Above are papers related to the following paper: [Paper_ID] Paper #1115291. 	[Title] How Many Clusters? Which Clustering Method? Answers Via Model-Based Cluster Analysis 1 [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6913. 	[Title] On Convergence of the EM Algorithm and the Gibbs Sampler  SUMMARY [Abstract] In this article we investigate the relationship between the two popular algorithms, the EM algorithm and the Gibbs sampler. We show that the approximate rate of convergence of the Gibbs sampler by Gaussian approximation is equal to that of the corresponding EM type algorithm. This helps in implementing either of the algorithms as improvement strategies for one algorithm can be directly transported to the other. In particular, by running the EM algorithm we know approximately how many iterations are needed for convergence of the Gibbs sampler. We also obtain a result that under conditions, the EM algorithm used for finding the maximum likelihood estimates can be slower to converge than the corresponding Gibbs sampler for Bayesian inference which uses proper prior distributions. We illustrate our results in a number of realistic examples all based on the generalized linear mixed models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1135108. 	[Title] A Gentle Tutorial of the EM Algorithm and its Application to Parameter Estimation for Gaussian [Abstract] We describe the maximum-likelihood parameter estimation problem and how the Expectation-Maximization (EM) algorithm can be used for its solution. We first describe the abstract form of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2) finding the parameters of a hidden Markov model (HMM) (i.e., the Baum-Welch algorithm) for both discrete and Gaussian mixture observation models. We derive the update equations in fairly explicit detail but we do not prove any convergence properties. We try to emphasize intuition rather than mathematical rigor. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4330. 	[Title] Hierarchical Mixtures of Experts and the EM Algorithm [Abstract] We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM's). Learning is treated as a maximum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an on-line learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain. This report describes research done at the Dept. of Brain and Cognitive Sciences, the Center for Biological and Computational Learning, and the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for CBCL is provided in part by a grant from the NSF (ASC-9217041). Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Dept. of Defense. The authors were supported by a grant from the McDonnell-Pew Foundation, by a grant from ATR Human Information Processing Research Laboratories, by a grant from Siemens Corporation, by by grant IRI-9013991 from the National Science Foundation, by grant N00014-90-J-1942 from the Office of Naval Research, and by NSF grant ECS-9216531 to support an Initiative in Intelligent Control at MIT. Michael I. Jordan is a NSF Presidential Young Investigator. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #109323. 	[Title] Estimating Bayes Factors via Posterior Simulation with the Laplace-Metropolis Estimator [Abstract] The key quantity needed for Bayesian hypothesis testing and model selection is the marginal likelihood for a model, also known as the integrated likelihood, or the marginal probability of the data. In this paper we describe a way to use posterior simulation output to estimate marginal likelihoods. We describe the basic Laplace-Metropolis estimator for models without random effects. For models with random effects the compound Laplace-Metropolis estimator is introduced. This estimator is applied to data from the World Fertility Survey and shown to give accurate results. Batching of simulation output is used to assess the uncertainty involved in using the compound Laplace-Metropolis estimator. The method allows us to test for the effects of independent variables in a random effects model, and also to test for the presence of the random effects. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #280876. 	[Title] Principal Curve Clustering With Noise [Abstract] Technical Report 317 Department of Statistics University of Washington. 1 Derek Stanford is Graduate Research Assistant and Adrian E. Raftery is Professor of Statistics and Sociology, both at the Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322, USA. E-mail: stanford@stat.washington.edu and raftery@stat.washington.edu. Web: http://www.stat.washington.edu/raftery. This research was supported by ONR grants N00014-96-1-0192 and N00014-96-1-0330. The authors are grateful to Simon Byers, Gilles Celeux and Christian Posse for helpful discussions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #50381. 	[Title] Training Algorithms for Hidden Markov Models Using Entropy Based Distance Functions [Abstract] We present new algorithms for parameter estimation of HMMs. By adapting a framework used for supervised learning, we construct iterative algorithms that maximize the likelihood of the observations while also attempting to stay close to the current estimated parameters. We use a bound on the relative entropy between the two HMMs as a distance measure between them. The result is new iterative training algorithms which are similar to the EM (Baum-Welch) algorithm for training HMMs. The proposed algorithms are composed of a step similar to the expectation step of Baum-Welch and a new update of the parameters which replaces the maximization (re-estimation) step. The algorithm takes only negligibly more time per iteration and an approximated version uses the same expectation step as Baum-Welch. We evaluate experimentally the new algorithms on synthetic and natural speech pronunciation data. For sparse models, i.e. models with relatively small number of non-zero parameters, the proposed algorithms require significantly fewer iterations. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4335. 	[Title] A VIEW OF THE EM ALGORITHM THAT JUSTIFIES INCREMENTAL, SPARSE, AND OTHER VARIANTS [Abstract] The EM algorithm performs maximum likelihood estimation for data in which some variables are unobserved. We present a function that resembles negative free energy and show that the M step maximizes this function with respect to the model parameters and the E step maximizes it with respect to the distribution over the unobserved variables. From this perspective, it is easy to justify an incremental variant of the EM algorithm in which the distribution for only one of the unobserved variables is recalculated in each E step. This variant is shown empirically to give faster convergence in a mixture estimation problem. A variant of the algorithm that exploits sparse conditional distributions is also described, and a wide range of other variant algorithms are also seen to be possible. