structural modeling and psychometrika an historical perspective on growth and achievements the field of linear structural equation modeling with continuous variables is reviewed trends in psychometric theory and data analysis across the five decades of publication ofpsychometrika are discussed especially the clarification of concepts of population and sample explication of the parametric structure of models delineation of concepts of exploratory and confirmatory data analysis expansion of statistical theory in psychometrics estimation via optimization of an explicit objective function and implementation of general function minimization methods developments in the ideas of factor analysis latent variables as well as structural and causal modeling are noted some major conceptual achievements involving general covariance structure representations multiple population models and moment structures are reviewed the major statistical achievements of normal theory generalized least squares estimation elliptical and distribution free estimation and higher moment estimation are discussed computer programs that implement some of the theoretical developments are described

a generalized rasch model for manifest predictors a logistic regression model is suggested for estimating the relation between a set of manifest predictors and a latent trait assumed to be measured by a set ofk dichotomous items usually the estimated subject parameters of latent trait models are biased especially for short tests therefore the relation between a latent trait and a set of predictors should not be estimated with a regression model in which the estimated subject parameters are used as a dependent variable direct estimation of the relation between the latent trait and one or more independent variables is suggested instead estimation methods and test statistics for the rasch model are discussed and the model is illustrated with simulated and empirical data

representation dimension and quasi hereditary algebras we study auslander s representation dimension of artin algebras which is by definition the minimal projective dimension of coherent functors on modules which are both generators and cogenerators we show the following statements 1 if an artin algebra a is stably hereditary then the representation dimension of a is at most 3 2 if two artin algebras are stably equivalent of morita type then they have the same representation dimension particularly if two self injective algebras are derived equivalent then they have the same representation dimension 3 any incidence algebra of a finite partially ordered set over a field has finite representation dimension moreover we use results on quasi hereditary algebras to show that 4 the auslander algebra of a nakayama algebra has finite representation dimension

model selection and akaike s information criterion aic the general theory and its analytical extensions during the last fifteen years akaike s entropy based information criterion aic has had a fundamental impact in statistical model evaluation problems this paper studies the general theory of the aic procedure and provides its analytical extensions in two ways without violating akaike s main principles these extensions make aic asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the true models these selection criteria are called caic and caicf asymptotic properties of aic and its extensions are investigated and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different monte carlo experiments under different conditions

variational learning of a dirichlet process of generalized dirichlet distributions for simultaneous clustering and feature selection this paper introduces a novel enhancement for unsupervised feature selection based on generalized dirichlet gd mixture models our proposal is based on the extension of the finite mixture model previously developed in 1 to the infinite case via the consideration of dirichlet process mixtures which can be viewed actually as a purely nonparametric model since the number of mixture components can increase as data are introduced the infinite assumption is used to avoid problems related to model selection i e determination of the number of clusters and allows simultaneous separation of data in to similar clusters and selection of relevant features our resulting model is learned within a principled variational bayesian framework that we have developed the experimental results reported for both synthetic data and real world challenging applications involving image categorization automatic semantic annotation and retrieval show the ability of our approach to provide accurate models by distinguishing between relevant and irrelevant features without over or under fitting the data

a note on the geometric interpretation of the em algorithm in estimating item characteristics and student abilities this note uses the em algorithm in an item response model as an illustration of a general method of parameter estimation which geometrically can be described as an alternating projection method

statistical inference for multiple choice tests finite sample inference procedures are considered for analyzing the observed scores on a multiple choice test with several items where for example the items are dissimilar or the item responses are correlated a discrete p parameter exponential family model leads to a generalized linear model framework and in a special case a convenient regression of true score upon observed score techniques based upon the likelihood function akaike s information criteria aic an approximate bayesian marginalization procedure based on conditional maximization bcm and simulations for exact posterior densities importance sampling are used to facilitate finite sample investigations of the average true score individual true scores and various probabilities of interest a simulation study suggests that when the examinees come from two different populations the exponential family can adequately generalize duncan s beta binomial model extensions to regression models the classical test theory model and empirical bayes estimation problems are mentioned the duncan keats and matsumura data sets are used to illustrate potential advantages and flexibility of the exponential family model and the bcm technique

generalized spike and slab priors for bayesian group feature selection using expectation propagation we describe a bayesian method for group feature selection in linear regression problems the method is based on a generalized version of the standard spike and slab prior distribution which is often used for individual feature selection exact bayesian inference under the prior considered is infeasible for typical regression problems however approximate inference can be carried out efficiently using expectation propagation ep a detailed analysis of the generalized spike and slab prior shows that it is well suited for regression problems that are sparse at the group level furthermore this prior can be used to introduce prior knowledge about specific groups of features that are a priori believed to be more relevant an experimental evaluation compares the performance of the proposed method with those of group lasso bayesian group lasso automatic relevance determination and additional variants used for group feature selection the results of these experiments show that a model based on the generalized spike and slab prior and the ep algorithm has state of the art prediction performance in the problems analyzed furthermore this model is also very useful to carry out sequential experimental design also known as active learning where the data instances that are most informative are iteratively included in the training set reducing the number of instances needed to obtain a particular level of prediction accuracy

bayesian factor analysis for multilevel binary observations multilevel covariance structure models have become increasingly popular in the psychometric literature in the past few years to account for population heterogeneity and complex study designs we develop practical simulation based procedures for bayesian inference of multilevel binary factor analysis models we illustrate how markov chain monte carlo procedures such as gibbs sampling and metropolis hastings methods can be used to perform bayesian inference model checking and model comparison without the need for multidimensional numerical integration we illustrate the proposed estimation methods using three simulation studies and an application involving student s achievement results in different areas of mathematics

