outlying noises and the input noise is assumed to be an independently and identically distributed (i.i.d.) Gaussian noise. A learning scheme based on the Errors-In-Variables (EIV) model and the Expectation Maximization (em) algorithm is proposed to derive a new Gaussian Process model whose kernel function is dependent on hyper-parameters describing both the input and output noises. The first and second moments of the predictive distribution are obtained based on the learned hyper-parameters through the proposed algorithm. Simulation examples as well as an industrial case study presented here demonstrate the effectiveness of the proposed method and its superiority to other existing methods.
Digital images often suffer from the common problem of stripe noise due to the inconsistent bias of each column. The existence of the stripe poses much more difficulties on image denoising since it requires another n ...
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Digital images often suffer from the common problem of stripe noise due to the inconsistent bias of each column. The existence of the stripe poses much more difficulties on image denoising since it requires another n parameters, where n is the width of the image, to characterize the total interference of the observed image. This paper proposes a novel em-based framework for simultaneous stripe estimation and image denoising. The great benefit of the proposed framework is that it splits the overall destriping and denoising problem into two independent sub-problems, i.e., calculating the conditional expectation of the true image given the observation and the estimated stripe from the last round of iteration, and estimating the column means of the residual image, such that a Maximum Likelihood Estimation (MLE) is guaranteed and it does not require any explicit parametric modeling of image priors. The calculation of the conditional expectation is the key, here we choose a modified Non-Local Means algorithm to calculate the conditional expectation because it has been proven to be a consistent estimator under some conditions. Besides, if we relax the consistency requirement, the conditional expectation could be interpreted as a general image denoiser. Therefore other state-of-the-art image denoising algorithms have the potentials to be incorporated into the proposed framework. Extensive experiments have demonstrated the superior performance of the proposed algorithm and provide some promising results that motivate future research on the em-based destriping and denoising framework.
This paper addresses the problems of parameter estimation of multivariable stationary stochastic systems on the basis of observed output *** main contribution is to employ the expectation-maximisation(em)method as a m...
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This paper addresses the problems of parameter estimation of multivariable stationary stochastic systems on the basis of observed output *** main contribution is to employ the expectation-maximisation(em)method as a means for computation of the maximum-likelihood(ML)parameter estimation of the *** form of the expectation of the studied system subjected to Gaussian distribution noise is derived and parameter choice that maximizes the expectation is also *** results in an iterative algorithm for parameter estimation and the robust algorithm implementation based on technique of QR-factorization and Cholesky factorization is also ***,algorithmic properties such as non-decreasing likelihood value,necessary and sufficient conditions for the algorithm to arrive at a local stationary parameter,the convergence rate and the factors affecting the convergence rate are *** study shows that the proposed algorithm has attractive properties such as numerical stability,and avoidance of difficult initial conditions.
We present in this paper general formulas for deriving the maximum likelihood estimates and the asymptotic variance-covariance matrix of the positions and effects of quantitative trait loci (QTLs) in a finite normal m...
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We present in this paper general formulas for deriving the maximum likelihood estimates and the asymptotic variance-covariance matrix of the positions and effects of quantitative trait loci (QTLs) in a finite normal mixture model when the em algorithm is used for mapping QTLs. The general formulas are based on two matrices D and Q, where D is the genetic design matrix, characterizing the genetic effects of the QTLs, and Q is the conditional probability matrix of QTL genotypes given flanking marker genotypes, containing the information on QTL positions. With the general formulas, it is relatively easy to extend QTL mapping analysis to using multiple marker intervals simultaneously for mapping multiple QTLs, for analyzing QTL epistasis, and for estimating the heritability of quantitative traits. Simulations were performed to evaluate the performance of the estimates of the asymptotic variances of QTL positions and effects.
The em algorithm is an efficient algorithm to obtain the ML estimate for incomplete data, but has the local optimality problem. The deterministic annealing em (DAem) algorithm was once proposed to solve this problem, ...
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ISBN:
(纸本)9783540855668
The em algorithm is an efficient algorithm to obtain the ML estimate for incomplete data, but has the local optimality problem. The deterministic annealing em (DAem) algorithm was once proposed to solve this problem, which begins a search from the primitive initial point (PIP). Then, proposed was the mes-em algorithm, which runs the em repeatedly in many various directions from the PIP, and achieves good solution quality with high computing cost. This paper proposes a variant of the mes-em, called mes-em(beta), which uses the temperature to select a small promising portion of the mes-em runs. Our experiments for the Gaussian mixture estimation showed the proposed algorithm was much faster than the original mes-em without degrading its solution quality.
It has recently been shown that the maximum-likelihood estimate of the parameters of a Markov-modulated Poisson process is consistent. In this paper we present an em algorithm for computing such estimates and discuss ...
