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 #46468. 	[Title] A Statistical Approach to Decision Tree Modeling [Abstract] A statistical approach to decision tree modeling is described. In this approach, each decision in the tree is modeled parametrically as is the process by which an output is generated from an input and a sequence of decisions. The resulting model yields a likelihood measure of goodness of fit, allowing ML and MAP estimation techniques to be utilized. An efficient algorithm is presented to estimate the parameters in the tree. The model selection problem is presented and several alternative proposals are considered. A hidden Markov version of the tree is described for data sequences that have temporal dependencies. 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 #1136393. 	[Title] Data-driven Modeling and Synthesis of Acoustical Instruments [Abstract] We present a framework for the analysis and synthesis of acoustical instruments based on data-driven probabilistic inference modeling. Audio time series and boundary conditions of a played instrument are recorded and the non-linear mapping from the control data into the audio space is inferred using the general inference framework of Cluster-Weighted Modeling. The resulting model is used for real-time synthesis of audio sequences from new input data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1136397. 	[Title] State Reconstruction for Determining Predictability in Driven Nonlinear Acoustical Systems [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #646286. 	[Title] Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY [Abstract] In this article we approximate the rate of convergence of the Gibbs sampler by a normal approximation of the target distribution. Based on this approximation, we consider many implementational issues for the Gibbs sampler, e.g., updating strategy, parameterization and blocking. We give theoretical results to justify our approximation and illustrate our methods in a number of realistic examples. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #69392. 	[Title] Forecasting electricity demand using nonlinear mixture of experts [Abstract] In this paper we study a forecasting model based on mixture of experts for predicting the French electric daily consumption energy. We split the task into two parts. Using mixture of experts, a first model predicts the electricity demand from the exogenous variables (such as temperature and degree of cloud cover) and can be viewed as a nonlinear regression model of mixture of Gaussians. Using a single neural network, a second model predicts the evolution of the residual error of the first one, and can be viewed as an nonlinear autoregression model. We analyze the splitting of the input space generated by the mixture of experts model, and compare the performance to models presently used. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #137873. 	[Title] Stacked Density Estimation [Abstract] Technical Report No. 97-36, Information and Computer Science Department, University of California, Irvine Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #646289. 	[Title] Bayesian Estimation and Model Choice in Item Response Models [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12946. 	[Title] Learning from incomplete data [Abstract] Real-world learning tasks often involve high-dimensional data sets with complex patterns of missing features. In this paper we review the problem of learning from incomplete data from two statistical perspectives|the likelihood-based and the Bayesian. The goal is two-fold: to place current neural network approaches to missing data within a statistical framework, and to describe a set of algorithms, derived from the likelihood-based framework, that handle clustering, classification, and function approximation from incomplete data in a principled and efficient manner. These algorithms are based on mixture modeling and make two distinct appeals to the Expectation-Maximization (EM) principle (Dempster et al., 1977)|both for the estimation of mixture components and for coping with the missing data. 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. The authors were supported in part by a grant from ATR Auditory and Visual Perception Research Laboratories, by a grant from Siemens Corporation, by grant IRI-9013991 from the National Science Foundation, and by grant N00014-90-J-1942 from the Office of Naval Research. Zoubin Ghahramani was supported by a grant from the McDonnell-Pew Foundation. 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 #119956. 	[Title] Function Approximation with Neural Networks and Local Methods: Bias, Variance and Smoothness [Abstract] We review the use of global and local methods for estimating a function mapping R m ) R n from samples of the function containing noise. The relationship between the methods is examined and an empirical comparison is performed using the multi-layer perceptron (MLP) global neural network model, the single nearest-neighbour model, a linear local approximation (LA) model, and the following commonly used datasets: the Mackey-Glass chaotic time series, the Sunspot time series, British English Vowel data, TIMIT speech phonemes, building energy prediction data, and the sonar dataset. We find that the simple local approximation models often outperform the MLP. No criterion such as classification/prediction, size of the training set, dimensionality of the training set, etc. can be used to distinguish whether the MLP or the local approximation method will be superior. However, we find that if we consider histograms of the k-NN density estimates for the training datasets then we can choose the best performing method a priori by selecting local approximation when the spread of the density histogram is large and choosing the MLP otherwise. This result correlates with the hypothesis that the global MLP model is less appropriate when the characteristics of the function to be approximated varies throughout the input space. We discuss the results, the smoothness assumption often made in function approximation, and the bias/variance dilemma. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152917. 	[Title]  [Abstract] Convergence Results for the EM Approach to Abstract The Expectation-Maximization (EM) algorithm is an iterative approach to maximum likelihood parameter estimation. Jordan and Jacobs (1993) recently proposed an EM algorithm for the mixture of experts architecture of Jacobs, Jordan, Nowlan and Hinton (1991) and the hierarchical mixture of experts architecture of Jordan and Jacobs (1992). They showed empirically that the EM algorithm for these architectures yields significantly faster convergence than gradient ascent. In the current paper we provide a theoretical analysis of this algorithm. We show that the algorithm can be regarded as a variable metric algorithm with its searching direction having a positive projection on the gradient of the log likelihood. We also analyze the convergence of the algorithm and provide an explicit expression for the convergence rate. In addition, we describe an acceleration technique that yields a significant speedup in simulation experiments. 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 #643221. 	[Title] A simulation approach to convergence rates for Markov chain Monte Carlo algorithms [Abstract] Markov chain Monte Carlo (MCMC) methods, including the Gibbs sampler and the Metropolis-Hastings algorithm, are very commonly used in Bayesian statistics for sampling from complicated, high-dimensional posterior distributions. A continuing source of uncertainty is how long such a sampler must be run in order to converge approximately to its target stationary distribution. Rosenthal (1995b) presents a method to compute rigorous theoretical upper bounds on the number of iterations required to achieve a specified degree of convergence in total variation distance by verifying drift and minorization conditions. We propose the use of auxiliary simulations to estimate the numerical values needed in Rosenthal's theorem. Our simulation method makes it possible to compute quantitative convergence bounds for models for which the requisite analytical computations would be prohibitively difficult or impossible. On the other hand, although our method appears to perform well in our example problems, it can not provide the guarantees offered by analytical proof. Acknowledgements. We thank Brad Carlin for assistance and encouragement. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1103737. 	[Title] On learning hierarchical classifications [Abstract] Many significant real-world classification tasks involve a large number of categories which are arranged in a hierarchical structure; for example, classifying documents into subject categories under the library of congress scheme, or classifying world-wide-web documents into topic hierarchies. We investigate the potential benefits of using a given hierarchy over base classes to learn accurate multi-category classifiers for these domains. First, we consider the possibility of exploiting a class hierarchy as prior knowledge that can help one learn a more accurate classifier. We explore the benefits of learning category-discriminants in a hard top-down fashion and compare this to a soft approach which shares training data among sibling categories. In doing so, we verify that hierarchies have the potential to improve prediction accuracy. But we argue that the reasons for this can be subtle. Sometimes, the improvement is only because using a hierarchy happens to constrain the expressiveness of a hypothesis class in an appropriate manner. However, various controlled experiments show that in other cases the performance advantage associated with using a hierarchy really does seem to be due to the prior knowledge it encodes. Please summarise all the given information.

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 #151708. 	[Title] Using the Stochastic Gradient Method to Fit Polychotomous Regression Models [Abstract] Technical Report No. 319 April 7, 1997 University of Washington Department of Statistics Seattle, Washington 98195-4322 Abstract Kooperberg, Bose, and Stone (1997) introduced polyclass, a methodology that uses adaptively selected linear splines and their tensor products to model conditional class probabilities. The authors attempted to develop a methodology that would work well on small and moderate size problems and would scale up to large problems. However, the version of polyclass that was developed for large problems was impractical in that it required two months of cpu time to apply it to a large data set. A modification to this methodology involving the use of the stochastic gradient (on-line) method in fitting polyclass models to given sets of basis functions is developed here that makes the methodology applicable to large data sets. In particular, it is successfully applied to a phoneme recognition problem involving 45 phonemes, 81 features, 150,000 cases in the training sample, 1000 basis functions, and 44,000 unknown parameters. Comparisons with neural networks are made both on the original problem and on a three-vowel subproblem. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #395553. 	[Title] Mixtures of Probabilistic Principal Component Analysers [Abstract] Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Previous attempts to formulate mixture models for PCA have therefore to some extent been ad hoc. In this paper, PCA is formulated within a maximum-likelihood framework, based on a specific form of Gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analysers, whose parameters can be determined using an EM algorithm. We discuss the advantages of this model in the context of clustering, density modelling and local dimensionality reduction, and we demonstrate its application to image compression and handwritten digit recognition. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #118436. 	