Papers by Adolfo Zepeda Hernández
Estimating a covariance structure from a sample correlation matrix requires complex non-linear co... more Estimating a covariance structure from a sample correlation matrix requires complex non-linear constraints among the model parameters. When the covariance structure is scale invariant, then a simpler approach is possible. We cover the continuous observed variables case, as well as the categorical observed variables case, the latter under discretized multivariate normality assumptions. In the categorical case, we show that the covariance structure parameters can be estimated from the sample polychoric correlations if and only if the covariance structure is scale invariant. Otherwise, they must be estimated from the sample thresholds and polychoric correlations jointly. In the continuous case, we show that one can estimate any covariance structure from a sample correlation matrix by minimizing a normal theory discrepancy function for sample covariances.
Studies in Computational Intelligence, 2007
Bayesian averaging over classification models allows the uncertainty of classification outcomes t... more Bayesian averaging over classification models allows the uncertainty of classification outcomes to be evaluated, which is of crucial importance for making reliable decisions in applications such as financial in which risks have to be estimated. The uncertainty of classification is determined by a trade-off between the amount of data available for training, the diversity of a classifier ensemble and the required performance. The interpretability of classification models can also give useful information for experts responsible for making reliable classifications. For this reason Decision Trees (DTs) seem to be attractive classification models. The required diversity of the DT ensemble can be achieved by using the Bayesian model averaging all possible DTs. In practice, the Bayesian approach can be implemented on the base of a Markov Chain Monte Carlo (MCMC) technique of random sampling from the posterior distribution. For sampling large DTs, the MCMC method is extended by Reversible Jump technique which allows inducing DTs under given priors. For the case when the prior information on the DT size is unavailable, the sweeping technique defining the prior implicitly reveals a better performance. Within this Chapter we explore the classification uncertainty of the Bayesian MCMC techniques on some datasets from the StatLog Repository and real financial data. The classification uncertainty is compared within an Uncertainty Envelope technique dealing with the class posterior distribution and a given confidence probability. This technique provides realistic estimates of the classification uncertainty which can be easily interpreted in statistical terms with the aim of risk evaluation. 2
Lecture Notes in Computer Science, 2004
In this paper we experimentally compare the classification uncertainty of the randomised Decision... more In this paper we experimentally compare the classification uncertainty of the randomised Decision Tree (DT) ensemble technique and the Bayesian DT technique with a restarting strategy on a synthetic dataset as well as on some datasets commonly used in the machine learning community. For quantitative evaluation of classification uncertainty, we use an Uncertainty Envelope dealing with the class posterior distribution and a given confidence probability. Counting the classifier outcomes, this technique produces feasible evaluations of the classification uncertainty. Using this technique in our experiments, we found that the Bayesian DT technique is superior to the randomised DT ensemble technique.
Developments in Risk-based Approaches to Safety, 2006
In this paper we demonstrate an application of data-driven software development in a Bayesian fra... more In this paper we demonstrate an application of data-driven software development in a Bayesian framework such that every computed result arises from within a context and so can be associated with a ‘confidence’ estimate whose validity is underpinned by Bayesian principles. This technique, which induces software modules from data samples (e.g., training a neural network), can be contrasted with more traditional, abstract specification driven, software development that has tended to compute a result and then added secondary computation to produce an associated ‘confidence’ measure. We demonstrate this approach applied to classification tasks — i.e., the challenge is to construct a software module that aims to classify its input vector as one of a number of potential target classes. Thus a series of features extracted from a mammogram (an input vector) might need to be classified as either tumour or non-tumour, in this case just two target classes. The set of classification probability estimates, which are fundamental to the Bayesian approach and constitute the ‘context’ of any classification result, are generated by means of massive, but systematic, recomputation of results. We use state-of-the-art Reversible-Jump Markov Chain Monte Carlo (RJMCMC) methods to simulate the otherwise intractable integrals that emerge in applications of Bayes’ Theorem. The focus of this paper is on ‘confidence’ estimates as an integral part of classification software and on the role of such estimates in critical systems rather than on the recomputation techniques employed to get the results.
SSRN Electronic Journal, 2000
We introduce a multidimensional latent trait model for binary data with non-monotone item respons... more We introduce a multidimensional latent trait model for binary data with non-monotone item response functions. We assume that the conditional probability of endorsing an item is a normal probability density function, and that the latent traits are normally distributed. The model yields ...