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It has recently been shown that the maximum-likelihood estimate of the parameters of a Markov-modulated Poisson process is consistent. In this paper we present an em algorithm for computing such estimates and discuss how it may be implemented. We also compare it to the Nelder-Mead downhill simplex algorithm for some numerical examples, and the results show that the number of iterations the em algorithm requires to converge is in general smaller than the number of likelihood evaluations required by the downhill simplex algorithm. An em iteration is more complicated than a likelihood evaluation, though, and thus also implementation aspects must be taken into account to determine the efficiencies of the algorithms.
The need to find new pattern recognition techniques that correctly classify complex structures has risen as an important held of research. A well-known solution to this problem, which has proven to be very powerful, i...
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The need to find new pattern recognition techniques that correctly classify complex structures has risen as an important held of research. A well-known solution to this problem, which has proven to be very powerful, is the use of mixture models, Mixture models are typically fitted using the expectation-maximization (em) algorithm. Unfortunately, optimal results are not always achieved because the em algorithm, iterative in nature, is only guaranteed to produce a local maximum. In this paper, a solution to this problem is proposed and tested in a complex structure where the classical em algorithm normally fails. This, we will do by means of a genetic algorithm (CA) which will allow the system to combine different solutions in a stochastic search so as to produce better results. The reported results show the usefulness of this approach, and suggest how it can be successfully implemented. Two new algorithms are proposed. The first one is useful when a priori information of the observed data is not available. The second solution is useful for those cases where some knowledge of the structure of the data-set is known. This second solution has proven to converge faster than the first one, although the final results reached are very similar to each other. (C) 2000 Published by Elsevier Science B.V. All rights reserved.
The Gamma-frailty proportional hazards (PH) model is commonly used to analyze correlated survival data. Despite this model's popularity, the analysis of correlated current status data under the Gamma-frailty PH mo...
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The Gamma-frailty proportional hazards (PH) model is commonly used to analyze correlated survival data. Despite this model's popularity, the analysis of correlated current status data under the Gamma-frailty PH model can prove to be challenging using traditional techniques. Consequently, in this paper we develop a novel expectation-maximization (em) algorithm under the Gamma-frailty PH model to study bivariate current status data. Our method uses a monotone spline representation to approximate the unknown conditional cumulative baseline hazard functions. Proceeding in this fashion leads to the estimation of a finite number of parameters while simultaneously allowing for modeling flexibility. The derivation of the proposed em algorithm relies on a three-stage data augmentation involving Poisson latent variables. The resulting algorithm is easy to implement, robust to initialization, and enjoys quick convergence. Simulation results suggest that the proposed method works well and is robust to the misspeciflcation of the frailty distribution. Our methodology is used to analyze chlamydia and gonorrhea data collected by the Nebraska Public Health Laboratory as a part of the Infertility Prevention Project. (C) 2014 Elsevier B.V. All rights reserved.
The Riesz probability distribution was introduced in 2001 as an extension of the Wishart one. Although the Wishart distribution was investigated in many engineering applications, the Riesz applicability seems to be fo...
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The Riesz probability distribution was introduced in 2001 as an extension of the Wishart one. Although the Wishart distribution was investigated in many engineering applications, the Riesz applicability seems to be forsaken. This can be explained by the lack of studies offering statistical models and algorithms dealing with this distribution. Within this framework, we extend the Bartlett decomposition to the Riesz and inverse Riesz probability distributions. We prove that they can be generated easily using gamma and Gaussian independent variates adequately parameterized. Then we develop an Expectation-Maximization algorithm to estimate the parameters of the Riesz mixture model, along with the inverse Riesz mixture. Finally, some simulations are conducted and show a good estimation of the mixture parameters and clusters number.
We address the problem of learning robot control by model-free reinforcement learning (RL). We adopt the probabilistic model for model-free RL of Vlassis and Toussaint (Proceedings of the international conference on m...
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We address the problem of learning robot control by model-free reinforcement learning (RL). We adopt the probabilistic model for model-free RL of Vlassis and Toussaint (Proceedings of the international conference on machine learning, Montreal, Canada, 2009), and we propose a Monte Carlo em algorithm (MCem) for control learning that searches directly in the space of controller parameters using information obtained from randomly generated robot trajectories. MCem is related to, and generalizes, the PoWER algorithm of Kober and Peters (Proceedings of the neural information processing systems, 2009). In the finite-horizon case MCem reduces precisely to PoWER, but MCem can also handle the discounted infinite-horizon case. An interesting result is that the infinite-horizon case can be viewed as a 'randomized' version of the finite-horizon case, in the sense that the length of each sampled trajectory is a random draw from an appropriately constructed geometric distribution. We provide some preliminary experiments demonstrating the effects of fixed (PoWER) vs randomized (MCem) horizon length in two simulated and one real robot control tasks.
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