[Title] Performance of On-Line Learning Methods in Predicting Multiprocessor Memory Access Patterns [Abstract] Technical Report UMIACS-TR-96-59 and CS-TR-3676 Institute for Advanced Computer Studies University of Maryland College Park, MD 20742 Abstract Shared memory multiprocessors require reconfigurable interconnection networks (INs) for scalability. These INs are reconfigured by an IN control unit. However, these INs are often plagued by undesirable reconfiguration time that is primarily due to control latency, the amount of time delay that the control unit takes to decide on a desired new IN configuration. To reduce control latency, a trainable prediction unit (PU) was devised and added to the IN controller. The PUs job is to anticipate and reduce control configuration time, the major component of the control latency. Three different on-line prediction techniques were tested to learn and predict repetitive memory access patterns for three typical parallel processing applications, the 2-D relaxation algorithm, matrix multiply and Fast Fourier Transform. The predictions were then used by a routing control algorithm to reduce control latency by configuring the IN to provide needed memory access paths before they were requested. Three prediction techniques were used and tested: 1). a Markov predictor, 2). a linear predictor and 3). a time delay neural network (TDNN) predictor. As expected, different predictors performed best on different applications, however, the TDNN produced the best overall results. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1110438. 	[Title] A Method of Combining Multiple Probabilistic Classifiers through Soft Competition on Different Feature Sets [Abstract] A novel method is proposed for combining multiple probabilistic classifiers on different feature sets. In order to achieve the improved classification performance, a generalized finite mixture model is proposed as a linear combination scheme and implemented based on radial basis function networks. In the linear combination scheme, soft competition on different feature sets is adopted as an automatic feature rank mechanism so that different feature sets can be always simultaneously used in an optimal way to determine linear combination weights. For training the linear combination scheme, a learning algorithm is developed based on Expectation-Maximization (EM) algorithm. The proposed method has been applied to a typical real world problem, viz. speaker identification, in which different feature sets often need consideration simultaneously for robustness. Simulation results show that the proposed method yields good performance in speaker identification. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #69418. 	[Title] Constructive Algorithms for Hierarchical Mixtures of Experts [Abstract] We present two additions to the hierarchical mixture of experts (HME) architecture. We view the HME as a tree structured classifier. Firstly, by applying a likelihood splitting criteria to each expert in the HME we "grow" the tree adaptively during training. Secondly, by considering only the most probable path through the tree we may "prune" branches away, either temporarily, or permanently if they become redundant. We demonstrate results for the growing and pruning algorithms which show significant speed ups and more efficient use of parameters over the conventional algorithms in discriminating between two interlocking spirals and classifying 8-bit parity patterns. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1132459. 	[Title] First experiments using a mixture of nonlinear experts for time series prediction [Abstract] This paper investigates the advantages and disadvantages of the mixture of experts (ME) model (introduced to the connectionist community in [JJNH91] and applied to time series analysis in [WM95]) on two time series where the dynamics is well understood. The first series is a computer-generated series, consisting of a mixture between a noise-free process (the quadratic map) and a noisy process (a composition of a noisy linear autoregressive and a hyperbolic tangent). There are three main results: (1) the ME model produces significantly better results than single networks; (2) it discovers the regimes correctly and also allows us to characterize the sub-processes through their variances. (3) due to the correct matching of the noise level of the model to that of the data it avoids overfitting. The second series is the laser series used in the Santa Fe competition; the ME model also obtains excellent out-of-sample predictions, allows for analysis and shows no overfitting. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #662572. 	[Title] Spatial-Temporal Analysis of Temperature Using Smoothing Spline ANOVA [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1132461. 	[Title] Avoiding overfitting by locally matching the noise level of the data gating network discovers the [Abstract] When trying to forecast the future behavior of a real-world system, two of the key problems are nonstationarity of the process (e.g., regime switching) and overfitting of the model (particularly serious for noisy processes). This articles shows how gated experts can point to solutions to these problems. The architecture, also called society of experts and mixture of experts consists of a (nonlinear) gating network and several (nonlinear) competing experts. Each expert learns a conditional mean (as usual), but each expert also has its own adaptive width. The gating network learns to assign a probability to each expert that depends on the input. This article first discusses the assumptions underlying this architecture and derives the weight update rules. It then evaluates the performance of gated experts in comparison to that of single networks, as well as to networks with two outputs, one predicting the mean, the other one the local error bar. This article also investigates the ability of gated experts to discover and characterize underlying the regimes. The results are: * there is significantly less overfitting compared to single nets, for two reasons: only subsets of the potential inputs are given to the experts and gating network (less of a curse of dimensionality), and the experts learn to match their variances to the (local) noise levels, thus only learning as This article focuses on the architecture and the overfitting problem. Applications to a computer-generated toy problem and the laser data from Santa Fe Competition are given in [Mangeas and Weigend, 1995], and the application to the real-world problem of predicting the electricity demand of France are given in [Mangeas et al., 1995]. much as the data support. 