Results 1  10
of
15
On the Convergence of Monte Carlo Maximum Likelihood Calculations
 Journal of the Royal Statistical Society B
, 1992
"... Monte Carlo maximum likelihood for normalized families of distributions (Geyer and Thompson, 1992) can be used for an extremely broad class of models. Given any family f h ` : ` 2 \Theta g of nonnegative integrable functions, maximum likelihood estimates in the family obtained by normalizing the the ..."
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Cited by 59 (3 self)
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Monte Carlo maximum likelihood for normalized families of distributions (Geyer and Thompson, 1992) can be used for an extremely broad class of models. Given any family f h ` : ` 2 \Theta g of nonnegative integrable functions, maximum likelihood estimates in the family obtained by normalizing the the functions to integrate to one can be approximated by Monte Carlo, the only regularity conditions being a compactification of the parameter space such that the the evaluation maps ` 7! h ` (x) remain continuous. Then with probability one the Monte Carlo approximant to the log likelihood hypoconverges to the exact log likelihood, its maximizer converges to the exact maximum likelihood estimate, approximations to profile likelihoods hypoconverge to the exact profile, and level sets of the approximate likelihood (support regions) converge to the exact sets (in Painlev'eKuratowski set convergence). The same results hold when there are missing data (Thompson and Guo, 1991, Gelfand and Carlin, 19...
An equivalence of the EM and ICE algorithm for exponential family
 IEEE Trans. Signal Processing
, 1997
"... Abstract—In this correspondence, we compare the expectation maximization (EM) algorithm with another iterative approach, namely, the iterative conditional estimation (ICE) algorithm, which was formally introduced in the field of statistical segmentation of images. We show that in case the probabilit ..."
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Cited by 33 (0 self)
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Abstract—In this correspondence, we compare the expectation maximization (EM) algorithm with another iterative approach, namely, the iterative conditional estimation (ICE) algorithm, which was formally introduced in the field of statistical segmentation of images. We show that in case the probability density function (PDF) belongs to the exponential family, the EM algorithm is one particular case of the ICE algorithm. I.
Expectation maximization and complex duration distributions for continuous time Bayesian networks
 In UAI ’05
, 2005
"... Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose ..."
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Cited by 18 (6 self)
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Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose transition model is a function of its parents. We address the problem of learning the parameters and structure of a CTBN from partially observed data. We show how to apply expectation maximization (EM) and structural expectation maximization (SEM) to CTBNs. The availability of the EM algorithm allows us to extend the representation of CTBNs to allow a much richer class of transition durations distributions, known as phase distributions. This class is a highly expressive semiparametric representation, which can approximate any duration distribution arbitrarily closely. This extension to the CTBN framework addresses one of the main limitations of both CTBNs and DBNs — the restriction to exponentially / geometrically distributed duration. We present experimental results on a real data set of people’s life spans, showing that our algorithm learns reasonable models — structure and parameters — from partially observed data, and, with the use of phase distributions, achieves better performance than DBNs. 1
Maxmargin minentropy models
 In AISTATS
, 2012
"... We propose a new family of latent variable models called maxmargin minentropy (m3e) models, which define a distribution over the output and the hidden variables conditioned on the input. Given an input, an m3e model predicts the output with the smallest corresponding Rényi entropy of generalized d ..."
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Cited by 5 (1 self)
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We propose a new family of latent variable models called maxmargin minentropy (m3e) models, which define a distribution over the output and the hidden variables conditioned on the input. Given an input, an m3e model predicts the output with the smallest corresponding Rényi entropy of generalized distribution. This is equivalent to minimizing a score that consists of two terms: (i) the negative loglikelihood of the output, ensuring that the output has a high probability; and (ii) a measure of uncertainty over the distribution of the hidden variables conditioned on the input and the output, ensuring that there is little confusion in the values of the hidden variables. Given a training dataset, the parameters of an m3e model are learned by maximizing the margin between the Rényi entropies of the groundtruth output and all other incorrect outputs. Training an m3e can be viewed as minimizing an upper bound on a userdefined loss, and includes, as a special case, the latent support vector machine framework. We demonstrate the efficacy of m3e models on two standard machine learning applications, discriminative motif finding and image classification, using publicly available datasets. 1
Statistical modeling of seedling mortality
 J. Agric. Biol. Environ. Stat
, 2002
"... Seedling mortality in tree populations limits population growth rates and controls the diversity of forests. To learn about seedling mortality, ecologists use repeated censuses of forest quadrats to determine the number of tree seedlings that have survived from the previous census and to � nd new on ..."
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Cited by 3 (2 self)
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Seedling mortality in tree populations limits population growth rates and controls the diversity of forests. To learn about seedling mortality, ecologists use repeated censuses of forest quadrats to determine the number of tree seedlings that have survived from the previous census and to � nd new ones. Typically, newly found seedlings are marked with � ags. But � agging is labor intensive and limits the spatial and temporal coverage of such studies. The alternative of not � agging has the advantage of ease but suffers from two main disadvantages. It complicates the analysis and loses information. The contributions of this article are (i) to introduce a method for using un � agged census data to learn about seedling mortality and (ii) to quantify the information loss so ecologists can make informed decisions about whether to � ag. Based on presented results, we believe that not � agging is often the preferred alternative. The labor saved by not � agging can be used to better advantage in extending the coverage of the study.
Estimation of the Diffusion Coefficient in a Mixture Model with Diffusing and Fixed Particles
, 2002
"... Particle positions have been observed and estimated in a series of images. The particles are assumed to perform a Brownian motion, however some of them seem to be fixed. A model is introduced with two kinds of particles, diffusing and fixed. To each particle position estimate we assume an additive n ..."
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Cited by 1 (0 self)
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Particle positions have been observed and estimated in a series of images. The particles are assumed to perform a Brownian motion, however some of them seem to be fixed. A model is introduced with two kinds of particles, diffusing and fixed. To each particle position estimate we assume an additive normal measurement error. The parameter of the model consists of the diffusion variance, the measurement error variance, and the proportion of diffusing particles. The problem can be considered as an incomplete data problem since we do not know a priori which particles are really diffusing. The complete data is of curved exponential type and the observed data is a mixture of two normal components. The maximum likelihood estimator is computed via the EM algorithm. The estimator is shown to be strongly consistent and asymptotically normal, as the number of particles approaches infinity, under a reasonable restriction on the parameter space.
Thoughts on Belief and Model Revision with Uncertain Evidence
"... Bayesian networks and other graphical probabilistic models became a popular framework for reasoning with uncertainty. Ecient methods have been developed for revising beliefs with new evidence. ..."
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Cited by 1 (0 self)
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Bayesian networks and other graphical probabilistic models became a popular framework for reasoning with uncertainty. Ecient methods have been developed for revising beliefs with new evidence.
Mathematical Statistics
, 2008
"... Classification of SNP genotypes by a Gaussian mixture model in competitive enzymatic assays ..."
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Classification of SNP genotypes by a Gaussian mixture model in competitive enzymatic assays
Estimating Diffusion Coefficients in Colloidal Particle Systems
, 2002
"... this paper and in order not to repeat to much from it here, we recommend that it is read in close conjunction ..."
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this paper and in order not to repeat to much from it here, we recommend that it is read in close conjunction