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 #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 #173863. 	[Title] Learning Belief Networks in the Presence of Missing Values and Hidden Variables [Abstract] In recent years there has been a flurry of works on learning probabilistic belief networks. Current state of the art methods have been shown to be successful for two learning scenarios: learning both network structure and parameters from complete data, and learning parameters for a fixed network from incomplete datathat is, in the presence of missing values or hidden variables. However, no method has yet been demonstrated to effectively learn network structure from incomplete data. In this paper, we propose a new method for learning network structure from incomplete data. This method is based on an extension of the Expectation-Maximization (EM) algorithm for model selection problems that performs search for the best structure inside the EM procedure. We prove the convergence of this algorithm, and adapt it for learning belief networks. We then describe how to learn networks in two scenarios: when the data contains missing values, and in the presence of hidden variables. We provide experimental results that show the effectiveness of our procedure in both scenarios. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #79817. 	[Title] Bayesian and Information-Theoretic Priors for Bayesian Network Parameters [Abstract] We consider Bayesian and information-theoretic approaches for determining non-informative prior distributions in a parametric model family. The information-theoretic approaches are based on the recently modified definition of stochastic complexity by Rissanen, and on the Minimum Message Length (MML) approach by Wallace. The Bayesian alternatives include the uniform prior, and the equivalent sample size priors. In order to be able to empirically compare the different approaches in practice, the methods are instantiated for a model family of practical importance, the family of Bayesian networks. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #66794. 	[Title] Automated Decomposition of Model-based Learning Problems [Abstract] A new generation of sensor rich, massively distributed autonomous systems is being developed that has the potential for unprecedented performance, such as smart buildings, reconfigurable factories, adaptive traffic systems and remote earth ecosystem monitoring. To achieve high performance these massive systems will need to accurately model themselves and their environment from sensor information. Accomplishing this on a grand scale requires automating the art of large-scale modeling. This paper presents a formalization of decompositional, model-based learning (DML), a method developed by observing a modeler's expertise at decomposing large scale model estimation tasks. The method exploits a striking analogy between learning and consistency-based diagnosis. Moriarty, an implementation of DML, has been applied to thermal modeling of a smart building, demonstrating a significant improvement in learning rate. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #94713. 	[Title] Update rules for parameter estimation in Bayesian networks [Abstract] This paper re-examines the problem of parameter estimation in Bayesian networks with missing values and hidden variables from the perspective of recent work in on-line learning [12]. We provide a unified framework for parameter estimation that encompasses both on-line learning, where the model is continuously adapted to new data cases as they arrive, and the more traditional batch learning, where a pre-accumulated set of samples is used in a one-time model selection process. In the batch case, our framework encompasses both the gradient projection algorithm [2, 3] and the EM algorithm [14] for Bayesian networks. The framework also leads to new on-line and batch parameter update schemes, including a parameterized version of EM. We provide both empirical and theoretical results indicating that parameterized EM allows faster convergence to the maximum likelihood parame ters than does standard EM. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #103537. 	[Title] Discovering Structure in Continuous Variables Using Bayesian Networks [Abstract] We study Bayesian networks for continuous variables using nonlinear conditional density estimators. We demonstrate that useful structures can be extracted from a data set in a self-organized way and we present sampling techniques for belief update based on Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #445938. 	[Title] Compositional Modeling With DPNs [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #143476. 	[Title] EXPERIMENTING WITH THE CHEESEMAN-STUTZ EVIDENCE APPROXIMATION FOR PREDICTIVE MODELING AND DATA MINING [Abstract] The work discussed in this paper is motivated by the need of building decision support systems for real-world problem domains. Our goal is to use these systems as a tool for supporting Bayes optimal decision making, where the action maximizing the expected utility, with respect to predicted probabilities of the possible outcomes, should be selected. For this reason, the models used need to be probabilistic in nature | the output of a model has to be a probability distribution, not just a set of numbers. For the model family, we have chosen the set of simple discrete finite mixture models which have the advantage of being computationally very efficient. In this work, we describe a Bayesian approach for constructing finite mixture models from sample data. Our approach is based on a two-phase unsupervised learning process which can be used both for exploratory analysis and model construction. In the first phase, the selection of a model class, i.e., the number of parameters, is performed by calculating the Cheeseman-Stutz approximation for the model class evidence. In the second phase, the MAP parameters in the selected class are estimated by the EM algorithm. In this framework, the overfitting problem common to many traditional learning approaches can be avoided, as the learning process automatically regulates the complexity of the model. This paper focuses on the model class selection phase and the approach is validated by presenting empirical results with both natural and synthetic data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #33013. 	