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 #328370. 	[Title] Expectation-Based Selective Attention for Visual Monitoring and Control of a Robot Vehicle [Abstract] Reliable vision-based control of an autonomous vehicle requires the ability to focus attention on the important features in an input scene. Previous work with an autonomous lane following system, ALVINN [Pomerleau, 1993], has yielded good results in uncluttered conditions. This paper presents an artificial neural network based learning approach for handling difficult scenes which will confuse the ALVINN system. This work presents a mechanism for achieving task-specific focus of attention by exploiting temporal coherence. A saliency map, which is based upon a computed expectation of the contents of the inputs in the next time step, indicates which regions of the input retina are important for performing the task. The saliency map can be used to accentuate the features which are important for the task, and de-emphasize those which are not. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #16819. 	[Title] Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review [Abstract] A critical issue for users of Markov Chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise for the future but currently has yielded relatively little that is of practical use in applied work. Consequently, most MCMC users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. After giving a brief overview of the area, we provide an expository review of thirteen convergence diagnostics, describing the theoretical basis and practical implementation of each. We then compare their performance in two simple models and conclude that all the methods can fail to detect the sorts of convergence failure they were designed to identify. We thus recommend a combination of strategies aimed at evaluating and accelerating MCMC sampler convergence, including applying diagnostic procedures to a small number of parallel chains, monitoring autocorrelations and cross-correlations, and modifying parameterizations or sampling algorithms appropriately. We emphasize, however, that it is not possible to say with certainty that a finite sample from an MCMC algorithm is representative of an underlying stationary distribution. Mary Kathryn Cowles is Assistant Professor of Biostatistics, Harvard School of Public Health, Boston, MA 02115. Bradley P. Carlin is Associate Professor, Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455. Much of the work was done while the first author was a graduate student in the Divison of Biostatistics at the University of Minnesota and then Assistant Professor, Biostatistics Section, Department of Preventive and Societal Medicine, University of Nebraska Medical Center, Omaha, NE 68198. The work of both authors was supported in part by National Institute of Allergy and Infectious Diseases FIRST Award 1-R29-AI33466. The authors thank the developers of the diagnostics studied here for sharing their insights, experiences, and software, and Drs. Thomas Louis and Luke Tierney for helpful discussions and suggestions which greatly improved the manuscript. 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 #684986. 	[Title] A Hierarchical Latent Variable Model for Data Visualization [Abstract] Visualization has proven to be a powerful and widely-applicable tool for the analysis and interpretation of multi-variate data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach on a toy data set, and we then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines, and to data in 36 dimensions derived from satellite images. A Matlab software implementation of the algorithm is publicly available from the world-wide web. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1103676. 	[Title] Memory-based Time Series Recognition  A New Methodology and Real World Applications [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #299197. 	[Title] TD Learning of Game Evaluation Functions with Hierarchical Neural Architectures [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1109439. 	[Title] Classifying Seismic Signals by Integrating Ensembles of Neural Networks [Abstract] This paper proposes a classification scheme based on integration of multiple Ensembles of ANNs. It is demonstrated on a classification problem, in which seismic signals of Natural Earthquakes must be distinguished from seismic signals of Artificial Explosions. A Redundant Classification Environment consists of several Ensembles of Neural Networks is created and trained on Bootstrap Sample Sets, using various data representations and architectures. The ANNs within the Ensembles are aggregated (as in Bagging) while the Ensembles are integrated non-linearly, in a signal adaptive manner, using a posterior confidence measure based on the agreement (variance) within the Ensembles. The proposed Integrated Classification Machine achieved 92.1% correct classifications on the seismic test data. Cross Validation evaluations and comparisons indicate that such integration of a collection of ANN's Ensembles is a robust way for handling high dimensional problems with a complex non-stationary signal space as in the current Seismic Classification problem. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1104449. 	[Title] Using Neural Networks for Descriptive Statistical Analysis of Educational Data [Abstract] In this paper we discuss the methodological issues of using a class of neural networks called Mixture Density Networks (MDN) for discriminant analysis. MDN models have the advantage of having a rigorous probabilistic interpretation, and they have proven to be a viable alternative as a classification procedure in discrete domains. We will address both the classification and interpretive aspects of discriminant analysis, and compare the approach to the traditional method of linear discrimin- ants as implemented in standard statistical packages. We show that the MDN approach adopted performs well in both aspects. Many of the observations made are not restricted to the particular case at hand, and are applicable to most applications of discriminant analysis in educational research. fl URL: http://www.cs.Helsinki.FI/research/cosco/ Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #240321. 	