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85
Models and Selection Criteria for Regression and Classification
 Uncertainty in Arificial Intelligence 13
, 1997
"... When performing regression or classification, we are interested in the conditional probability distribution for an outcome or class variable Y given a set of explanatory or input variables X. We consider Bayesian models for this task. In particular, we examine a special class of models, which we ca ..."
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Cited by 23 (2 self)
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When performing regression or classification, we are interested in the conditional probability distribution for an outcome or class variable Y given a set of explanatory or input variables X. We consider Bayesian models for this task. In particular, we examine a special class of models, which we call Bayesian regression/classification (BRC) models, that can be factored into independent conditional (yjx) and input (x) models. These models are convenient, because the conditional model (the portion of the full model that we care about) can be analyzed by itself. We examine the practice of transforming arbitrary Bayesian models to BRC models, and argue that this practice is often inappropriate because it ignores prior knowledge that may be important for learning. In addition, we examine Bayesian methods for learning models from data. We discuss two criteria for Bayesian model selection that are appropriate for repression/classification: one described by Spiegelhalter et al. (1993), and an...
RHODES,J.A.(2009). Identifiability of parameters in latent structure models with many observed variables
 Ann. Statist
"... While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones, we demonstr ..."
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Cited by 21 (4 self)
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While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones, we demonstrate a general approach for establishing identifiability utilizing algebraic arguments. A theorem of J. Kruskal for a simple latentclass model with finite state space lies at the core of our results, though we apply it to a diverse set of models. These include mixtures of both finite and nonparametric product distributions, hidden Markov models and random graph mixture models, and lead to a number of new results and improvements to old ones. In the parametric setting, this approach indicates that for such models, the classical definition of identifiability is typically too strong. Instead generic identifiability holds, which implies that the set of nonidentifiable parameters has measure zero, so that parameter inference is still meaningful. In particular, this sheds light on the properties of finite mixtures of Bernoulli products, which have been used for decades despite being known to have nonidentifiable parameters. In the nonparametric setting, we again obtain identifiability only when certain restrictions are placed on the distributions that are mixed, but we explicitly describe the conditions. 1. Introduction. Statistical
The Gifi System Of Descriptive Multivariate Analysis
 STATISTICAL SCIENCE
, 1998
"... The Gifi system of analyzing categorical data through nonlinear varieties of classical multivariate analysis techniques is reviewed. The system is characterized by the optimal scaling of categorical variables which is implemented through alternating least squares algorithms. The main technique of h ..."
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Cited by 18 (3 self)
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The Gifi system of analyzing categorical data through nonlinear varieties of classical multivariate analysis techniques is reviewed. The system is characterized by the optimal scaling of categorical variables which is implemented through alternating least squares algorithms. The main technique of homogeneity analysis is presented, along with its extensions and generalizations leading to nonmetric principal components analysis and canonical correlation analysis. A brief account of stability issues and areas of applications of the techniques is also given.
Probabilistic latent variable models as nonnegative factorizations,” Computational intelligence and Neuroscience
, 2008
"... In this paper we present a family of probabilistic latent variable models which can be used for analysis of nonnegative data. We show that there strong ties between nonnegative matrix factorization and this family, and we also provide some straightforward extensions which can help in dealing with ..."
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Cited by 18 (5 self)
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In this paper we present a family of probabilistic latent variable models which can be used for analysis of nonnegative data. We show that there strong ties between nonnegative matrix factorization and this family, and we also provide some straightforward extensions which can help in dealing with shiftinvariances, higher order decompositions and sparsity constraints. Through these extensions we argue that the use of this approach allows for rapid development of complex statistical models for analyzing nonnegative data.
A Bayesian approach to the selection and testing of mixture models
 Statistica Sinica
, 2001
"... Abstract: An important aspect of mixture modeling is the selection of the number of mixture components. In this paper, we discuss the Bayes factor as a selection tool. The discussion will focus on two aspects: computation of the Bayes factor and prior sensitivity. For the computation, we propose a v ..."
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Cited by 9 (3 self)
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Abstract: An important aspect of mixture modeling is the selection of the number of mixture components. In this paper, we discuss the Bayes factor as a selection tool. The discussion will focus on two aspects: computation of the Bayes factor and prior sensitivity. For the computation, we propose a variant of Chib’s estimator that accounts for the nonidentifiability of the mixture components. To reduce the prior sensitivity of the Bayes factor, we propose to extend the model with a hyperprior. We further discuss the use of posterior predictive checks for examining the fit of the model. The ideas are illustrated by means of a psychiatric diagnosis example.