displacement following of hidden objects in a video sequence in a video sequence computing the motion of an object requires the continuity of the apparent velocity field this property does not hold when the object is hidden by an occlusion during its motion the minimization of an energy functional leads to a simple algorithm which allows the recovery of the most likely trajectory of the occluded object from optical flow data at the border of the occlusion optical flow used for developing our method is an improvement on any variational technique of computing it this improvement is based on a multichannel segmentation

analysis of residuals for the multinomial item response model using the item response model as developed on the multinomial distribution asymptotic variances are obtained for residuals associated with response patterns and first and second order marginal frequencies of manifest variables when the model does not fit well an examination of these residuals may reveal the source of the poor fit finally a limited information test of fit for the model is developed by using residuals defined for the first and second order marginals model evaluation based on residuals for these marginals is particularly useful when the response pattern frequencies are sparse

stochastic variational inference we develop stochastic variational inference a scalable algorithm for approximating posterior distributions we develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models latent dirichlet allocation and the hierarchical dirichlet process topic model using stochastic variational inference we analyze several large collections of documents 300k articles from nature 1 8m articles from the new york times and 3 8m articles from wikipedia stochastic inference can easily handle data sets of this size and outperforms traditional variational inference which can only handle a smaller subset we also show that the bayesian nonparametric topic model outperforms its parametric counterpart stochastic variational inference lets us apply complex bayesian models to massive data sets

finitistic dimension and igusa todorov algebras abstract the notion of igusa todorov algebras is introduced in connection with the little finitistic dimension conjecture and the conjecture is proved for those algebras such algebras contain many known classes of algebras over which the finitistic dimension conjecture holds e g algebras with the representation dimension at most 3 algebras with radical cube zero monomial algebras and left serial algebras etc it is an open question whether all artin algebras are igusa todorov we provide some methods to construct many new classes of 2 igusa todorov algebras and thus obtain many algebras such that the finitistic dimension conjecture holds in particular we show that the class of 2 igusa todorov algebras is closed under taking endomorphism algebras of projective modules hence if all quasi hereditary algebras are 2 igusa todorov then all artin algebras are 2 igusa todorov by v dlab c m ringel every semiprimary ring is the endomorphism ring of a projective module over a quasihereditary ring proc amer math soc 107 1 1989 1 5 and have finite finitistic dimension

a comparison of three simple test theory models in very simple test theory models such as the rasch model a single parameter is used to represent the ability of any examinee or the difficulty of any item simple models such as these provide very important points of departure for more detailed modeling when a substantial amount of data are available and are themselves of real practical value for small or even medium samples they can also serve a normative role in test design as an alternative to the rasch model or the rasch model with a correction for guessing a simple model is introduced which characterizes strength of response in terms of the ratio of ability and difficulty parameters rather than their difference this model provides a natural account of guessing and has other useful things to contribute as well it also offers an alternative to the rasch model with the usual correction for guessing the three models are compared in terms of statistical properties and fits to actual data the goal of the paper is to widen the range of minimal models available to test analysts

high dimensional maximum marginal likelihood item factor analysis by adaptive quadrature although the bock aitkin likelihood based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations a serious limitation of the method is its reliance on fixed point gauss hermite g h quadrature in the solution of the likelihood equations and likelihood ratio tests when the number of latent dimensions is large computational considerations require that the number of quadrature points per dimension be few but with large numbers of items the dispersion of the likelihood given the response pattern becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space in this paper we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data in particular we show that adaptive g h quadrature combined with mean and covariance adjustments at each iteration of an em algorithm produces an accurate fast converging solution with as few as two points per dimension evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions unlike an earlier application of adaptive gibbs sampling to this problem by meng and schilling the simulations also confirm the validity of the present method in calculating likelihood ratio chi square statistics for determining the number of factors required in the model finally we apply the method to a sample of real data from a test of teacher qualifications

on the representation dimension of tilted and laura algebras abstract we prove that the representation dimension of a tilted or of a strict laura algebra is at most three

biologically inspired feature manifold for scene classification biologically inspired feature bif and its variations have been demonstrated to be effective and efficient for scene classification it is unreasonable to measure the dissimilarity between two bifs based on their euclidean distance this is because bifs are extrinsically very high dimensional and intrinsically low dimensional i e bifs are sampled from a low dimensional manifold and embedded in a high dimensional space therefore it is essential to find the intrinsic structure of a set of bifs obtain a suitable mapping to implement the dimensionality reduction and measure the dissimilarity between two bifs in the low dimensional space based on their euclidean distance in this paper we study the manifold constructed by a set of bifs utilized for scene classification form a new dimensionality reduction algorithm by preserving both the geometry of intra bifs and the discriminative information inter bifs termed discriminative and geometry preserving projections dgpp and construct a new framework for scene classification in this framework we represent an image based on a new bif which combines the intensity channel the color channel and the c1 unit of a color image then we project the high dimensional bif to a low dimensional space based on dgpp and finally we conduct the classification based on the multiclass support vector machine svm thorough empirical studies based on the usc scene dataset demonstrate that the proposed framework improves the classification rates around 100 relatively and the training speed 60 times for different sites in comparing with previous gist proposed by siagian and itti in 2007