[Title] Nonlinear gated experts for time series: discovering regimes and avoiding overfitting [Abstract] In: International Journal of Neural Systems 6 (1995) p. 373 - 399. URL of this paper: ftp://ftp.cs.colorado.edu/pub/Time-Series/MyPapers/experts.ps.Z, or http://www.cs.colorado.edu/~andreas/Time-Series/MyPapers/experts.ps.Z University of Colorado Computer Science Technical Report CU-CS-798-95. In the analysis and prediction of real-world systems, two of the key problems are nonstationarity(often in the form of switching between regimes), and overfitting (particularly serious for noisy processes). This article addresses these problems using gated experts, consisting of a (nonlinear) gating network, and several (also nonlinear) competing experts. Each expert learns to predict the conditional mean, and each expert adapts its width to match the noise level in its regime. The gating network learns to predict the probability of each expert, given the input. This article focuses on the case where the gating network bases its decision on information from the inputs. This can be contrasted to hidden Markov models where the decision is based on the previous state(s) (i.e., on the output of the gating network at the previous time step), as well as to averaging over several predictors. In contrast, gated experts soft-partition the input space. This article discusses the underlying statistical assumptions, derives the weight update rules, and compares the performance of gated experts to standard methods on three time series: (1) a computer-generated series, obtained by randomly switching between two nonlinear processes, (2) a time series from the Santa Fe Time Series Competition (the light intensity of a laser in chaotic state), and (3) the daily electricity demand of France, a real-world multivariate problem with structure on several time scales. The main results are (1) the gating network correctly discovers the different regimes of the process, (2) the widths associated with each expert are important for the segmentation task (and they can be used to characterize the sub-processes), and (3) there is less overfitting compared to single networks (homogeneous multi-layer perceptrons), since the experts learn to match their variances to the (local) noise levels. This can be viewed as matching the local complexity of the model to the local complexity of the data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #428610. 	[Title] Non-linear Models for Time Series Using Mixtures of Experts [Abstract] We consider a novel non-linear model for time series analysis. The study of this model emphasizes both theoretical aspects as well as practical applicability. The architecture of the model is demonstrated to be sufficiently rich, in the sense of approximating unknown functional forms, yet it retains some of the simple and intuitive characteristics of linear models. A comparison to some more established non-linear models will be emphasized, and theoretical issues are backed by prediction results for benchmark time series, as well as computer generated data sets. Efficient estimation algorithms are seen to be applicable, made possible by the mixture based structure of the model. Large sample properties of the estimators are discussed as well, in both well specified as well as misspecified settings. We also demonstrate how inference pertaining to the data structure may be made from the parameterization of the model, resulting in a better, more intuitive, understanding of the structure and performance of the model. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #120013. 	[Title] From Isolation to Cooperation: An Alternative View of a System of Experts [Abstract] We introduce a constructive, incremental learning system for regression problems that models data by means of locally linear experts. In contrast to other approaches, the experts are trained independently and do not compete for data during learning. Only when a prediction for a query is required do the experts cooperate by blen ding their individual predictions. Each expert is trained by minimizing a penalized local cross validation error using second order methods. In this way, an expert is able to adjust the size and shape of the receptive field in which its predictions are valid, and also to adjust its bias on the importance of individual input dimensions. The size and shape adjustment corresponds to finding a local distance metric, while the bias adjustment accomplishes local dimensio n-ality reduction. We derive asymptotic results for our method. In a variety of simulations we demonstrate the properties of the algorithm with respect to interference, learning speed, prediction accuracy, feature detection, and task or i-ented incremental learning. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #642894. 	[Title] Rates of convergence of the Hastings and Metropolis algorithms [Abstract] We apply recent results in Markov chain theory to Hastings and Metropolis algorithms with either independent or symmetric candidate distributions, and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution . In the independence case (in IR k ) these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of ; in the symmetric case (in IR only) we show geometric convergence essentially occurs if and only if has geometric tails. We also evaluate recently developed computable bounds on the rates of convergence in this context: examples show that these theoretical bounds can be inherently extremely conservative, although when the chain is stochastically monotone the bounds may well be effective. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #126927. 	[Title] Convergence properties of perturbed Markov chains [Abstract] Acknowledgements. We thank Neal Madras, Radford Neal, Peter Rosenthal, and Richard Tweedie for helpful conversations. This work was partially supported by EPSRC of the U.K., and by NSERC of Canada. 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 #703953. 	[Title] Convergence in Norm for Alternating Expectation-Maximization (EM) Type Algorithms 1 [Abstract] We provide a sufficient condition for convergence of a general class of alternating estimation-maximization (EM) type continuous-parameter estimation algorithms with respect to a given norm. This class includes EM, penalized EM, Green's OSL-EM, and other approximate EM algorithms. The convergence analysis can be extended to include alternating coordinate-maximization EM algorithms such as Meng and Rubin's ECM and Fessler and Hero's SAGE. The condition for monotone convergence can be used to establish norms under which the distance between successive iterates and the limit point of the EM-type algorithm approaches zero monotonically. For illustration, we apply our results to estimation of Poisson rate parameters in emission tomography and establish that in the final iterations the logarithm of the EM iterates converge monotonically in a weighted Euclidean norm. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35797. 	[Title] Proben1 A Set of Neural Network Benchmark Problems and Benchmarking Rules [Abstract] Proben1 is a collection of problems for neural network learning in the realm of pattern classification and function approximation plus a set of rules and conventions for carrying out benchmark tests with these or similar problems. Proben1 contains 15 data sets from 12 different domains. All datasets represent realistic problems which could be called diagnosis tasks and all but one consist of real world data. The datasets are all presented in the same simple format, using an attribute representation that can directly be used for neural network training. Along with the datasets, Proben1 defines a set of rules for how to conduct and how to document neural network benchmarking. The purpose of the problem and rule collection is to give researchers easy access to data for the evaluation of their algorithms and networks and to make direct comparison of the published results feasible. This report describes the datasets and the benchmarking rules. It also gives some basic performance measures indicating the difficulty of the various problems. These measures can be used as baselines for comparison. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #11093. 	[Title] Factorial Learning and the EM Algorithm [Abstract] Many real world learning problems are best characterized by an interaction of multiple independent causes or factors. Discovering such causal structure from the data is the focus of this paper. Based on Zemel and Hinton's cooperative vector quantizer (CVQ) architecture, an unsupervised learning algorithm is derived from the Expectation-Maximization (EM) framework. Due to the combinatorial nature of the data generation process, the exact E-step is computationally intractable. Two alternative methods for computing the E-step are proposed: Gibbs sampling and mean-field approximation, and some promising empirical results are presented. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #168410. 	[Title] A Modular Q-Learning Architecture for Manipulator Task Decomposition `Data storage in the cerebellar model ar [Abstract] Compositional Q-Learning (CQ-L) (Singh 1992) is a modular approach to learning to perform composite tasks made up of several elemental tasks by reinforcement learning. Skills acquired while performing elemental tasks are also applied to solve composite tasks. Individual skills compete for the right to act and only winning skills are included in the decomposition of the composite task. We extend the original CQ-L concept in two ways: (1) a more general reward function, and (2) the agent can have more than one actuator. We use the CQ-L architecture to acquire skills for performing composite tasks with a simulated two-linked manipulator having large state and action spaces. The manipulator is a non-linear dynamical system and we require its end-effector to be at specific positions in the workspace. Fast function approximation in each of the Q-modules is achieved through the use of an array of Cerebellar Model Articulation Controller (CMAC) (Albus Our research interests involve the scaling up of machine learning methods, especially reinforcement learning, for autonomous robot control. We are interested in function approximators suitable for reinforcement learning in problems with large state spaces, such as the Cerebellar Model Articulation Controller (CMAC) (Albus 1975) which permit fast, online learning and good local generalization. In addition, we are interested in task decomposition by reinforcement learning and the use of hierarchical and modular function approximator architectures. We are examining the effectiveness of a modified Hierarchical Mixtures of Experts (HME) (Jordan & Jacobs 1993) approach for reinforcement learning since the original HME was developed mainly for supervised learning and batch learning tasks. The incorporation of domain knowledge into reinforcement learning agents is an important way of extending their capabilities. Default policies can be specified, and domain knowledge can also be used to restrict the size of the state-action space, leading to faster learning. We are investigating the use of Q-Learning (Watkins 1989) in planning tasks, using a classifier system (Holland 1986) to encode the necessary condition-action rules. Jordan, M. & Jacobs, R. (1993), Hierarchical mixtures of experts and the EM algorithm, Technical Report 9301, MIT Computational Cognitive Science. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131230. 	