Joint Clustering With Correlated Variables

Coordinate Descent Optimized Trace Difference Model for Joint Clustering and Feature Extraction

The revised ICH E14 Question and Answer (R3) document issued in December 2015 enables pharmaceutical companies to use concentration-QTc (C-QTc) modeling as the primary analysis for assessing QTc prolongation risk of new drugs. A new approach by including the time effect into the current C-QTc model is introduced. Through a simulation study, we evaluated performances of different C-QTc modeling with different dependent variables, covariates, and covariance structures. This simulation study shows that C-QTc models with ΔQTc being dependent variable without time effect inflate false negative rate and that fitting C-QTc models with different dependent variables, covariates, and covariance structures impacts the control of false negative and false positive rates. Appropriate C-QTc modeling strategies with good control of false negative rate and false positive rate are recommended.

This study focused on the development of Bayesian bivariate semiparametric models for ozone and PM2.5 emissions. The semiparametric models rely on a Dirichlet mixture, which accounts for unobserved heterogeneity by employing random distribution for the intercept of each entity. The models with and without spatially structured random effects were also evaluated. Overall, four models were developed: three semiparametric with a flexible intercept and one parametric to serve as a reference. The significance of simultaneous estimation of PM2.5 and ozone was demonstrated by selection of common contributing factors as well as the statistically significant bivariate error term. In terms of relationship between dependent and independent variables, the areas with higher population and poverty, along with lesser educated residents, were observed to experience higher ozone and PM2.5 concentration. Also, the entities with higher vehicular traffic density and larger geographic areas were observed to be positively correlated with ozone and PM2.5 concentration. The underlying influential factor for both such variables may be the vehicular emissions, which is directly associated with traffic density and indirectly with land area as larger entities may tend to have higher traffic activity. The superiority of the semiparametric models, compared with parametric, signified the advantage associated with the flexible Dirichlet approach. The models with and without spatial correlation structures illustrated the mixed performance across the cases of parametric and semiparametric bivariate ones. The lack of consistent advantages associated with the inclusion of spatial effects may be due to the fact that the spatial correlation was not observed to be significant for the current dataset. Other spatial structure specifications may lead to different performance results.

Statistical mediation analysis is used to investigate intermediate variables in the relation between independent and dependent variables. Causal interpretation of mediation analyses is challenging because randomization of subjects to levels of the independent variable does not rule out the possibility of unmeasured confounders of the mediator to outcome relation. Furthermore, commonly used frequentist methods for mediation analysis compute the probability of the data given the null hypothesis, which is not the probability of a hypothesis given the data as in Bayesian analysis. Under certain assumptions, applying the potential outcomes framework to mediation analysis allows for the computation of causal effects, and statistical mediation in the Bayesian framework gives indirect effects probabilistic interpretations. This tutorial combines causal inference and Bayesian methods for mediation analysis so the indirect and direct effects have both causal and probabilistic interpretations. Steps in Bayesian causal mediation analysis are shown in the application to an empirical example.

This article discusses the innovation of statistical modeling in regression analysis with a semiparametric approach applied to health data. Regression analysis is a method in statistics that takes a lot of roles in statistical modeling. Regression analysis is used to model the relationship between the independent variable (x) and the dependent variable (y). There are three approaches to regression analysis, namely parametric, nonparametric, and a combination of the two, namely semiparametric. Semiparametric regression is used when the dependent variable has a known relationship with some of the independent variables and has an unknown pattern of a relationship with some of the other independent variables. The purpose of this study was to model hemoglobin levels in dengue fever patients, with the independent variables used being the number of hematocrits (x1) and the number of leukocytes (x2). The method used is spline truncated semiparametric regression. The truncated spline estimator was chosen for the nonparametric component because it has many advantages in modeling, one of which is being able to model patterns where the form of the relationship is unknown. The parameter estimation used is the maximum estimation. Selection of the optimal knot point using Generalized Cross-Validation (GCV). Based on the results of the analysis, the truncated spline semiparametric regression model was obtained which was applied to the hemoglobin level data in a model with three knots which have a coefficient of determination of 89.074%. Based on the results of testing the hypothesis simultaneously, it can be concluded that simultaneously the independent variable has a significant effect on the dependent variable. In the partial test, it is concluded that the variables x1 and x2 have a significant influence on the dependent variable y .