finitistic dimension conjecture and relative hereditary algebras abstract we introduce the notion of relative hereditary artin algebras as a generalization of algebras with representation dimension at most 3 we prove the following results 1 the relative hereditariness of an artin algebra is left right symmetric and is inherited by endomorphism algebras of projective modules 2 the finitistic dimensions of a relative hereditary algebra and its opposite algebra are finite as a consequence the finitistic projective dimension conjecture the finitistic injective dimension conjecture the gorenstein symmetry conjecture the wakamatsu tilting conjecture and the generalized nakayama conjecture hold for relative hereditary artin algebras and endomorphism algebras of projective modules over them in particular over algebras with representation dimension at most 3 we also show that the torsionless finiteness of an artin algebra is inherited by endomorphism algebras of projective modules and consequently give a partial answer to the question if the representation dimension of the endomorphism algebra of any projective module over an artin algebra a is bounded by the representation dimension of a

radical embeddings and representation dimension given a representation finite algebra b and a subalgebra a of b such that the jacobson radicals of a and b coincide we prove that the representation dimension of a is at most three by a result of igusa and todorov this implies that the finitistic dimension of a is finite

on the bock aitkin procedure from an em algorithm perspective the relationship between the em algorithm and the bock aitkin procedure is described with a continuous distribution of ability latent trait from an em algorithm perspective previous work has been restricted to the discrete case from a probit analysis perspective

on the finitistic dimension conjecture iii related to the pair eae a let a be an artin algebra and e an idempotent element in a in this paper we use co homological conditions on a to control the finitistic dimension of eae such a consideration is of particular interest for understanding the finitistic dimension conjecture let us denote the finitistic dimension and global dimension of a by fin dim a and gl dim a respectively suppose gl dim a 4 then fin dim eae if one of the following conditions holds 1 a aea has representation dimension at most 3 2 a 3 a is an a aea module 3 proj dim sa 3 for all simple a aea modules s this result can be considered as a first step to the question of whether gl dim a 4 implies fin dim eae moreover we show the following let a be an arbitrary artin algebra and e an idempotent element of a such that the syzygy dimension or the gorenstein dimension of the eae module ae is finite if fin dim a then fin dim eae

universal analytical forms for modeling image probabilities seeking probability models for images we employ a spectral approach where the images are decomposed using bandpass filters and probability models are imposed on the filter outputs also called spectral components we employ a two parameter family of probability densities called bessel k forms for modeling the marginal densities of the spectral components and demonstrate their fit to the observed histograms for video infrared and range images motivated by object based models for image analysis a relationship between the bessel parameters and the imaged objects is established using l sup 2 metric on the set of bessel k forms we propose a pseudometric on the image space for quantifying image similarities differences some applications including clutter classification and pruning of hypotheses for target recognition are presented

psychometric latent response models in this paper some psychometric models will be presented that belong to the larger class oflatent response models lrms first lrms are introduced by means of an application in the field ofcomponential item response theory embretson 1980 1984 second a general definition of lrms not specific for the psychometric subclass is given third some more psychometric lrms and examples of how they can be applied are presented fourth a method for obtaining maximum likelihood ml and some maximum a posteriori map estimates of the parameters of lrms is presented this method is then applied to theconjunctive rasch model fifth and last an application of the conjunctive rasch model is presented this model was applied to responses to typical verbal ability items open synonym items

on the finitistic dimension conjecture of artin algebras abstract let a be an artin algebra and e be an idempotent element of a we prove that if a has representation dimension at most three then the finitistic dimension of eae is finite and deduce that if quasi hereditary algebras have representation dimensions at most three then the finitistic dimension conjecture holds

a latent trait finite mixture model for the analysis of rating agreement this article presents a latent distribution model for the analysis of agreement on dichotomous or ordered category ratings the model includes parameters that characterize bias category definitions and measurement error for each rater or test parameter estimates can be used to evaluate rater performance and to improve classification or measurement with use of multiple ratings a simple maximum likelihood estimation procedure is described two examples illustrate the approach although considered in the context of analyzing rater agreement the model provides a general approach for mixture analysis using two or more ordered caregory measures

homological theory of recollements of abelian categories abstract we investigate several homological aspects of recollements of abelian categories in particular we study how various homological invariants and dimensions of the categories involved in a recollement situation are related and when recollements of abelian categories induce recollements at the level of the bounded derived categories finally we give applications to global finitistic and representation dimension of rings and artin algebras and to rouquier s dimension of triangulated categories

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

maximum marginal likelihood estimation of a monotonic polynomial generalized partial credit model with applications to multiple group analysis we present a semi parametric approach to estimating item response functions irf useful when the true irf does not strictly follow commonly used functions our approach replaces the linear predictor of the generalized partial credit model with a monotonic polynomial the model includes the regular generalized partial credit model at the lowest order polynomial our approach extends liang s a semi parametric approach to estimate irfs unpublished doctoral dissertation 2007 method for dichotomous item responses to the case of polytomous data furthermore item parameter estimation is implemented with maximum marginal likelihood using the bock aitkin em algorithm thereby facilitating multiple group analyses useful in operational settings our approach is demonstrated on both educational and psychological data we present simulation results comparing our approach to more standard irf estimation approaches and other non parametric and semi parametric alternatives

generalizing logistic regression by nonparametric mixing abstract logistic regression is a common technique for analyzing the effect of a covariate vector x on the number of successes y in m trials when y has a binomial distribution but at times either the logistic curve does not describe the probability of success p x adequately or m is larger than 1 and y is more variable than the binomial distribution allows overdispersion relative to the binomial distribution is possible if the m trials in a set or litter are positively correlated an important covariate is omitted or x is measured with error a simple way to accommodate departures from the logit link and overdispersion is to introduce a random intercept and thus permit a random propensity toward success when varies between individual binary trials according to a discrete or multimodal distribution p x has smooth steps and y has a binomial m p x distribution when the random is constant for a set of m binary trials and varies between sets of m trials according to a discrete or multimodal