Latent class factor and cluster models, biplots, and related graphical displays
 Sociological Methodology
"... Heijden for helpful comments. We propose an alternative method of conducting exploratory latent class analysis that utilizes latent class factor models, and compare it to the more traditional approach based on latent class cluster models. We show that when formulated in terms of R mutually independe ..."
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Cited by 8 (3 self)
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Heijden for helpful comments. We propose an alternative method of conducting exploratory latent class analysis that utilizes latent class factor models, and compare it to the more traditional approach based on latent class cluster models. We show that when formulated in terms of R mutually independent, dichotomous latent factors, the LC factor model has the same number of distinct parameters as an LC cluster model with R+1 clusters. Analyses over several data sets suggest that LC factor models typically fit data better and provide results that are easier to interpret than the corresponding LC cluster models. We also introduce a new graphical “biplot ” display for LC factor models and compare it to similar plots used in correspondence analysis and to a barycentric coordinate display for LC cluster models. We conclude by describing various model extensions and an approach for eliminating boundary solutions that we have implemented in a new computer program called Latent GOLD®.
PennAspect: TwoWay Aspect Model Implementation
"... The twoway aspect model is a latent class statistical mixture model for performing soft clustering of cooccurrence data observations. It acts on data such as document/word pairs (words occurring in documents) or movie/people pairs (people see certain movies) to produce their joint distribution e ..."
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Cited by 7 (3 self)
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The twoway aspect model is a latent class statistical mixture model for performing soft clustering of cooccurrence data observations. It acts on data such as document/word pairs (words occurring in documents) or movie/people pairs (people see certain movies) to produce their joint distribution estimate. This document describes our software implementation of the aspect model available under GNU Public License (included with the distribution). We call this package PennAspect. The distribution is packaged as Java source and class les. The software comes with no guarantees of any kind. We welcome user feedback and comments. To download PennAspect, visit: http://www.cis.upenn.edu/datamining/software dist/PennAspect/index.html. University of Pennsylvania Department of Computer and Information Science Technical Report MSCIS0125. y Corresponding Author. 1 1 A (Very Brief)
poLCA: Polytomous Variable Latent Class Analysis. R Package Version 1.1. http://userwww.service.emory.edu/~dlinzer/poLCA
, 2007
"... poLCA is a software package for the estimation of latent class and latent class regression models for polytomous outcome variables, implemented in the R statistical computing environment. Both models can be called using a single simple command line. The basic latent class model is a finite mixture m ..."
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Cited by 7 (0 self)
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poLCA is a software package for the estimation of latent class and latent class regression models for polytomous outcome variables, implemented in the R statistical computing environment. Both models can be called using a single simple command line. The basic latent class model is a finite mixture model in which the component distributions are assumed to be multiway crossclassification tables with all variables mutually independent. The latent class regression model further enables the researcher to estimate the effects of covariates on predicting latent class membership. poLCA uses expectationmaximization and NewtonRaphson algorithms to find maximum likelihood estimates of the model parameters. This user’s guide to the poLCA software package draws extensively from Linzer and Lewis (Forthcoming). 1 1 Quick Start This section is provided for users who wish to skip the technical details and proceed directly to the estimation of latent class and latent class regression models.
Identifiability of latent class models with many observed variables
"... While latent class models of various types arise in many statistical applications, it is often difficult to establish their identifiability. Focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones, we demonstrate a general ap ..."
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Cited by 6 (2 self)
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While latent class models of various types arise in many statistical applications, it is often difficult to establish their identifiability. Focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones, we demonstrate a general approach for establishing identifiability, utilizing algebraic arguments. A theorem of J. Kruskal for a simple latent class model with finite state space lies at the core of our results, though we apply it to a diverse set of models. These include mixtures of both finite and nonparametric product distributions, hidden Markov models, and random graph models, and lead to a number of new results and improvements to old ones. In the parametric setting we argue that the classical definition of identifiability is too strong, and should be replaced by the concept of generic identifiability. Generic identifiability implies that the set of nonidentifiable parameters has zero measure, so that the model remains useful for inference. In particular, this sheds light on the properties of finite mixtures of Bernoulli products, which have been used for decades despite being known to be nonidentifiable models. In the nonparametric setting, we again obtain identifiability only when certain restrictions are placed on the distributions that are mixed, but we explicitly describe the conditions.