BackgroundA Bayesian approach based on a Dirichlet process (DP) prior is useful for inferring genetic population structures because it can infer the number of populations and the assignment of individuals simultaneously. However, the properties of the DP prior method are not well understood, and therefore, the use of this method is relatively uncommon. We characterized the DP prior method to increase its practical use.ResultsFirst, we evaluated the usefulness of the sequentially-allocated merge-split (SAMS) sampler, which is a technique for improving the mixing of Markov chain Monte Carlo algorithms. Although this sampler has been implemented in a preceding program, HWLER, its effectiveness has not been investigated. We showed that this sampler was effective for population structure analysis. Implementation of this sampler was useful with regard to the accuracy of inference and computational time. Second, we examined the effect of a hyperparameter for the prior distribution of allele frequencies and showed that the specification of this parameter was important and could be resolved by considering the parameter as a variable. Third, we compared the DP prior method with other Bayesian clustering methods and showed that the DP prior method was suitable for data sets with unbalanced sample sizes among populations. In contrast, although current popular algorithms for population structure analysis, such as those implemented in STRUCTURE, were suitable for data sets with uniform sample sizes, inferences with these algorithms for unbalanced sample sizes tended to be less accurate than those with the DP prior method.ConclusionsThe clustering method based on the DP prior was found to be useful because it can infer the number of populations and simultaneously assign individuals into populations, and it is suitable for data sets with unbalanced sample sizes among populations. Here we presented a novel program, DPART, that implements the SAMS sampler and can consider the hyperparameter for the prior distribution of allele frequencies to be a variable.

In survival analysis interest lies in modeling data that describe the time to a particular event. Informative functions, namely the hazard function and mean residual life function, can be obtained from the model's distribution function. We focus on the mean residual life function which provides the expected remaining life given that the subject has survived (i.e., is event-free) up to a particular time. This function is of direct interest in reliability, medical, and actuarial fields. In addition to its practical interpretation, the mean residual life function characterizes the survival distribution. In terms of mean residual life function inference, there are two shortcomings present in the current literature. First off, the shape of the functional is often restricted, which forces the researcher to make an assumption that may not be appropriate. Secondly, in cases where the shape of the functional is not parametrically specified, full inference is not obtained. The aim of our research is to provide a modeling approach that yields full inference for the mean residual life function, and is not restrictive on the shape of the functional. In particular, we develop general Bayesian nonparametric modeling methods for inference for mean residual life functions built from a mixture model for the associated survival distribution. Although the prior model is not placed on the mean residual life function directly, our methods offer rich inference for the desired functional. We place a Dirichlet process mixture model on the survival function, and discuss the importance of careful kernel selection to ensure desirable properties for the mean residual life function. We advocate for a mixture model with a gamma kernel and dependent baseline distribution for the Dirichlet process prior. We extend our model to the regression setting by modeling the joint distribution for the survival response and random covariates. This approach provides a flexible method for obtaining inference for the regression functionals when the number of random covariates is small to moderate. We further extend our methods to the scenario where interest lies in comparison of survival between two experimental groups. Typically, we expect the range of survival in the two groups to be the same, but exhibiting different characteristics over that range. Here, we develop a dependent Dirichlet process prior for the mixing distributions having shared locations across the two groups and varying weights to incorporate dependency between populations and achieve richer inferential results. The final scenario we consider is the case in which the researcher believes two populations have ordered mean residual life functions. For such applications, a prior model that incorporates an ordering constraint on the mean residual life functions is attractive. We introduce a mixture of Erlang distributions with weights constructed using Dirichlet process priors that provides the mean residual life ordering result. We demonstrate the utility of our modeling methods through simulation and real data examples. In addition, we draw comparisons with both parametric and semiparametric models.

In this last chapter, we discuss various other topics in Bayesian survival analysis. Specifically, we discuss semiparametric proportional hazards models built from monotone function, accelerated failure time models, Dirichlet process and Polya tree priors in survival analysis, Bayesian survival analysis using multivariate adaptive regression splines (MARS), change point models, poly-Weibull models, hierarchical survival models using neural networks, Bayesian model diagnostics, and future research topics.KeywordsMultivariate Adaptive Regression SplineDirichlet ProcessFrailty ModelPredictive ScoreAccelerate Failure Time ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This volume has been inspired by the aim of gathering a number of theoretical papers that, though from different schools of inference—frequentist andBayesian, share the same interest towards studying complex statistical models. Indeed, both frequentist and Bayesian inference can entail various drawbacks, due to the complexity or misspecification of the model, or to the presence of many nuisance parameters. These difficulties may be overcome from a theoretical point of view through approximate likelihoods and scoring rules, and from a computational point of view through higher-order asymptotic expansions or computational tools from Bayesian inference. Specifically, the volume focuses on the interplay between Bayesian and frequentist inference in addressing these problems. The goal is to highlight and to disseminate some of the topics emerged in the international Workshop Recent advances in Statistical Inference: Theory and case studies, held in Padova, Italy, March 21–23, 2013. The Workshop has been a forum for the exchange of new ideas and thoughts on recent and ongoing research in both Bayesian methodology and modern likelihood inference. Although the topics covered in this volume are diverse, similar themes recur, as research ismostly fueled by the need to deal with complex models, for which traditional methods do not provide viable solutions. Among the topics presented we have Bayesian/frequentist challenges for categorical data analysis, Bayesian-frequentist sample size determination, integrated likelihood inference in semi parametric regression models, approximate Bayesian computation with modified log-likelihood ratios, theory and applications of proper scoring rules, quasi likelihood approximation of posterior distributions for likelihood-intractable complex models, mitigating multicollinearity with spike-and-slab priors, empirical Bayes methods in classical and Bayesian inference. While not exhaustive, this list should give a feeling of the issues discussed at the Workshop.