a model for evaluating sensitivity and specificity for correlated diagnostic tests in efficacy studies with an imperfect reference test abstract the purpose of a diagnostic efficacy study is to evaluate and compare the sensitivities and specificities of several diagnostic tests usually the diagnostic tests are correlated conditional on disease status and the reference test is subject to error in the chlamydia trachomatis study five screening tests for detecting chlamydia in endocervical specimens were compared the five tests are correlated and the reference test the cell culture test has less than 100 sensitivity the conventional method ignores both the correlations between the tests and the misclassification of the reference test and thus cannot provide a valid analysis we propose a model to evaluate and compare the sensitivities and specificities of correlated diagnostic tests when there is either an imperfect reference test or even no reference test the model also can estimate the effects of covariates it is a generalized linear mixed model with two unobserved variables one continuous and one dichotomous we use a hybrid

variational learning for switching state space models we introduce a new statistical model for time series that iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes this model combines and generalizes two of the most widely used stochastic time series models hidden markov models and linear dynamical systems and is closely related to models that are widely used in the control and econometrics literatures it can also be derived by extending the mixture of experts neural network jacobs jordan nowlan hinton 1991 to its fully dynamical version in which both expert and gating networks are recurrent inferring the posterior probabilities of the hidden states of this model is computationally intractable and therefore the exact expectation maximization em algorithm cannot be applied however we present a variational approximation that maximizes a lower bound on the log likelihood and makes use of both the forward and backward recursions for hidden markov models and the kalman filter recursions for linear dynamical systems we tested the algorithm on artificial data sets and a natural data set of respiration force from a patient with sleep apnea the results suggest that variational approximations are a viable method for inference and learning in switching state space models

the dutch identity a new tool for the study of item response models the dutch identity is a useful way to reexpress the basic equations of item response models that relate the manifest probabilities to the item response functions irfs and the latent trait distribution the identity may be exploited in several ways for example a to suggest how item response models behave for large numbers of items they are approximate submodels of second order loglinear models for 2 j tables b to suggest new ways to assess the dimensionality of the latent trait principle components analysis of matrices composed of second order interactions from loglinear models c to give insight into the structure of latent class models and d to illuminate the problem of identifying the irfs and the latent trait distribution from sample data

unsupervised clustering and feature weighting based on generalized dirichlet mixture modeling abstract we propose a possibilistic approach for generalized dirichlet mixture parameter estimation data clustering and feature weighting the proposed algorithm called robust and unsupervised learning of finite generalized dirichlet mixture models rule gdm exploits a property of the generalized dirichlet distributions that transforms the data to make the features independent and follow beta distributions then it learns optimal relevance weights for each feature within each cluster this property makes rule gdm suitable for noisy and high dimensional feature spaces in addition rule gdm associates two types of memberships with each data sample the first one is the posterior probability and indicates how well a sample fits each estimated distribution the second membership represents the degree of typicality and is used to identify and discard noise points and outliers rule gdm minimizes one objective function which combines learning the two membership functions distribution parameters and the relevance weights for each feature within each distribution we also extend our algorithm to find the optimal number of clusters in an unsupervised and efficient way by exploiting some properties of the possibilistic membership function the performance of rule gdm is illustrated and compared to similar algorithms we use synthetic data to illustrate its robustness to noisy and high dimensional features we also compare our approach to other relevant algorithms using several standard data sets

analysis of multiple partially ordered responses to belief items with don t know option understanding beliefs values and preferences of patients is a tenet of contemporary health sciences this application was motivated by the analysis of multiple partially ordered set poset responses from an inventory on layman beliefs about diabetes the partially ordered set arises because of two features in the data first the response options contain a don t know dk option and second there were two consecutive occasions of measurement as predicted by the common sense model of illness beliefs about diabetes were not necessarily stable across the two measurement occasions instead of analyzing the two occasions separately we studied the joint responses across the occasions as a poset response few analytic methods exist for data structures other than ordered or nominal categories poset responses are routinely collapsed and then analyzed as either rank ordered or nominal data leading to the loss of nuanced information that might be present within poset categories in this paper we developed a general class of item response models for analyzing the poset data collected from the common sense model of diabetes inventory the inferential object of interest is the latent trait that indicates congruence of belief with the biomedical model to apply an item response model to the poset diabetes inventory we proved that a simple coding algorithm circumvents the requirement of writing new codes such that standard irt software could be directly used for the purpose of item estimation and individual scoring simulation experiments were used to examine parameter recovery for the proposed poset model

hierarchical dirichlet processes we consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups we assume that the number of mixture components is unknown a priori and is to be inferred from the data in this setting it is natural to consider sets of dirichlet processes one for each group where the well known clustering property of the dirichlet process provides a nonparametric prior for the number of mixture components within each group given our desire to tie the mixture models in the various groups we consider a hierarchical model specifically one in which the base measure for the child dirichlet processes is itself distributed according to a dirichlet process such a base measure being discrete the child dirichlet processes necessarily share atoms thus as desired the mixture models in the different groups necessarily share mixture components we discuss representations of hierarchical dirichlet processes

on holland s dutch identity conjecture the manifest probabilities of observed examinee response patterns resulting from marginalization with respect to the latent ability distribution produce the marginal likelihood function in item response theory under the conditions that the posterior distribution of examinee ability given some test response pattern is normal and the item logit functions are linear holland 1990a gives a quadratic form for the log manifest probabilities by using the dutch identity further holland conjectures that this special quadratic form is a limiting one for all smooth unidimensional item response models as test length tends to infinity the purpose of this paper is to give three counterexamples to demonstrate that holland s dutch identity conjecture does not hold in general the counterexamples suggest that only under strong assumptions can it be true that the limits of log manifest probabilities are quadratic three propositions giving sets of such strong conditions are given

