Above are papers related to the following paper: [Paper_ID] Paper #91581. 	[Title] Finding Overlapping Distributions with MML [Abstract] This paper considers an aspect of mixture modelling. Significantly overlapping distributions require more data for their parameters to be accurately estimated than well separated distributions. For example, two Gaussian distributions are considered to significantly overlap when their means are within three standard deviations of each other. If insufficient data is available, only a single component distribution will be estimated, although the data originates from two component distributions. We consider how much data is required to distinguish two component distributions from one distribution in mixture modelling using the minimum message length (MML) criterion. First, we perform experiments which show the MML criterion performs well relative to other Bayesian criteria. Second, we make two improvements to the existing MML estimates, that improve its performance with overlapping distributions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6784. 	[Title] A Quantitative Study of Experimental Evaluations of Neural Network Learning Algorithms: Current Research Practice [Abstract] 190 articles about neural network learning algorithms published in 1993 and 1994 are examined for the amount of experimental evaluation they contain. 29% of them employ not even a single realistic or real learning problem. Only 8% of the articles present results for more than one problem using real world data. Furthermore, one third of all articles do not present any quantitative comparison with a previously known algorithm. These results suggest that we should strive for better assessment practices in neural network learning algorithm research. For the long-term benefit of the field, the publication standards should be raised in this respect and easily accessible collections of benchmark problems should be built. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #24966. 	[Title] A Practical Bayesian Framework for Backprop Networks [Abstract] A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible: (1) objective comparisons between solutions using alternative network architectures; (2) objective stopping rules for network pruning or growing procedures; (3) objective choice of magnitude and type of weight decay terms or additive regularisers (for penalising large weights, etc.); (4) a measure of the effective number of well-determined parameters in a model; (5) quantified estimates of the error bars on network parameters and on network output; (6) objective comparisons with alternative learning and interpolation models such as splines and radial basis functions. The Bayesian `evidence' automatically embodies `Occam's razor,' penalising over-flexible and over-complex models. The Bayesian approach helps detect poor underlying assumptions in learning models. For learning models well matched to a problem, a good correlation between generalisation ability and the Bayesian evidence is obtained. This paper makes use of the Bayesian framework for regularisation and model comparison described in the companion paper `Bayesian interpolation' (MacKay, 1991a). This framework is due to Gull and Skilling (Gull, 1989a). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #38537. 	[Title] BAYESIAN STATISTICS 6, pp. 000--000  Exact sampling for Bayesian inference: towards general purpose algorithms [Abstract] There are now methods for organising a Markov chain Monte Carlo simulation so that it can be guaranteed that the state of the process at a given time is exactly drawn from the target distribution. The question of assessing convergence totally vanishes. Such methods are known as exact or perfect sampling. The approach that has received most attention uses the protocol of coupling from the past devised by Propp and Wilson (Random Structures and Algorithms,1996), in which multiple dependent paths of the chain are run from different initial states at a sequence of initial times going backwards into the past, until they satisfy the condition of coalescence by time 0. When this is achieved the state at time 0 is distributed according to the required target. This process must be implemented very carefully to assure its validity (including appropriate re-use of random number streams), and also requires one of various tricks to enable us to follow infinitely many sample paths with a finite amount of work. With the ultimate objective of Bayesian MCMC with guaranteed convergence, the purpose of this paper is to describe recent efforts to construct exact sampling methods for continuous-state Markov chains. We review existing methods based on gamma-coupling and rejection sampling (Murdoch and Green, Scandinavian Journal of Statistics, 1998), that are quite straightforward to understand, but require a closed form for the transition kernel and entail cumbersome algebraic manipulation. We then introduce two new methods based on random walk Metropolis, that offer the prospect of more automatic use, not least because the difficult, continuous, part of the transition mechanism can be coupled in a generic way, using a proposal distribution of convenience. One of the methods is based on a neat decomposition of any unimodal (multivariate) symmetric density into pieces that may be re-assembled to construct any translated copy of itself: that allows coupling of a continuum of Metropolis proposals to a finite set, at least for a compact state space. We discuss methods for economically coupling the subsequent accept/reject decisions. Our second new method deals with unbounded state spaces, using a trick due to W. S. Kendall of running a coupled dominating process in parallel with the sample paths of interest. The random subset of the state space below the dominating path is compact, allowing efficient coupling and coalescence. We look towards the possibility that application of such methods could become sufficiently convenient that they could become the basis for routine Bayesian computation in the foreseeable future. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #642827. 	[Title] Decomposable graphical Gaussian model determination [Abstract] We propose a methodology for Bayesian model determination in decomposable graphical Gaussian models. To achieve this aim we consider a hyper inverse Wishart prior distribution on the concentration matrix for each given graph. To ensure compatibility across models, such prior distributions are obtained by marginalisation from the prior conditional on the complete graph. We explore alternative structures for the hyperparameters of the latter, and their consequences for the model. Model determination is carried out by implementing a reversible jump MCMC sampler. In particular, the dimension-changing move we propose involves adding or dropping an edge from the graph. We characterise the set of moves which preserve the decomposability of the graph, giving a fast algorithm for maintaining the junction tree representation of the graph at each sweep. As state variable, we propose to use the incomplete variance-covariance matrix, containing only the elements for which the corresponding element of the inverse is nonzero. This allows all computations to be performed locally, at the clique level, which is a clear advantage for the analysis of large and complex data-sets. Finally, the statistical and computational performance of the procedure is illustrated by means of both artificial and real multidimensional data-sets. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #137868. 	[Title] On Bayesian analysis of mixtures with an unknown number of components  Summary [Abstract] New methodology for fully Bayesian mixture analysis is developed, making use of reversible jump Markov chain Monte Carlo methods, that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture. A sample from the full joint distribution of all unknown variables is thereby generated, and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution. The methodology is applied here to the analysis of univariate normal mixtures, using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131277. 	[Title] Bayesian Detection of Clusters and Discontinuities in Disease Maps [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1154068. 	[Title] Bayesian MARS [Abstract] A Bayesian approach to multivariate adaptive regression spline (MARS) fitting (Friedman, 1991) is proposed. This takes the form of a probability distribution over the space of possible MARS models which is explored using reversible jump Markov chain Monte Carlo methods (Green, 1995). The generated sample of MARS models produced is shown to have good predictive power when averaged and allows easy interpretation of the relative importance of predictors to the overall fit. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131300. 	[Title] Reparameterisation Issues in Mixture Modelling and their bearing on MCMC algorithms [Abstract] There is increasing need for efficient estimation of mixture distributions, especially following the explosion in the use of these as modelling tools in many applied fields. We propose in this paper a Bayesian noninformative approach for the estimation of normal mixtures which relies on a reparameterisation of the secondary components of the mixture in terms of divergence from the main component. As well as providing an intuitively appealing representation at the modelling stage, this reparameterisation has important bearing on both the prior distribution and the performance of MCMC algorithms. We compare two possible reparameterisations extending Mengersen and Robert (1996) and show that the reparameterisation which does not link the secondary components together is associated with poor convergence properties of MCMC algorithms. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #560936. 	[Title] Monte Carlo Comparison of Non-hierarchical Unsupervised Classifiers [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #79809. 	[Title] MDL and MML Similarities and Differences (Introduction to Minimum Encoding Inference Part III) [Abstract] Tech Report 207 Department of Computer Science, Monash University, Clayton, Vic. 3168, Australia Abstract: This paper continues the introduction to minimum encoding inductive inference given by Oliver and Hand. This series of papers was written with the objective of providing an introduction to this area for statisticians. We describe the message length estimates used in Wallace's Minimum Message Length (MML) inference and Rissanen's Minimum Description Length (MDL) inference. The differences in the message length estimates of the two approaches are explained. The implications of these differences for applications are discussed. 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 #1131466. 	