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #32688. 	[Title] CLASSIFICATION USING HIERARCHICAL MIXTURES OF EXPERTS [Abstract] There has recently been widespread interest in the use of multiple models for classification and regression in the statistics and neural networks communities. The Hierarchical Mixture of Experts (HME) [1] has been successful in a number of regression problems, yielding significantly faster training through the use of the Expectation Maximisation algorithm. In this paper we extend the HME to classification and results are reported for three common classification benchmark tests: Exclusive-Or, N-input Parity and Two Spirals. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1116336. 	[Title] On Computing the Largest Fraction of Missing Information for the EM Algorithm and the Worst [Abstract] We address the problem of computing the largest fraction of missing information for the EM algorithm and the worst linear function for data augmentation. These are the largest eigenvalue and its associated eigenvector for the Jacobian of the EM operator at a maximum likelihood estimate, which are important for assessing convergence in iterative simulation. An estimate of the largest fraction of missing information is available from the EM iterates; this is often adequate since only a few figures of accuracy are needed. In some instances the EM iteration also gives an estimate of the worst linear function. We show that the power method for eigencomputation can be used to compute efficient and accurate estimates of both quantities. Unlike eigenvalue decomposition, the power method computes only the largest eigenvalue and eigenvector of a matrix, it can take advantage of a good eigenvector estimate as an initial value and it can be terminated after only a few figures of accuracy are obtained. Moreover, the matrix products needed in the power method can be computed by extrapolation, obviating the need to form the Jacobian of the EM operator. We give results of simultation studies on multivariate normal data showing this approach becomes more efficient as the data dimension increases than methods that use a finite-difference approximation to the Jacobian, which is the only general-purpose alternative available. fl Funded by National Institutes of Health Small Business Innovation Reseach Grant 5R44CA65147-03, and by Office of Naval Research contracts N00014-96-1-0192 and N00014-96-1-0330. We are indebted to Tim Hesterberg, Jim Schimert, Doug Clarkson, Anne Greenbaum, and Adrian Raftery for comments and discussion that helped advance this research and improve this paper. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #733167. 	[Title] Soft Vector Quantization and the EM Algorithm Running Title: Soft Vector Quantization and EM Section: [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3187. 	[Title] A Reference Bayesian Test for Nested Hypotheses And its Relationship to the Schwarz Criterion [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1717. 	[Title] On Convergence Properties of the EM Algorithm for Gaussian Mixtures [Abstract] We build up the mathematical connection between the "Expectation-Maximization" (EM) algorithm and gradient-based approaches for maximum likelihood learning of finite Gaussian mixtures. We show that the EM step in parameter space is obtained from the gradient via a projection matrix P , and we provide an explicit expression for the matrix. We then analyze the convergence of EM in terms of special properties of P and provide new results analyzing the effect that P has on the likelihood surface. Based on these mathematical results, we present a comparative discussion of the advantages and disadvantages of EM and other algorithms for the learning of Gaussian mixture models. This report describes research done at the Center for Biological and Computational Learning and the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the Center is provided in part by a grant from the National Science Foundation under contract ASC-9217041. Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00000-00-A-0000. The authors were also supported by the HK RGC Earmarked Grant CUHK250/94E, by a grant from the McDonnell-Pew Foundation, by a grant from ATR Human Information Processing Research Laboratories, by a grant from Siemens Corporation, and by grant N00014-90-1-0777 from the Office of Naval Research. Michael I. Jordan is an NSF Presidential Young Investigator. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #137849. 	[Title] Inference in Model-Based Cluster Analysis [Abstract] Technical Report no. 285 Department of Statistics University of Washington. March 10, 1995 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #17242. 	[Title] Detecting Features in Spatial Point Processes with Clutter via Model-Based Clustering [Abstract] Technical Report No. 295 Department of Statistics, University of Washington October, 1995 1 Abhijit Dasgupta is a graduate student at the Department of Biostatistics, University of Washington, Box 357232, Seattle, WA 98195-7232, and his e-mail address is dasgupta@biostat.washington.edu. Adrian E. Raftery is Professor of Statistics and Sociology, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322, and his e-mail address is raftery@stat.washington.edu. This research was supported by Office of Naval Research Grant no. N-00014-91-J-1074. The authors are grateful to Peter Guttorp, Girardeau Henderson and Robert Muise for helpful discussions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #5086. 	[Title] Approximate Bayes Factors and Accounting for Model Uncertainty in Generalized Linear Models [Abstract] Technical Report no. 255 Department of Statistics, University of Washington August 1993; Revised March 1994 Please summarise all the given information.

Paper #1115291 has the title `How Many Clusters? Which Clustering Method? Answers Via Model-Based Cluster Analysis 1  
` and the abstract `nan`.
Question: Which category should Paper #1115291 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1115291 has the title `How Many Clusters? Which Clustering Method? Answers Via Model-Based Cluster Analysis 1  
` and the abstract `nan`.
Question: Which category should Paper #1115291 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Probabilistic_Methods