a two layer mixture model of gaussian process functional regressions and its mcmc em algorithm the mixture of gaussian processes gps is capable of learning any general stochastic process based on a given set of sample curves for the regression and prediction problems however it is ineffective for curve clustering and prediction when the sample curves are derived from different stochastic processes as independent sources linearly mixed together in this paper we propose a two layer mixture model of gp functional regressions gpfrs to describe such a mixture of general stochastic processes or independent sources especially for curve clustering and prediction specifically in the lower layer the mixture of gpfrs mgpfrs is developed for a cluster or class of curves within the input space in the higher layer the mixture of mgpfrs is further established to divide the curves into clusters according to its components in the output space for the parameter estimation of the two layer mixture of gpfrs we develop a monte carlo em algorithm based on a monte carlo markov chain mcmc method in short the mcmc em algorithm we validate the hierarchical mixture of gpfrs and mcmc em algorithm using synthetic and real world data sets our results show that our new model outperforms the conventional mixture models in curve clustering and prediction

asymptotic standard errors of irt observed score equating methods a method of the irt observed score equating using chain equating through a third test without equating coefficients is presented with the assumption of the three parameter logistic model the asymptotic standard errors of the equated scores by this method are obtained using the results given by m liou and p e cheng the asymptotic standard errors of the irt observed score equating method using a synthetic examinee group with equating coefficients which is a currently used method are also provided numerical examples show that the standard errors by these observed score equating methods are similar to those by the corresponding true score equating methods except in the range of low scores

on the representation dimension of some classes of algebras abstract we show that the representation dimension of the following classes of algebras is at most 3 a artin algebras a such that the functor hom a d a has finite length or dually hom a a has finite length these algebras coincide with the right left glued algebras as introduced in i assem f u coelho j pure appl algebra 96 3 1994 225 and b trivial extensions of iterated tilted algebras

joint consistency of nonparametric item characteristic curve and ability estimation the simultaneous and nonparametric estimation of latent abilities and item characteristic curves is considered the asymptotic properties of ordinal ability estimation and kernel smoothed nonparametric item characteristic curve estimation are investigated under very general assumptions on the underlying item response theory model as both the test length and the sample size increase a large deviation probability inequality is stated for ordinal ability estimation the mean squared error of kernel smoothed item characteristic curve estimates is studied and a strong consistency result is obtained showing that the worst case error in the item characteristic curve estimates over all items and ability levels converges to zero with probability equal to one

bayesian estimation of a multilevel irt model using gibbs sampling in this article a two level regression model is imposed on the ability parameters in an item response theory irt model the advantage of using latent rather than observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error another advantage is that contrary to observed scores latent scores are test independent which offers the possibility of using results from different tests in one analysis where the parameters of the irt model and the multilevel model can be concurrently estimated the two parameter normal ogive model is used for the irt measurement model it will be shown that the parameters of the two parameter normal ogive model and the multilevel model can be estimated in a bayesian framework using gibbs sampling examples using simulated and real data are given

weighted likelihood estimation of ability in item response theory applications of item response theory which depend upon its parameter invariance property require that parameter estimates be unbiased a new method weighted likelihood estimation wle is derived and proved to be less biased than maximum likelihood estimation mle with the same asymptotic variance and normal distribution wle removes the first order bias term from mle two monte carlo studies compare wle with mle and bayesian modal estimation bme of ability in conventional tests and tailored tests assuming the item parameters are known constants the monte carlo studies favor wle over mle and bme on several criteria over a wide range of the ability scale

a hybrid sem algorithm for high dimensional unsupervised learning using a finite generalized dirichlet mixture this paper applies a robust statistical scheme to the problem of unsupervised learning of high dimensional data we develop analyze and apply a new finite mixture model based on a generalization of the dirichlet distribution the generalized dirichlet distribution has a more general covariance structure than the dirichlet distribution and offers high flexibility and ease of use for the approximation of both symmetric and asymmetric distributions we show that the mathematical properties of this distribution allow high dimensional modeling without requiring dimensionality reduction and thus without a loss of information this makes the generalized dirichlet distribution more practical and useful we propose a hybrid stochastic expectation maximization algorithm hsem to estimate the parameters of the generalized dirichlet mixture the algorithm is called stochastic because it contains a step in which the data elements are assigned randomly to components in order to avoid convergence to a saddle point the adjective hybrid is justified by the introduction of a newton raphson step moreover the hsem algorithm autonomously selects the number of components by the introduction of an agglomerative term the performance of our method is tested by the classification of several pattern recognition data sets the generalized dirichlet mixture is also applied to the problems of image restoration image object recognition and texture image database summarization for efficient retrieval for the texture image summarization problem results are reported for the vistex texture image database from the mit media lab

probability matrix decomposition models in this paper we consider a class of models for two way matrices with binary entries of 0 and 1 first we considerboolean matrix decomposition conceptualize it as alatent response model lrm and by making use of this conceptualization generalize it to a larger class of matrix decomposition models second probability matrix decomposition pmd models are introduced as a probabilistic version of this larger class of deterministic matrix decomposition models third an algorithm for the computation of the maximum likelihood ml and the maximum a posteriori map estimates of the parameters of pmd models is presented this algorithm is an em algorithm and is a special case of a more general algorithm that can be used for the whole class of lrms and fourth as an example a pmd model is applied to data on decision making in psychiatric diagnosis