[Title] Learning Conventions in Multiagent Stochastic Domains using Likelihood Estimates [Abstract] Fully cooperative multiagent systemsthose in which agents share a joint utility modelis of special interest in AI. A key problem is that of ensuring that the actions of individual agents are coordinated, especially in settings where the agents are autonomous decision makers. We investigate approaches to learning coordinated strategies in stochastic domains where an agent's actions are not directly observable by others. Much recent work in game theory has adopted a Bayesian learning perspective to the more general problem of equilibrium selection, but tends to assume that actions can be observed. We discuss the special problems that arise when actions are not observable, including effects on rates of convergence, and the effect of action failure probabilities and asymmetries. We also use likelihood estimates as a means of generalizing fictitious play learning models in our setting. Finally, we propose the use of maximum likelihood as a means of removing strategies from consideration, with the aim of convergence to a conventional equilibrium, at which point learning and deliberation can cease. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #116790. 	[Title] Sequential Update of Bayesian Network Structure [Abstract] There is an obvious need for improving the performance and accuracy of a Bayesian network as new data is observed. Because of errors in model construction and changes in the dynamics of the domains, we cannot afford to ignore the information in new data. While sequential update of parameters for a fixed structure can be accomplished using standard techniques, sequential update of network structure is still an open problem. In this paper, we investigate sequential update of Bayesian networks were both parameters and structure are expected to change. We introduce a new approach that allows for the flexible manipulation of the tradeoff between the quality of the learned networks and the amount of information that is maintained about past observations. We formally describe our approach including the necessary modifications to the scoring functions for learning Bayesian networks, evaluate its effectiveness through and empirical study, and extend it to the case of missing data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #18774. 	[Title] On the Sample Complexity of Learning Bayesian Networks [Abstract] In recent years there has been an increasing interest in learning Bayesian networks from data. One of the most effective methods for learning such networks is based on the minimum description length (MDL) principle. Previous work has shown that this learning procedure is asymptotically successful: with probability one, it will converge to the target distribution, given a sufficient number of samples. However, the rate of this convergence has been hitherto unknown. In this work we examine the sample complexity of MDL based learning procedures for Bayesian networks. We show that the number of samples needed to learn an *-close approximation (in terms of entropy distance) with confidence ffi is O * ) 3 log 1 ffi log log 1 . This means that the sample complexity is a low-order polynomial in the error threshold and sub-linear in the confidence bound. We also discuss how the constants in this term depend on the complexity of the target distribution. Finally, we address questions of asymptotic minimality and propose a method for using the sample complexity results to speed up the learning process. 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 #18777. 	[Title] A Tutorial on Learning With Bayesian Networks [Abstract] Technical Report MSR-TR-95-06 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #73146. 	[Title] LEARNING BAYESIAN NETWORKS WITH LOCAL STRUCTURE [Abstract] We examine a novel addition to the known methods for learning Bayesian networks from data that improves the quality of the learned networks. Our approach explicitly represents and learns the local structure in the conditional probability distributions (CPDs) that quantify these networks. This increases the space of possible models, enabling the representation of CPDs with a variable number of parameters. The resulting learning procedure induces models that better emulate the interactions present in the data. We describe the theoretical foundations and practical aspects of learning local structures and provide an empirical evaluation of the proposed learning procedure. This evaluation indicates that learning curves characterizing this procedure converge faster, in the number of training instances, than those of the standard procedure, which ignores the local structure of the CPDs. Our results also show that networks learned with local structures tend to be more complex (in terms of arcs), yet require fewer parameters. 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 #345340. 	[Title] Generalized Prioritized Sweeping [Abstract] Prioritized sweeping is a model-based reinforcement learning method that attempts to focus an agent's limited computational resources to achieve a good estimate of the value of environment states. To choose effectively where to spend a costly planning step, classic prioritized sweeping uses a simple heuristic to focus computation on the states that are likely to have the largest errors. In this paper, we introduce generalized prioritized sweeping, a principled method for generating such estimates in a representation-specific manner. This allows us to extend prioritized sweeping beyond an explicit, state-based representation to deal with compact representations that are necessary for dealing with large state spaces. We apply this method for generalized model approximators (such as Bayesian networks), and describe preliminary experiments that compare our approach with classical prioritized sweeping. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #510718. 	[Title] Learning Bayesian Networks from Incomplete Data [Abstract] Much of the current research in learning Bayesian Networks fails to effectively deal with missing data. Most of the methods assume that the data is complete, or make the data complete using fairly ad-hoc methods; other methods do deal with missing data but learn only the conditional probabilities, assuming that the structure is known. We present a principled approach to learn both the Bayesian network structure as well as the conditional probabilities from incomplete data. The proposed algorithm is an iterative method that uses a combination of Expectation-Maximization (EM) and Imputation techniques. Results are presented on synthetic data sets which show that the performance of the new algorithm is much better than ad-hoc methods for handling missing data. Please summarise all the given information.

Paper #1112686 has the title `Bayesian Finite Mixtures for Nonlinear Modeling of Educational data  
` and the 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.
`.
Question: Which category should Paper #1112686 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1112686 has the title `Bayesian Finite Mixtures for Nonlinear Modeling of Educational data  
` and the 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.
`.
Question: Which category should Paper #1112686 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