Developments in Risk-based Approaches to Safety, 2006
Abstract The operation of many safety related systems is dependent upon a number of interacting p... more Abstract The operation of many safety related systems is dependent upon a number of interacting parameters. Frequently these parameters must be 'tuned' to the particular operating environment to provide the best possible performance. We focus on the Short Term Conflict Alert ...
Modern Applied Science, 2008
The non-parametric smoothing of the location model proposed by for allocating objects with mixtur... more The non-parametric smoothing of the location model proposed by for allocating objects with mixtures of variables into two groups is studied. The strategy for selecting the smoothing parameter through the maximisation of the pseudo-likelihood function is reviewed. Problems with previous methods are highlighted, and two alternative strategies are proposed. Some investigations into other possible smoothing procedures for estimating cell probabilities are discussed. A leave-one-out method is proposed for constructing the allocation rule and evaluating its performance by estimating the true error rate. Results of a numerical study on simulated data highlight the feasibility of the proposed allocation rule as well as its advantages over previous methods, and an example using real data is presented.
Structural Equation Modeling: A Multidisciplinary Journal, 2011
Linear factor analysis (FA) models can be reliably tested using test statistics based on residual... more Linear factor analysis (FA) models can be reliably tested using test statistics based on residual covariances. We show that the same statistics can be used to reliably test the fit of item response theory (IRT) models for ordinal data (under some conditions). Hence, the fit of an FA model and of an IRT model to the same data set can now be compared. When applied to a binary data set, our experience suggests that IRT and FA models yield similar fits. However, when the data are polytomous ordinal, IRT models yield a better fit because they involve a higher number of parameters. But when fit is assessed using the root mean square error of approximation (RMSEA), similar fits are obtained again. We explain why. These test statistics have little power to distinguish between FA and IRT models; they are unable to detect that linear FA is misspecified when applied to ordinal data generated under an IRT model. The common factor model is used to relate linearly a set of observed variables to a smaller set of unobserved continuous variables, the common factors or latent traits. When the model holds, the latent traits are then used to explain the dependencies between the variables observed. However, the factor model is most often applied to response variables that are discrete, such as binary variables, or ratings scored using successive integers. Indeed, when applied to discrete data we know a priori that the factor model is always misspecified to some extent, because the predicted responses under this model can never be exact integers .
Multivariate Behavioral Research, 2007
The interpretation of a Thurstonian model for paired comparisons where the utilities' covariance ... more The interpretation of a Thurstonian model for paired comparisons where the utilities' covariance matrix is unrestricted proved to be difficult due to the comparative nature of the data. We show that under a suitable constraint the utilities' correlation matrix can be estimated, yielding a readily interpretable solution. This set of identification constraints can recover any true utilities' covariance matrix, but it is not unique. Indeed, we show how to transform the estimated correlation matrix into alternative correlation matrices that are equally consistent with the data but may be more consistent with substantive theory. Also, we show how researchers can investigate the sample size needed to estimate a particular model by exploiting the simulation capabilities of a popular structural equation modeling statistical package.