estimating difficulty from polytomous categorical data a comprehensive analysis of difficulty for multiple choice items requires information at different levels the test the items and the alternatives this paper introduces a new parameterization of the nominal categories model ncm for analyzing difficulty at these three levels the new parameterization is referred to as the ne ncm and is statistically equivalent to the ncm the ne ncm is applied to a sample of responses from a logical analysis test the results suggest that the individuals execute a self terminated response process that is mostly determined by working memory load

variational approximations for categorical causal modeling with latent variables latent class models in the social and behavioral sciences have remained structurally simple one reason for this is that inference in statistical models can be computationally difficult methods for approximate inference known as variational approximations which have been developed in the machine learning graphical modeling and statistical physics literatures can be used to alleviate the computational difficulties of inference for latent variable models the aim of the present article is to set these methods alongside some social and behavioral science literature to which they are relevant and in particular to consider their potential for categorical causal modeling using latent class analysis we have collated a number of popular categorical data models with latent variables and causal structure typically incorporating a markovian structure the efficacy of the approximation methods has been demonstrated through simulations related to an important behavioral science model

variational learning for finite dirichlet mixture models and applications in this paper we focus on the variational learning of finite dirichlet mixture models compared to other algorithms that are commonly used for mixture models such as expectation maximization our approach has several advantages first the problem of over fitting is prevented furthermore the complexity of the mixture model i e the number of components can be determined automatically and simultaneously with the parameters estimation as part of the bayesian inference procedure finally since the whole inference process is analytically tractable with closed form solutions it may scale well to large applications both synthetic and real data generated from real life challenging applications namely image databases categorization and anomaly intrusion detection are experimented to verify the effectiveness of the proposed approach

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

estimation of latent group effects abstract conventional methods of multivariate normal analysis do not apply when the variables of interest are not observed directly but must be inferred from fallible or incomplete data a method of estimating such effects by marginal maximum likelihood implemented by means of an em algorithm is proposed asymptotic standard errors and likelihood ratio tests of fit are provided the procedures are illustrated with data from the administration of the armed services vocational aptitude battery to a probability sample of american youth

the two parameter poisson dirichlet distribution derived from a stable subordinator the two parameter poisson dirichlet distribution denoted mathsf pd alpha theta is a probability distribution on the set of decreasing positive sequences with sum 1 the usual poisson dirichlet distribution with a single parameter theta introduced by kingman is mathsf pd 0 theta known properties of mathsf pd 0 theta including the markov chain description due to vershik shmidt and ignatov are generalized to the two parameter case the size biased random permutation of mathsf pd alpha theta is a simple residual allocation model proposed by engen in the context of species diversity and rediscovered by perman and the authors in the study of excursions of brownian motion and bessel processes for 0 alpha 1 mathsf pd alpha 0 is the asymptotic distribution of ranked lengths of excursions of a markov chain away from a state whose recurrence time distribution is in the domain of attraction of a stable law of index alpha formulae in this case trace back to work of darling lamperti and wendel in the 1950s and 1960s the distribution of ranked lengths of excursions of a one dimensional brownian motion is mathsf pd 1 2 0 and the corresponding distribution for a brownian bredge is mathsf pd 1 2 1 2 the mathsf pd alpha 0 and mathsf pd alpha alpha distributions admit a similar interpretation in terms of the ranked lengths of excursions of a semistable markov process whose zero set is the range of a stable subordinator of index alpha

upper bounds for the dominant dimension of nakayama and related algebras abstract optimal upper bounds are provided for the dominant dimensions of nakayama algebras and more general algebras a with an idempotent e such that there is a minimal faithful injective projective module ea and such that eae is a nakayama algebra this answers a question of abrar and proves a conjecture of yamagata for monomial algebras

a hybrid feature extraction selection approach for high dimensional non gaussian data clustering this paper presents an unsupervised approach for feature selection and extraction in mixtures of generalized dirichlet gd distributions our method defines a new mixture model that is able to extract independent and non gaussian features without loss of accuracy the proposed model is learned using the expectation maximization algorithm by minimizing the message length of the data set experimental results show the merits of the proposed methodology in the categorization of object images

on the finitistic dimension conjecture ii related to finite global dimension abstract in this paper we study the finitistic dimensions of artin algebras by establishing a relationship between the global dimensions of the given algebras on the one hand and the finitistic dimensions of their subalgebras on the other hand this is a continuation of the project in j pure appl algebra 193 2004 287 305 for an artin algebra a we denote by gl dim a fin dim a and rep dim a the global dimension finitistic dimension and representation dimension of a respectively the jacobson radical of a is denoted by rad a the main results in the paper are as follows let b be a subalgebra of an artin algebra a such that rad b is a left ideal in a then 1 if gl dim a 4 and rad a rad b a then fin dim b 2 if rep dim a 3 then fin dim b the results are applied to pullbacks of algebras over semi simple algebras moreover we have also the following dual statement 3 let b a be a surjective homomorphism between two algebras b and a suppose that the kernel of is contained in the socle of the right b module b b if gl dim a 4 or rep dim a 3 then fin dim b finally we provide a class of algebras with representation dimension at most three 4 if a is stably hereditary and rad b is an ideal in a then rep dim b 3

generalized latent trait models in this paper we discuss a general model framework within which manifest variables with different distributions in the exponential family can be analyzed with a latent trait model a unified maximum likelihood method for estimating the parameters of the generalized latent trait model will be presented we discuss in addition the scoring of individuals on the latent dimensions the general framework presented allows not only the analysis of manifest variables all of one type but also the simultaneous analysis of a collection of variables with different distributions the approach used analyzes the data as they are by making assumptions about the distribution of the manifest variables directly