[Title] Identifiability, Improper Priors and Gibbs Sampling for Generalized Linear Models [Abstract] Alan E. Gelfand is a Professor in the Department of Statistics at the University of Connecti-cut, Storrs, CT 06269. Sujit K. Sahu is a Lecturer at the School of Mathematics, University of Wales, Cardiff, CF2 4YH, UK. The research of the first author was supported in part by NSF grant DMS 9301316 while the second author was supported in part by an EPSRC grant from UK. The authors thank Brad Carlin, Kate Cowles, Gareth Roberts and an anonymous referee for valuable comments. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12638. 	[Title] Soft Classification, a.k.a. Risk Estimation, via Penalized Log Likelihood and Smoothing Spline Analysis of Variance [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #949217. 	[Title] Comparison of Neural and Statistical Classifiers| Theory and Practice [Abstract] Research Reports A13 January 1996 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1112929. 	[Title] Combining Linear Discriminant Functions with Neural Networks for Supervised Learning [Abstract] A novel supervised learning method is presented by combining linear discriminant functions with neural networks. The proposed method results in a tree-structured hybrid architecture. Due to constructive learning, the binary tree hierarchical architecture is automatically generated by a controlled growing process for a specific supervised learning task. Unlike the classic decision tree, the linear discriminant functions are merely employed in the intermediate level of the tree for heuristically partitioning a large and complicated task into several smaller and simpler subtasks in the proposed method. These subtasks are dealt with by component neural networks at the leaves of the tree accordingly. For constructive learning, growing and credit-assignment algorithms are developed to serve for the hybrid architecture. The proposed architecture provides an efficient way to apply existing neural networks (e.g. multi-layered perceptron) for solving a large scale problem. We have already applied the proposed method to a universal approximation problem and several benchmark classification problems in order to evaluate its performance. Simulation results have shown that the proposed method yields better results and faster training in comparison with the multi-layered perceptron. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1108834. 	[Title] ce: [39] <author> Yoda, M. </author> <year> (1994). </year> <title> Predicting the Tokyo stock market. </title> <editor> In Deboeck, G.J. (Ed.) </editor> <year> (1994). </year> <title> Trading on the Edge. </title> <address> New York: </address> <publisher> Wiley., </publisher> <pages> 66-79. </pages> <institution> VITA Graduate School Southern Illinois University Daniel Nikolaev Nikovski Date of Birth: </institution> <address> April 13, 1969 606 West College Street, Apt.4, Rm. 6, Carbondale, Illinois 62901 150 Hristo Botev Boulevard, Apt. </address> <month> 54, </month> <title> 4004 Plovdiv, Bulgaria Technical University - Sofia, Bulgaria Engineer of Computer Systems and Control Thesis Title: Adaptive Computation Techniques for Time Series Analysis Major Professor: </title> <journal> Dr. Mehdi Zargham </journal> [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #431206. 	[Title] Backfitting in Smoothing Spline ANOVA [Abstract] A scheme to compute smoothing spline ANOVA estimates for large data sets with a (near) tensor-product structure is proposed. Such data sets are common in spatial-temporal analysis and image analysis. This scheme combines backfitting algorithm with iterative imputation algorithm in order to save both computational space and time. The convergence of this algorithm and various ways to further speed it up, such as collapsing component functions and successive over-relaxation, are discussed. Issues related to its application in spatial-temporal analysis are discussed too. An application to a global analysis of historical surface temperature data is described. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #390889. 	[Title] A HIERARCHICAL COMMUNITY OF EXPERTS [Abstract] We describe a directed acyclic graphical model that contains a hierarchy of linear units and a mechanism for dynamically selecting an appropriate subset of these units to model each observation. The non-linear selection mechanism is a hierarchy of binary units each of which gates the output of one of the linear units. There are no connections from linear units to binary units, so the generative model can be viewed as a logistic belief net (Neal 1992) which selects a skeleton linear model from among the available linear units. We show that Gibbs sampling can be used to learn the parameters of the linear and binary units even when the sampling is so brief that the Markov chain is far from equilibrium. 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 #4329. 	[Title] Supervised learning from incomplete data via an EM approach [Abstract] Real-world learning tasks may involve high-dimensional data sets with arbitrary patterns of missing data. In this paper we present a framework based on maximum likelihood density estimation for learning from such data sets. We use mixture models for the density estimates and make two distinct appeals to the Expectation-Maximization (EM) principle (Dempster et al., 1977) in deriving a learning algorithm|EM is used both for the estimation of mixture components and for coping with missing data. The resulting algorithm is applicable to a wide range of supervised as well as unsupervised learning problems. Results from a classification benchmark|the iris data set|are presented. 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 #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 #1114352. 	