Above are papers related to the following paper: [Paper_ID] Paper #510715. 	[Title] Estimating Dependency Structure as a Hidden Variable [Abstract] This paper introduces a probability model, the mixture of trees that can account for sparse, dynamically changing dependence relationships. We present a family of efficient algorithms that use EM and the Minimum Spanning Tree algorithm to find the ML and MAP mixture of trees for a variety of priors, including the Dirichlet and the MDL priors. This report describes research done at the Dept. of Electrical Engineering and Computer Science, 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 the artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Dept. of Defense and by the Office of Naval Research. Michael I. Jordan is a NSF Presidential Young Investigator. The authors can be reached at M.I.T., Center for Biological and Computational Learning, 45 Carleton St., Cambridge MA 02142, USA. E-mail: mmp@ai.mit.edu, jordan@psyche.mit.edu, quaid@ai.mit.edu. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #20920. 	[Title] Comparing Predictive Inference Methods for Discrete Domains [Abstract] Predictive inference is seen here as the process of determining the predictive distribution of a discrete variable, given a data set of training examples and the values for the other problem domain variables. We consider three approaches for computing this predictive distribution, and assume that the joint probability distribution for the variables belongs to a set of distributions determined by a set of parametric models. In the simplest case, the predictive distribution is computed by using the model with the maximum a posteriori (MAP) posterior probability. In the evidence approach, the predictive distribution is obtained by averaging over all the individual models in the model family. In the third case, we define the predictive distribution by using Rissanen's new definition of stochastic complexity. Our experiments performed with the family of Naive Bayes models suggest that when using all the data available, the stochastic complexity approach produces the most accurate predictions in the log-score sense. However, when the amount of available training data is decreased, the evidence approach clearly outperforms the two other approaches. The MAP predictive distribution is clearly inferior in the log-score sense to the two more sophisticated approaches, but for the 0/1-score the MAP approach may still in some cases produce the best results. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #18812. 	[Title] Constructing Bayesian finite mixture models by the EM algorithm [Abstract] Email: Firstname.Lastname@cs.Helsinki.FI Report C-1996-9, University of Helsinki, Department of Computer Science. Abstract In this paper we explore the use of finite mixture models for building decision support systems capable of sound probabilistic inference. Finite mixture models have many appealing properties: they are computationally efficient in the prediction (reasoning) phase, they are universal in the sense that they can approximate any problem domain distribution, and they can handle multimod-ality well. We present a formulation of the model construction problem in the Bayesian framework for finite mixture models, and describe how Bayesian inference is performed given such a model. The model construction problem can be seen as missing data estimation and we describe a realization of the Expectation-Maximization (EM) algorithm for finding good models. To prove the feasibility of our approach, we report crossvalidated empirical results on several publicly available classification problem datasets, and compare our results to corresponding results obtained by alternative techniques, such as neural networks and decision trees. The comparison is based on the best results reported in the literature on the datasets in question. It appears that using the theoretically sound Bayesian framework suggested here the other reported results can be outperformed with a relatively small effort. Please summarise all the given information.

Paper #510715 has the title `Estimating Dependency Structure as a Hidden Variable  
` and the abstract `This paper introduces a probability model, the mixture of trees that can account for sparse, dynamically changing dependence relationships. We present a family of efficient algorithms that use EM and the Minimum Spanning Tree algorithm to find the ML and MAP mixture of trees for a variety of priors, including the Dirichlet and the MDL priors. This report describes research done at the Dept. of Electrical Engineering and Computer Science, 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 the artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Dept. of Defense and by the Office of Naval Research. Michael I. Jordan is a NSF Presidential Young Investigator. The authors can be reached at M.I.T., Center for Biological and Computational Learning, 45 Carleton St., Cambridge MA 02142, USA. E-mail: mmp@ai.mit.edu, jordan@psyche.mit.edu, quaid@ai.mit.edu. 
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Question: Which category should Paper #510715 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #510715 has the title `Estimating Dependency Structure as a Hidden Variable  
` and the abstract `This paper introduces a probability model, the mixture of trees that can account for sparse, dynamically changing dependence relationships. We present a family of efficient algorithms that use EM and the Minimum Spanning Tree algorithm to find the ML and MAP mixture of trees for a variety of priors, including the Dirichlet and the MDL priors. This report describes research done at the Dept. of Electrical Engineering and Computer Science, 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 the artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Dept. of Defense and by the Office of Naval Research. Michael I. Jordan is a NSF Presidential Young Investigator. The authors can be reached at M.I.T., Center for Biological and Computational Learning, 45 Carleton St., Cambridge MA 02142, USA. E-mail: mmp@ai.mit.edu, jordan@psyche.mit.edu, quaid@ai.mit.edu. 
`.
Question: Which category should Paper #510715 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