homological domino effects and the first finitistic dimension conjecture counterexamples to the first finitistic dimension conjecture are constructed in fact for any fieldk and any integerm 2 there exist finite dimensionalk algebras such that the little finitistic dimension of ism while the big finitistic dimension ism 1 our examples are monomial relation algebras within this class of algebras the big and little finitistic dimensions cannot differ by more than 1 the analysis of the examples is based on a sharp picture of arbitrary second syzygies over monomial relation algebras

psychometric engineering as art the psychometric society is devoted to the development of psychology as a quantitative rational science engineering is often set in contradistinction with science art is sometimes considered different from science why then juxtapose the words in the title psychometric engineering andart because an important aspect of quantitative psychology is problem solving and engineering solves problems and an essential aspect of a good solution is beauty hence art in overview and with examples this presentation describes activities that are quantitative psychology as engineering and art that is as design extended illustrations involve systems for scoring tests in realistic contexts allusions are made to other examples that extend the conception of quantitative psychology as engineering and art across a wider range of psychometric activities

estimating multiple classification latent class models this paper presents a new class of models for persons by items data the essential new feature of this class is the representation of the persons every person is represented by its membership tomultiple latent classes each of which belongs to onelatent classification the models can be considered as a formalization of the hypothesis that the responses come about in a process that involves the application of a number ofmental operations two algorithms for maximum likelihood ml and maximum a posteriori map estimation are described they both make use of the tractability of the complete data likelihood to maximize the observed data likelihood properties of the map estimators i e uniqueness and goodness of recovery and the existence of asymptotic standard errors were examined in a simulation study then one of these models is applied to the responses to a set of fraction addition problems finally the models are compared to some related models in the literature

on the approximation of the quadratic exponential distribution in a latent variable context summary following cox wermuth 1994 2002 we show that the distribution of a set of binary observable variables induced by a certain discrete latent variable model may be approximated by a quadratic exponential distribution this discrete latent variable model is equivalent to the latent class version of the two parameter logistic model of birnbaum 1968 which may be seen as a generalized version of the rasch model rasch 1960 1961 on the basis of this result we develop an approximate maximum likelihood estimator of the item parameters of the two parameter logistic model which is very simply implemented the proposed approach is illustrated through an example based on a dataset on educational assessment

on the relationship between item response theory and factor analysis of discretized variables equivalence of marginal likelihood of the two parameter normal ogive model in item response theory irt and factor analysis of dichotomized variables fa was formally proved the basic result on the dichotomous variables was extended to multicategory cases both ordered and unordered categorical data pair comparison data arising from multiple judgment sampling were discussed as a special case of the unordered categorical data a taxonomy of data for the irt and fa models was also attempted

online learning of hierarchical pitman yor process mixture of generalized dirichlet distributions with feature selection in this paper a novel statistical generative model based on hierarchical pitman yor process and generalized dirichlet distributions gds is presented the proposed model allows us to perform joint clustering and feature selection thanks to the interesting properties of the gd distribution we develop an online variational inference algorithm formulated in terms of the minimization of a kullback leibler divergence of our resulting model that tackles the problem of learning from high dimensional examples this variational bayes formulation allows simultaneously estimating the parameters determining the model s complexity and selecting the appropriate relevant features for the clustering structure moreover the proposed online learning algorithm allows data instances to be processed in a sequential manner which is critical for large scale and real time applications experiments conducted using challenging applications namely scene recognition and video segmentation where our approach is viewed as an unsupervised technique for visual learning in high dimensional spaces showed that the proposed approach is suitable and promising

binary programming and test design an algorithmic approach to test design using information functions is presented the approach uses a special branch of linear programming i e binary programming in addition results of some benchmark problems are presented within the same framework it is also possible to formulate the problem of individualized testing

representation dimension of exterior algebras we determine the representation dimension of exterior algebras this provides the first known examples of representation dimension 3 we deduce that the loewy length of the group algebra over f2 of a finite group is strictly bounded below by the 2 rank of the group a conjecture of benson a key tool is the use of the concept of dimension of a triangulated category

distributed em algorithm for gaussian mixtures in sensor networks this paper presents a distributed expectation maximization em algorithm over sensor networks in the e step of this algorithm each sensor node independently calculates local sufficient statistics by using local observations a consensus filter is used to diffuse local sufficient statistics to neighbors and estimate global sufficient statistics in each node by using this consensus filter each node can gradually diffuse its local information over the entire network and asymptotically the estimate of global sufficient statistics is obtained in the m step of this algorithm each sensor node uses the estimated global sufficient statistics to update model parameters of the gaussian mixtures which can maximize the log likelihood in the same way as in the standard em algorithm because the consensus filter only requires that each node communicate with its neighbors the distributed em algorithm is scalable and robust it is also shown that the distributed em algorithm is a stochastic approximation to the standard em algorithm thus it converges to a local maximum of the log likelihood several simulations of sensor networks are given to verify the proposed algorithm

high dimensional exploratory item factor analysis by a metropolis hastings robbins monro algorithm a metropolis hastings robbins monro mh rm algorithm for high dimensional maximum marginal likelihood exploratory item factor analysis is proposed the sequence of estimates from the mh rm algorithm converges with probability one to the maximum likelihood solution details on the computer implementation of this algorithm are provided the accuracy of the proposed algorithm is demonstrated with simulations as an illustration the proposed algorithm is applied to explore the factor structure underlying a new quality of life scale for children it is shown that when the dimensionality is high mh rm has advantages over existing methods such as numerical quadrature based em algorithm extensions of the algorithm to other modeling frameworks are discussed