Multivariate Behavioral Research, 2006
We introduce a multidimensional item response theory (IRT) model for binary data based on a proxi... more We introduce a multidimensional item response theory (IRT) model for binary data based on a proximity response mechanism. Under the model, a respondent at the mode of the item response function (IRF) endorses the item with probability one. The mode of the IRF is the ideal point, or in the multidimensional case, an ideal hyperplane. The model yields closed form expressions for the cell probabilities. We estimate and test the goodness of fit of the model using only information contained in the univariate and bivariate moments of the data. Also, we pit the new model against the multidimensional normal ogive model estimated using NOHARM in four applications involving (a) attitudes toward censorship, (b) satisfaction with life, (c) attitudes of morality and equality, and (d) political efficacy. The normal PDF model is not invariant to simple operations such as reverse scoring. Thus, when there is no natural category to be modeled, as in many personality applications, it should be fit separately with and without reverse scoring for comparisons. MULTIVARIATE BEHAVIORAL RESEARCH, 41(4),
Journal of Mathematical Modelling and Algorithms, 2006
Multiple Classifier Systems (MCSs) allow evaluation of the uncertainty of classification outcomes... more Multiple Classifier Systems (MCSs) allow evaluation of the uncertainty of classification outcomes that is of crucial importance for safety critical applications. The uncertainty of classification is determined by a trade-off between the amount of data available for training, the classifier diversity and the required performance. The interpretability of MCSs can also give useful information for experts responsible for making reliable classifications. For this reason Decision Trees (DTs) seem to be attractive classification models for experts. The required diversity of MCSs exploiting such classification models can be achieved by using two techniques, the Bayesian model averaging and the randomised DT ensemble. Both techniques have revealed promising results when applied to real-world problems. In this paper we experimentally compare the classification uncertainty of the Bayesian model averaging with a restarting strategy and the randomised DT ensemble on a synthetic dataset and some domain problems commonly used in the machine learning community. To make the Bayesian DT averaging feasible, we use a Markov Chain Monte Carlo technique. The classification uncertainty is evaluated within an Uncertainty Envelope technique dealing with the class posterior distribution and a given confidence probability. Exploring a full posterior distribution, this technique produces realistic estimates which can be easily interpreted in statistical terms. In our experiments we found out that the Bayesian DTs are superior to the randomised DT ensembles within the Uncertainty Envelope technique.
Journal of Multivariate Analysis, 2005
ABSTRACT The limit behavior of the conditional probability of error of linear and quadratic discr... more ABSTRACT The limit behavior of the conditional probability of error of linear and quadratic discriminant analyses is studied under wide assumptions on the class conditional distributions. Results obtained may help to explain analytically the behavior in applications of linear and quadratic discrimination techniques.
Journal of Computational and Graphical Statistics, 2005
Page 1. Dimension Reduction in Nonparametric Kernel Discriminant Analysis Adolfo HERNÁNDEZ and Sa... more Page 1. Dimension Reduction in Nonparametric Kernel Discriminant Analysis Adolfo HERNÁNDEZ and Santiago VELILLA This article develops a dimension-reduction method in kernel discriminant analysis, based on a general concept of separation of populations. ...
The present paper intents to make up a development proposal compressive approach of the horticult... more The present paper intents to make up a development proposal compressive approach of the horticultural sector, it lets integrate different research effort and technologica l intervention by CORPOICA, in the frame of long time program which promotes the sustainability of this sector. The approach is built over System Dynamics attempting make synthesis with the Sustainable Human Development conception and inquiring the System Dynamics models use in agricultural planning and the organizational learning role in the social web built. In the frame of the sustainability, alimentary security become more important as research subject, technological intervention and social strategy. In the context of our country, it is support in the agriculture, beginning with local alimentary security proposal and actually as rural space rebuilt alternative, employment generation space and competitively strategy. In this context, the social capital is seen as an strategy for Organizational Learning, in other...
IEEE Transactions on Information Technology in Biomedicine, 2000
Bayesian averaging (BA) over ensembles of decision models allows evaluation of the uncertainty of... more Bayesian averaging (BA) over ensembles of decision models allows evaluation of the uncertainty of decisions that is of crucial importance for safety-critical applications such as medical diagnostics. The interpretability of the ensemble can also give useful information for experts responsible for making reliable decisions. For this reason, decision trees (DTs) are attractive decision models for experts. However, BA over such models makes an ensemble of DTs uninterpretable. In this paper, we present a new approach to probabilistic interpretation of Bayesian DT ensembles. This approach is based on the quantitative evaluation of uncertainty of the DTs, and allows experts to find a DT that provides a high predictive accuracy and confident outcomes. To make the BA over DTs feasible in our experiments, we use a Markov Chain Monte Carlo technique with a reversible jump extension. The results obtained from clinical data show that in terms of predictive accuracy, the proposed method outperforms the maximum a posteriori (MAP) method that has been suggested for interpretation of DT ensembles.
