231 research outputs found
Looking for independent factors: a new factor rotation method
No full textIn the statistical literature on factor analysis many ingenious graphical and analytical procedures have been developed for transforming arbitrary factor loading matrices into meaningful ones while preserving factor scores orthogonality. All of them aim at obtaining an interpretable set of factors, according to Thurstons simple-structure principle, by focusing on and suitably modifying the factor loading matrix. Recently, starting from the signal processing
community, the literature has witnessed a growing interest towards modeling a set of observed non gaussian variables through linear combinations of non gaussian independent latent ones.
In this paper we show that if such a model holds, it can be easily estimated by suitably rotating the ordinary factor analysis solution (obtained by a distribution free method, as the problem
is outside the classic gaussian context in which independence and uncorrelatedness coincide).
This involves shifting the attention from the structure of the factor loading matrix to the fac-
tor scores relationship, as independence does not necessarily impose a simple structure on the
factor loading matrix. The question is then: how can one transform a set of sphered variables
(the factor scores which are assumed unit variance and uncorrelated) into a set of as many
independent ones? An answer is o®ered by Independent Component Analysis proposed by
Comon (1994) in order to model p given variables as linear mixtures of p unknown independent
ones: as the factor scores are sphered, performing ICA on them simply amounts to look for the
orthogonal rotation which leads to the least gaussian projections of the original factor scores.
We illustrate the performances of the proposed method both on real and simulated data and
also highlight the links of the method with another recently proposed model also allowing for
independent latent variables, the independent factor analysis model (Attias, 1999; Montanari
and Viroli, 2004)
Multivariate Latent Variable Transition Models of Longitudinal Mixed Data: an Analysis on Alcohol Use Disorder
No full textAlcohol abuse is a dangerous habit in young people. The National Youth Survey is a longitudinal American study in part devoted to the investigation of alcohol disorder during time. The symptoms of alcohol disorder are measured by binary and ordinal items. In the literature it is well recognized that the alcohol abuse can be measured by a latent construct; therefore generalized latent variable models for mixed data represents the ideal framework to analyze these data. However, it might be desirable to cluster individuals according to the different severity of the alcohol use disorder and to investigate how the groups vary during time. We present a new methodological framework that includes two levels of latent variables: one continuous hidden variable for dimension reduction and clustering and a discrete random variable accounting for the dynamics of the alcohol disorder symptoms. The effect of covariates is also measured and a testing procedure for the temporal assumption is developed. This work addresses three important issues. First, it represents a unified framework for the analysis of longitudinal multivariate mixed data. Secondly, it captures and models the unobserved heterogeneity of the data. Finally it describes the dynamics of the data through the definition of latent constructs
Quantile-based classifiers
No full text: Classification with small samples of high-dimensional data is important in many application areas. Quantile classifiers are distance-based classifiers that require a single parameter, regardless of the dimension, and classify observations according to a sum of weighted componentwise distances of the components of an observation to the within-class quantiles. An optimal percentage for the quantiles can be chosen by minimizing the misclassification error in the training sample. It is shown that this choice is consistent for the classification rule with the asymptotically optimal quantile and that under some assumptions, as the number of variables goes to infinity, the probability of correct classification converges to unity. The effect of skewness of the distributions of the predictor variables is discussed. The optimal quantile classifier gives low misclassification rates in a comprehensive simulation study and in a real-data application
Model based clustering for three-way data structures
No full textThe technological progress of the last decades has made a huge amount of information available, often expressed in unconventional formats. Among these, three-way data occur in different application domains from the simultaneous observation of various attributes on a set of units in different situations or locations. These include data coming from longitudinal studies of multiple responses, spatio- temporal data or data collecting multivariate repeated measures. In this work we propose model based clustering for the wide class of continuous three-way data by a general mixture model which can be adapted to the different kinds of three-way data. In so doing we also provide a tool for simultaneously performing model estimation and model selection. The effectiveness of the proposed method is illustrated on a simulation study and on real examples