mixed effects analyses of rank ordered data this paper presents a synthesis of bock s 1972 nominal categories model and luce s 1959 choice model for mixed effects analyses of rank ordered data it is shown that the proposed ranking model is both parsimonious and flexible in accounting for preference heterogeneity as well as fixed and random effects of covariates relationships to other approaches including takane s 1987 ideal point discriminant model and croon s 1989 latent class version of luce s ranking model are also discussed the application focuses on a ranking study of behavioral traits that parents find desirable in children

high dimensional multivariate probit analysis a computationally practical form of probit analysis for multiple response variables based on an assumed common factor model for the latent tolerances is proposed numerical integration over the factor space provides maximum likelihood estimation of the probit regression parameters and of the probabilities of response combinations under the model the procedure is applied to five variables from the pneumoconiosis field trial two variables of which were previously analyzed by ashford and sowden 1970 biometrics 26 535 546

global convergence of the em algorithm for unconstrained latent variable models with categorical indicators convergence of the expectation maximization em algorithm to a global optimum of the marginal log likelihood function for unconstrained latent variable models with categorical indicators is presented the sufficient conditions under which global convergence of the em algorithm is attainable are provided in an information theoretic context by interpreting the em algorithm as alternating minimization of the kullback leibler divergence between two convex sets it is shown that these conditions are satisfied by an unconstrained latent class model yielding an optimal bound against which more highly constrained models may be compared

on structural equation modeling with data that are not missing completely at random a general latent variable model is given which includes the specification of a missing data mechanism this framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data here missing completely at random is not a prerequisite for unbiased estimation in large samples as when using the traditional listwise or pairwise present data approaches the theory is connected with old and new results in the area of selection and factorial invariance it is pointed out that in many applications maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software such as lisrel and liscomp several sets of artifical data are generated within the general model framework the proposed estimator is compared to the two traditional ones and found superior

variational inference in nonconjugate models mean field variational methods are widely used for approximate posterior inference in many probabilistic models in a typical application mean field methods approximately compute the posterior with a coordinate ascent optimization algorithm when the model is conditionally conjugate the coordinate updates are easily derived and in closed form however many models of interest like the correlated topic model and bayesian logistic regression are nonconjugate in these models mean field methods cannot be directly applied and practitioners have had to develop variational algorithms on a case by case basis in this paper we develop two generic methods for nonconjugate models laplace variational inference and delta method variational inference our methods have several advantages they allow for easily derived variational algorithms with a wide class of nonconjugate models they extend and unify some of the existing algorithms that have been derived for specific models and they work well on real world data sets we studied our methods on the correlated topic model bayesian logistic regression and hierarchical bayesian logistic regression

online model selection based on the variational bayes the bayesian framework provides a principled way of model selection this framework estimates a probability distribution over an ensemble of models and the prediction is done by averaging over the ensemble of models accordingly the uncertainty of the models is taken into account and complex models with more degrees of freedom are penalized however integration over model parameters is often intractable and some approximation scheme is needed recently a powerful approximation scheme called the variational bayes vb method has been proposed this approach defines the free energy for a trial probability distribution which approximates a joint posterior probability distribution over model parameters and hidden variables the exact maximization of the free energy gives the true posterior distribution the vb method uses factorized trial distributions the integration over model parameters can be done analytically and an iterative expectation maximization like algorithm whose convergence is guaranteed is derived in this article we derive an online version of the vb algorithm and prove its convergence by showing that it is a stochastic approximation for finding the maximum of the free energy by combining sequential model selection procedures the online vb method provides a fully online learning method with a model selection mechanism in preliminary experiments using synthetic data the online vb method was able to adapt the model structure to dynamic environments

incremental online learning in high dimensions locally weighted projection regression lwpr is a new algorithm for incremental nonlinear function approximation in high dimensional spaces with redundant and irrelevant input dimensions at its core it employs nonparametric regression with locally linear models in order to stay computationally efficient and numerically robust each local model performs the regression analysis with a small number of univariate regressions in selected directions in input space in the spirit of partial least squares regression we discuss when and how local learning techniques can successfully work in high dimensional spaces and review the various techniques for local dimensionality reduction before finally deriving the lwpr algorithm the properties of lwpr are that it 1 learns rapidly with second order learning methods based on incremental training 2 uses statistically sound stochastic leave one out cross validation for learning without the need to memorize training data 3 adjusts its weighting kernels based on only local information in order to minimize the danger of negative interference of incremental learning 4 has a computational complexity that is linear in the number of inputs and 5 can deal with a large number of possibly redundant inputs as shown in various empirical evaluations with up to 90 dimensional data sets for a probabilistic interpretation predictive variance and confidence intervals are derived to our knowledge lwpr is the first truly incremental spatially localized learning method that can successfully and efficiently operate in very high dimensional spaces

consistent estimation in the rasch model based on nonparametric margins consider the class of two parameter marginal logistic rasch models for a test ofm true false items where the latent ability is assumed to be bounded using results of karlin and studen we show that this class of nonparametric marginal logistic nml models is equivalent to the class of marginal logistic models where the latent ability assumes at most m 2 2 values this equivalence has two implications first estimation for the nml model is accomplished by estimating the parameters of a discrete marginal logistic model second consistency for the maximum likelihood estimates of the nml model can be shown whenm is odd using the results of kiefer and wolfowitz an example is presented which demonstrates the estimation strategy and contrasts the nml model with a normal marginal logistic model