Reumatología Clínica, 2005
Interacciones entre de antiinflamatorios no esteroideos y otros fármacos en pacientes con enferme... more Interacciones entre de antiinflamatorios no esteroideos y otros fármacos en pacientes con enfermedades reumatológicas Objetivo: Determinar la prevalencia e identificar las interacciones (INTMED) entre antiinflamatorios no esteroideos (AINE) y otros fármacos en una base de datos de prescripción a enfermos reumáticos. Material y métodos: Se trata de un estudio transversal de una base de datos de prescripción de 35.000 beneficiarios de un sistema de atención médica de prepago para trabajadores bancarios y sus familiares. El análisis abarca un año (de enero a diciembre de 1998). La lista y la clasificación de las AINE-INTMED en 3 niveles (1: mínimo; 2: moderado, y 3: alto riesgo para la salud/peligro de muerte) se hicieron de acuerdo con DRUGDEX ® y búsquedas en MEDLINE y EMBASE. Resultados: Se analizaron 3.207 prescripciones de AINE (1,7 ± 1,6 por paciente) a 1.855 pacientes reumáticos (el 76,7% adultos, el 20,2% geriátricos y el 3,0% pediátricos; reumatismo extraarticular: 52%; osteoartrosis: 19%; artritis reumatoide: 10%). Se encontraron 648 (20,20%) AINE-INTMED, de las que 594 (91,66%) correspondieron al nivel 1, 46 (7,09%) al nivel 2 y 8 (1,23%) al nivel 3. Además, encontramos 96 (2,99%) prescripciones con duplicación de AINE. No encontramos AINE-INTMED con anticoagulantes, anticonvulsionantes o hipoglucemiantes orales. Conclusiones: La prevalencia de AINE-INTMED en prescripciones a 1.855 pacientes reumáticos en un año fue del 20,20%. La mayoría (91,66%) fue del nivel 1 y raramente del 3 (1,23%). El 2,99% de ellas tuvieron duplicaciones de AINE. Nuestros resultados proporcionan información de la prevalencia de INTMED que potencialmente podrían producir daños al individuo y datos que podrían influir en el desarrollo de estudios de la importancia clínica de las AINE-INMED.
Electronic Journal of Statistics, 2014
ABSTRACT Given n independent, identically distributed random vectors in ℝ d , drawn from a common... more ABSTRACT Given n independent, identically distributed random vectors in ℝ d , drawn from a common density f, one wishes to find out whether the support of f is convex or not. We describe a decision rule which decides correctly for sufficiently large n, with probability 1, whenever f is bounded away from zero in its compact support. We also show that the assumption of boundedness is necessary. The rule is based on a statistic that is a second-order U-statistic with a random kernel. Moreover, we suggest a way of approximating the distribution of the statistic under the hypothesis of convexity of the support. The performance of the proposed method is illustrated on simulated data sets. As an example of its potential statistical implications, the decision rule is used to automatically choose the tuning parameter of ISOMAP, a nonlinear dimensionality reduction method.
Revista médica del Instituto Mexicano del Seguro Social
to compare the direct cost of open cholecystectomy (OCL) with laparoscopic cholecystectomy (LCL),... more to compare the direct cost of open cholecystectomy (OCL) with laparoscopic cholecystectomy (LCL), using a microcosting approach. in patients who underwent cholecystectomy (C) in the Hospital General de Mexico, we collected patient age and sex, time in the operative room (OR), anesthesia and surgical procedure; health personal (HP) involved; materials (M) and medications consumed; medical instruments (MI) and medical equipment (ME) used. there were 355 patients operated by C, were 248 included, 94 with CAB and 74 with CLP. CAB surgical time was longer than CLP (102 versus 82, p<0.00.1); CLP had a higher use of materials intraoperative ($5 329 versus $1 403, p<0.001). There are no differences in: cost for HP, MI and ME. The total direct cost was $7238 (US$615) for CAB and $12 507 (US$1 063) for CLP (p <0.001) at 11.76 Mexican pesos per dollar. the difference in costs between OCL and LCL is primarily explained by the cost of lab exams which represent 79% of the M cost for CLP.
Computational Statistics & Data Analysis, 2006
A new clustering method for time series is proposed, based on the full probability density of the... more A new clustering method for time series is proposed, based on the full probability density of the forecasts. First, a resampling method combined with a nonparametric kernel estimator provides estimates of the forecast densities. A measure of discrepancy is then defined between these estimates and the resulting dissimilarity matrix is used to carry out the required cluster analysis. Applications of this method to both simulated and real life data sets are discussed.
Uploads
Papers by Adolfo Zepeda Hernández