Dimensionally Reduced Model-Based Clustering Through Mixtures of Factor Mixture Analyzers
No full textDimensionally reduced model-based clustering methods are recently receiving a wide interest in statistics as a tool for performing simultaneously clustering and dimension reduction through one or more latent variables. Among these, Mixtures of Factor Analyzers assume that, within each component, the data are generated according to a factor model, thus reducing the number of parameters on which the covariance matrices depend. In Factor Mixture Analysis clustering is performed through the factors of an ordinary factor analysis which are jointly modelled by a Gaussian mixture. The two approaches differ in genesis, parameterization and consequently clustering performance. In this work we propose a model which extends and combines them. The proposed Mixtures of Factor Mixture Analyzers provide a unified class of dimensionally reduced mixture models which includes the previous ones as special cases and could offer a powerful tool for modelling non-Gaussian latent variables
A supervised classification strategy based on the novel directional distribution depth function
No full textStudi sul repubblicanesimo. In onore di Maurizio Viroli
No full textMaurizio Viroli è Professor Emeritus of Politics alla Princeton University e Professor of Government alla University of Texas at Austin. Nel suo lungo e prolifico percorso di ricerca, sviluppatosi in diversi ambiti di studio pur gravitando sempre intorno alla tradizione politica del repubblicanesimo e alla figura di Machiavelli, ha costantemente dialogato con studiose e studiosi europei e americani. Questo volume, curato da Marcello Gisondi e Giorgio Volpe, vuole rendere omaggio a quel percorso intellettuale ravvivando quel dialogo grazie ai contributi di Gennaro Maria Barbuto, Gianfranco Borrelli, Thomas Casadei, Hilary Gatti, Robert P. George, Tommaso Greco, Jorge Islas López, Giacomo Jori, Fabrizio Lomonaco, Harvey C. Mansfield, Jean-Jacques Marchand, Sauro Mattarelli, Dino Mengozzi, Thomas L. Pangle, Nicola Panichi, Gianfranco Pasquino, Quentin Skinner, Lorraine Smith Pangle, Pasquale Stoppelli, David L. Tubbs, Jeffrey K. Tulis e Gianfrancesco Zanetti. Il volume contiene inoltre una bibliografia degli scritti di Viroli, utile a chi voglia accostarsi o approfondire la sua opera
Deep mixtures of unigrams for uncovering topics in textual data
No full textMixtures of unigrams are one of the simplest and most efficient tools for clustering textual data, as they assume that documents related to the same topic have similar distributions of terms, naturally described by multinomials. When the classification task is particularly challenging, such as when the document-term matrix is high-dimensional and extremely sparse, a more composite representation can provide better insight into the grouping structure. In this work, we developed a deep version of mixtures of unigrams for the unsupervised classification of very short documents with a large number of terms, by allowing for models with further deeper latent layers; the proposal is derived in a Bayesian framework. The behavior of the deep mixtures of unigrams is empirically compared with that of other traditional and state-of-the-art methods, namely k-means with cosine distance, k-means with Euclidean distance on data transformed according to semantic analysis, partition around medoids, mixture of Gaussians on semantic-based transformed data, hierarchical clustering according to Ward’s method with cosine dissimilarity, latent Dirichlet allocation, mixtures of unigrams estimated via the EM algorithm, spectral clustering and affinity propagation clustering. The performance is evaluated in terms of both correct classification rate and Adjusted Rand Index. Simulation studies and real data analysis prove that going deep in clustering such data highly improves the classification accuracy
Dealing with overdispersion in multivariate count data
No full textThe problem of overdispersion in multivariate count data is a challenging issue. It covers a central role mainly due to the relevance of modern technology-based data, such as Next Generation Sequencing and textual data from the web or digital collections. A comprehensive analysis of the likelihood-based models for extra-variation data is presented. Particular attention is paid to the models feasible for high-dimensional data. A new approach together with its parametric-estimation procedure is proposed. It can be viewed as a deeper version of the Dirichlet-Multinomial distribution and it leads to important results allowing to get a better approximation of the observed variability. A significative comparison of the proposed model and existing strategies is made through two different simulation studies and an empirical data set, that confirm a better capability to describe overdispersion
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