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 #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 #1106401. 	[Title] Model Selection based on Minimum Description Length [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1112686. 	[Title] Bayesian Finite Mixtures for Nonlinear Modeling of Educational data [Abstract] In this paper we discuss a Bayesian approach for finding latent classes in the data. In our approach we use finite mixture models to describe the underlying structure in the data, and demonstrate that the possibility to use full joint probability models raises interesting new prospects for exploratory data analysis. The concepts and methods discussed are illustrated with a case study using a data set from a recent educational study. The Bayesian classification approach described has been implemented, and presents an appealing addition to the standard toolbox for exploratory data analysis of educational data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #18811. 	[Title] Comparing Bayesian Model Class Selection Criteria by Discrete Finite Mixtures [Abstract] We investigate the problem of computing the posterior probability of a model class, given a data sample and a prior distribution for possible parameter settings. By a model class we mean a group of models which all share the same parametric form. In general this posterior may be very hard to compute for high-dimensional parameter spaces, which is usually the case with real-world applications. In the literature several methods for computing the posterior approximately have been proposed, but the quality of the approximations may depend heavily on the size of the available data sample. In this work we are interested in testing how well the approximative methods perform in real-world problem domains. In order to conduct such a study, we have chosen the model family of finite mixture distributions. With certain assumptions, we are able to derive the model class posterior analytically for this model family. We report a series of model class selection experiments on real-world data sets, where the true posterior and the approximations are compared. The empirical results support the hypothesis that the approximative techniques can provide good estimates of the true posterior, especially when the sample size grows large. Please summarise all the given information.

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 #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.

Above are papers related to the following paper: [Paper_ID] Paper #18815. 	[Title] Probabilistic Instance-Based Learning [Abstract] Traditional instance-based learning methods base their predictions directly on (training) data that has been stored in the memory. The predictions are based on weighting the contributions of the individual stored instances by a distance function implementing a domain-dependent similarity metrics. This basic approach suffers from three drawbacks: com-putationally expensive prediction when the database grows large, overfitting in the presence of noisy data, and sensitivity to the selection of a proper distance function. We address all these issues by giving a probabilistic interpretation to instance-based learning, where the goal is to approximate predictive distributions of the attributes of interest. In this probabilistic view the instances are not individual data items but probability distributions, and we perform Bayesian inference with a mixture of such prototype distributions. We demonstrate the feasibility of the method empirically for a wide variety of public domain classification data sets. Please summarise all the given information.

Paper #20920 has the title `Comparing Predictive Inference Methods for Discrete Domains  
` and the 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. 
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Question: Which category should Paper #20920 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #20920 has the title `Comparing Predictive Inference Methods for Discrete Domains  
` and the 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. 
`.
Question: Which category should Paper #20920 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