[Title] Stochastic Complexity Based Estimation of Missing Elements in Questionnaire Data [Abstract] In this paper we study a new information-theoretically justified approach to missing data estimation for multivariate categorical data. The approach discussed is a model-based imputation procedure relative to a model class (i.e., a functional form for the probability distribution of the complete data matrix), which in our case is the set of multinomial models with some independence assumptions. Based on the given model class assumption an information-theoretic criterion can be derived to select between the different complete data matrices. Intuitively this general criterion, called stochastic complexity, represents the shortest code length needed for coding the complete data matrix relative to the model class chosen. Using this information-theoretic criteria, the missing data problem is reduced to a search problem, i.e., finding the data completion with minimal stochastic complexity. In the experimental part of the paper we present empirical results of the approach using two real data sets, and compare these results to those achived by commonly used techniques such as case deletion and imputating sample averages. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #562123. 	[Title] Comparison of Bayesian and Neural Net Unsupervised Classification Techniques [Abstract] Unsupervised classification is the classification of data into a number of classes in such a way that data in each class are all similar to each other. In the past there have been few if any studies done to compare the performance of different unsupervised classification techniques. In this paper we review Bayesian and neural net approaches to unsupervised classification and present results of experiments that we did to compare Autoclass, a Bayesian classification system, and ART2, a neural net classification algorithm. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #11342. 	[Title] On Pruning and Averaging Decision Trees [Abstract] Pruning a decision tree is considered by some researchers to be the most important part of tree building in noisy domains. While, there are many approaches to pruning, an alternative approach of averaging over decision trees has not received as much attention. We perform an empirical comparison of pruning with the approach of averaging over decision trees. For this comparison we use a computa-tionally efficient method of averaging, namely averaging over the extended fanned set of a tree. Since there are a wide range of approaches to pruning, we compare tree averaging with a traditional pruning approach, along with an optimal pruning approach. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #358866. 	[Title] BAYESIAN ESTIMATION OF THE VON MISES CONCENTRATION PARAMETER [Abstract] The von Mises distribution is a maximum entropy distribution. It corresponds to the distribution of an angle of a compass needle in a uniform magnetic field of direction, , with concentration parameter, . The concentration parameter, , is the ratio of the field strength to the temperature of thermal fluctuations. Previously, we obtained a Bayesian estimator for the von Mises distribution parameters using the information-theoretic Minimum Message Length (MML) principle. Here, we examine a variety of Bayesian estimation techniques by examining the posterior distribution in both polar and Cartesian co-ordinates. We compare the MML estimator with these fellow Bayesian techniques, and a range of Classical estimators. We find that the Bayesian estimators outperform the Classical estimators. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1121659. 	[Title] Causal Discovery via MML [Abstract] Automating the learning of causal models from sample data is a key step toward incorporating machine learning in the automation of decision-making and reasoning under uncertainty. This paper presents a Bayesian approach to the discovery of causal models, using a Minimum Message Length (MML) method. We have developed encoding and search methods for discovering linear causal models. The initial experimental results presented in this paper show that the MML induction approach can recover causal models from generated data which are quite accurate reflections of the original models; our results compare favorably with those of the TETRAD II program of Spirtes et al. [25] even when their algorithm is supplied with prior temporal information and MML is not. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1365. 	[Title] Cholinergic suppression of transmission may allow combined associative memory function and self-organization in the neocortex. [Abstract] Selective suppression of transmission at feedback synapses during learning is proposed as a mechanism for combining associative feedback with self-organization of feedforward synapses. Experimental data demonstrates cholinergic suppression of synaptic transmission in layer I (feedback synapses), and a lack of suppression in layer IV (feed-forward synapses). A network with this feature uses local rules to learn mappings which are not linearly separable. During learning, sensory stimuli and desired response are simultaneously presented as input. Feedforward connections form self-organized representations of input, while suppressed feedback connections learn the transpose of feedfor-ward connectivity. During recall, suppression is removed, sensory input activates the self-organized representation, and activity generates the learned response. Please summarise all the given information.