Joint clustering and feature learning methods have shown remarkable performance in unsupervised representation learning. However, the training schedule alternating between feature clustering and network parameters update leads to unstable learning of visual representations. To overcome this challenge, we propose Online Deep Clustering (ODC) that performs clustering and network update simultaneously rather than alternatingly. Our key insight is that the cluster centroids should evolve steadily in keeping the classifier stably updated. Specifically, we design and maintain two dynamic memory modules, i.e., samples memory to store samples' labels and features, and centroids memory for centroids evolution. We break down the abrupt global clustering into steady memory update and batch-wise label re-assignment. The process is integrated into network update iterations. In this way, labels and the network evolve shoulder-to-shoulder rather than alternatingly. Extensive experiments demonstrate that ODC stabilizes the training process and boosts the performance effectively.

For fully taking into account the feature of environmental data set the Gaussian mixture model (GMM) is combined with the Dirichlet Process (DP) to solve the problem of specifying the initial cluster number. The Gibbs sampling algorithm is also used as the substitute of the Expectation Maximization algorithm to estimate the parameter of the model with Dirichlet Process. The clustering process is implemented under the framework of Spark so as to deal with farm environmental data set stored in distributed computer cluster. Experiment results with external criterion show that the improved clustering method has a better ability in data anomaly detection compared with other common cluster methods. Farm environmental data anomaly detection is implemented by the improved clustering method.

Crash risk analysis for Shanghai urban expressways: A Bayesian semi-parametric modeling approach

Chapter 41 Estimation of semiparametric models

We propose a Bayesian method for multiple hypothesis testing in random effects models that uses Dirichlet process (DP) priors for a nonparametric treatment of the random effects distribution. We consider a general model formulation which accommodates a variety of multiple treatment conditions. A key feature of our method is the use of a product of spiked distributions, i.e., mixtures of a point-mass and continuous distributions, as the centering distribution for the DP prior. Adopting these spiked centering priors readily accommodates sharp null hypotheses and allows for the estimation of the posterior probabilities of such hypotheses. Dirichlet process mixture models naturally borrow information across objects through model-based clustering while inference on single hypotheses averages over clustering uncertainty. We demonstrate via a simulation study that our method yields increased sensitivity in multiple hypothesis testing and produces a lower proportion of false discoveries than other competitive methods. While our modeling framework is general, here we present an application in the context of gene expression from microarray experiments. In our application, the modeling framework allows simultaneous inference on the parameters governing differential expression and inference on the clustering of genes. We use experimental data on the transcriptional response to oxidative stress in mouse heart muscle and compare the results from our procedure with existing nonparametric Bayesian methods that provide only a ranking of the genes by their evidence for differential expression.

We address the problem of X/gamma-ray spectra estimation in the fields of nuclear physics. Bayesian estimation of experimental backgrounds has been studied in [1] involving splines. Since Dirichlet processes (DP) sit on discrete measures, they provide an appealing prior for photopeaks. On the other hand, in order to tackle the complexity of experimental backgrounds, we consider a Polya Tree Mixture (PTM) - with suitable parameters yielding distribution continuity - for which predictive densities exhibit better smoothness properties than a single Polya Tree. Furthermore, it is easy to introduce some physical Compton line approximation formula (e.g. Klein-Nishina) in the base measure of the Polya Tree, or some physically driven local modifications of the PTM prior parameters. As backgrounds depend on photopeaks locations, we propose a hierarchical model where the PTM is conditioned on the DP. We use a beta prior for the mixing proportion between the DP and the PTM. Energies are not directly observed due to detection devices noises which introduce a convolution of both discrete and continuous measures by an assumed gaussian kernel whose variance is an unknown linear function of energy. Thus, the proposed semiparametric model for experimental data becomes a hierarchical Polya Tree-Dirichlet mixture of normal kernels. Besides, observed energies are binned in an histogram introducing additional quantification noise. The quantities of interest are usually posterior functionals of the DP mixing distribution. This implies an inverse problem which is carried out in the framework of finite stick-breaking representation. Thanks to conjugacy, draws from the posterior DP and PTM are easily obtained. The approach yields to a global peaks/background separation while offering spectrum resolution enhancement. The method is illustrated on experimental HPGe spectra.