[Title] Cortical Mechanisms of Visual Recognition and Learning: A Hierarchical Kalman Filter Model [Abstract] We describe a biologically plausible model of dynamic recognition and learning in the visual cortex based on the statistical theory of Kalman filtering from optimal control theory. The model utilizes a hierarchical network whose successive levels implement Kalman filters operating over successively larger spatial and temporal scales. Each hierarchical level in the network predicts the current visual recognition state at a lower level and adapts its own recognition state using the residual error between the prediction and the actual lower-level state. Simultaneously, the network also learns an internal model of the spatiotemporal dynamics of the input stream by adapting the synaptic weights at each hierarchical level in order to minimize prediction errors. The Kalman filter model respects key neuroanatomical data such as the reciprocity of connections between visual cortical areas, and assigns specific computational roles to the inter-laminar connections known to exist between neurons in the visual cortex. Previous work elucidated the usefulness of this model in explaining neurophysiological phenomena such as endstopping and other related extra-classical receptive field effects. In this paper, in addition to providing a more detailed exposition of the model, we present a variety of experimental results demonstrating the ability of this model to perform robust spatiotemporal segmentation and recognition of objects and image sequences in the presence of varying amounts of occlusion, background clutter, and noise. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6898. 	[Title] Sample Size Calculations for Smoothing Splines Based on Bayesian Confidence Intervals [Abstract] Bayesian confidence intervals of a smoothing spline are often used to distinguish two curves. In this paper, we provide an asymptotic formula for sample size calculations based on Bayesian confidence intervals. Approximations and simulations on special functions indicate that this asymptotic formula is reasonably accurate. Key Words: Bayesian confidence intervals; sample size; smoothing spline. fl Address: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106-3110. Tel.: (805)893-4870. Fax: (805)893-2334. E-mail: yuedong@pstat.ucsb.edu. Supported by the National Institute of Health under Grants R01 EY09946, P60 DK20572 and P30 HD18258. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1105011. 	[Title] On the Connection Between Stochastic Smoothing, Filtering and Estimation with Incomplete Data [Abstract] Connections between stochastic smoothing/filtering and estimation with incomplete data are investigated. It is shown, under the right censoring scheme, that the Kaplan-Meier estimator can be characterized as a moment estimate based on a stochastic filter/smoother(a pseudo-filter/smoother). Motivated by this result, a potentially useful martingale approach for estimation and convergence with incomplete data is proposed: estimators are characterized as pseudo-stochastic smoothers (which sometimes reduce to filters), which are described by a (system of) stochastic integral equation(s); recent results in convergence of stochastic integrals and stochastic differential equations are then applied to address convergence issues. As an illustration, the double censoring problem is revisited under this framework, a closed form estimator is proposed and convergence properties studied. Martingale theory plays a vital role in the entire analysis. This approach is in essence a self-consistency method. 1 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #753265. 	[Title] Validation of Average Error Rate Over Classifiers [Abstract] We examine methods to estimate the average and variance of test error rates over a set of classifiers. We begin with the process of drawing a classifier at random for each example. Given validation data, the average test error rate can be estimated as if validating a single classifier. Given the test example inputs, the variance can be computed exactly. Next, we consider the process of drawing a classifier at random and using it on all examples. Once again, the expected test error rate can be validated as if validating a single classifier. However, the variance must be estimated by validating all classifers, which yields loose or uncertain bounds. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #642681. 	[Title] Assessing Convergence of Markov Chain Monte Carlo Algorithms [Abstract] We motivate the use of convergence diagnostic techniques for Markov Chain Monte Carlo algorithms and review various methods proposed in the MCMC literature. A common notation is established and each method is discussed with particular emphasis on implementational issues and possible extensions. The methods are compared in terms of their interpretability and applicability and recommendations are provided for particular classes of problems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #37884. 	[Title] Hidden Markov decision trees [Abstract] We study a time series model that can be viewed as a decision tree with Markov temporal structure. The model is intractable for exact calculations, thus we utilize variational approximations. We consider three different distributions for the approximation: one in which the Markov calculations are performed exactly and the layers of the decision tree are decoupled, one in which the decision tree calculations are performed exactly and the time steps of the Markov chain are decoupled, and one in which a Viterbi-like assumption is made to pick out a single most likely state sequence. We present simulation results for artificial data and the Bach chorales. Accepted for oral presentation at NIPS*96. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6910. 	[Title] Smoothing Spline ANOVA for Exponential Families, with Application to the Wisconsin Epidemiological Study of Diabetic [Abstract]  Please summarise all the given information.

Paper #6913 has the title `On Convergence of the EM Algorithm and the Gibbs Sampler  SUMMARY  
` and the 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. 
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Question: Which category should Paper #6913 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #6913 has the title `On Convergence of the EM Algorithm and the Gibbs Sampler  SUMMARY  
` and the 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. 
`.
Question: Which category should Paper #6913 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