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

Above are papers related to the following paper: [Paper_ID] Paper #358884. 	[Title] THE DISCOVERY OF ALGORITHMIC PROBABILITY [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #358887. 	[Title] SINGLE FACTOR ANALYSIS BY MML ESTIMATION [Abstract] The Minimum Message Length (MML) technique is applied to the problem of estimating the parameters of a multivariate Gaussian model in which the correlation structure is modelled by a single common factor. Implicit estimator equations are derived and compared with those obtained from a Maximum Likelihood (ML) analysis. Unlike ML, the MML estimators remain consistent when used to estimate both the factor loadings and factor scores. Tests on simulated data show the MML estimates to be on av erage more accurate than the ML estimates when the former exist. If the data show little evidence for a factor, the MML estimate collapses. It is shown that the condition for the existence of an MML estimate is essentially that the log likelihood ratio in favour of the factor model exceed the value expected under the null (no-factor) hypotheses. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #358894. 	[Title] MML mixture modelling of multi-state, Poisson, von Mises circular and Gaussian distributions [Abstract] Minimum Message Length (MML) is an invariant Bayesian point estimation technique which is also consistent and efficient. We provide a brief overview of MML inductive inference (Wallace and Boulton (1968), Wallace and Freeman (1987)), and how it has both an information-theoretic and a Bayesian interpretation. We then outline how MML is used for statistical parameter estimation, and how the MML mixture mod-elling program, Snob (Wallace and Boulton (1968), Wal-lace (1986), Wallace and Dowe(1994)) uses the message lengths from various parameter estimates to enable it to combine parameter estimation with selection of the number of components. The message length is (to within a constant) the logarithm of the posterior probability of the theory. So, the MML theory can also be regarded as the theory with the highest posterior probability. Snob currently assumes that variables are uncorrelated, and permits multi-variate data from Gaussian, discrete multi-state, Poisson and von Mises circular distributions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1110000. 	[Title] FLEXIBLE PARAMETRIC MEASUREMENT ERROR MODELS [Abstract] Inferences in measurement error models can be sensitive to modeling assumptions. Specifically, if the model is incorrect then the estimates can be inconsistent. To reduce sensitivity to modeling assumptions and yet still retain the efficiency of parametric inference we propose to use flexible parametric models which can accommodate departures from standard parametric models. We use mixtures of normals for this purpose. We study two cases in detail: a linear errors-in-variables model and a change-point Berkson model. fl Raymond J. Carroll is Professor of Statistics, Nutrition and Toxicology, Department of Statistics, Texas A&M University, College Station, TX 77843-3143. Kathryn Roeder is Associate Professor, and Larry Wasser-man is Professor, Department of Statistics, Carnegie-Mellon University, Pittsburgh PA 15213-3890. Carroll's research was supported by a grant from the National Cancer Institute (CA-57030). Roeder's research was supported by NSF grant DMS-9496219. Wasserman's research was supported by NIH grant RO1-CA54852 and NSF grants DMS-9303557 and DMS-9357646. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #31863. 	[Title] Unsupervised Learning Using MML [Abstract] This paper discusses the unsupervised learning problem. An important part of the unsupervised learning problem is determining the number of constituent groups (components or classes) which best describes some data. We apply the Minimum Message Length (MML) criterion to the unsupervised learning problem, modifying an earlier such MML application. We give an empirical comparison of criteria prominent in the literature for estimating the number of components in a data set. We conclude that the Minimum Message Length criterion performs better than the alternatives on the data considered here for unsupervised learning tasks. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1272. 	[Title] Learning a set of primitive actions with an Induction of decision trees. Machine Learning, 1(1):81-106, [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1153275. 	[Title]  [Abstract] Tech Report 4-94 Department of Statistics, Open University, Walton Hall, MK7 6AA, UK Tech Report 205 Department of Computer Science, Monash University, Clayton, Vic. 3168, Australia Abstract: This paper examines the minimum encoding approaches to inference, Minimum Message Length (MML) and Minimum Description Length (MDL). This paper was written with the objective of providing an introduction to this area for statisticians. We describe coding techniques for data, and examine how these techniques can be applied to perform inference and model selection. Please summarise all the given information.

Paper #91581 has the title `Finding Overlapping Distributions with MML  
` and the abstract `This paper considers an aspect of mixture modelling. Significantly overlapping distributions require more data for their parameters to be accurately estimated than well separated distributions. For example, two Gaussian distributions are considered to significantly overlap when their means are within three standard deviations of each other. If insufficient data is available, only a single component distribution will be estimated, although the data originates from two component distributions. We consider how much data is required to distinguish two component distributions from one distribution in mixture modelling using the minimum message length (MML) criterion. First, we perform experiments which show the MML criterion performs well relative to other Bayesian criteria. Second, we make two improvements to the existing MML estimates, that improve its performance with overlapping distributions. 
`.
Question: Which category should Paper #91581 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #91581 has the title `Finding Overlapping Distributions with MML  
` and the abstract `This paper considers an aspect of mixture modelling. Significantly overlapping distributions require more data for their parameters to be accurately estimated than well separated distributions. For example, two Gaussian distributions are considered to significantly overlap when their means are within three standard deviations of each other. If insufficient data is available, only a single component distribution will be estimated, although the data originates from two component distributions. We consider how much data is required to distinguish two component distributions from one distribution in mixture modelling using the minimum message length (MML) criterion. First, we perform experiments which show the MML criterion performs well relative to other Bayesian criteria. Second, we make two improvements to the existing MML estimates, that improve its performance with overlapping distributions. 
`.
Question: Which category should Paper #91581 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