Bayesian binary regression model: an application to in-hospital death after AMI prediction

Um modelo bayesiano de regressão binária é desenvolvido para predizer óbito hospitalar em pacientes acometidos por infarto agudo do miocárdio. Métodos de Monte Carlo via Cadeias de Markov (MCMC) são usados para fazer inferência e validação. Uma estratégia para construção de modelos, baseada no uso do fator de Bayes, é proposta e aspectos de validação são extensivamente discutidos neste artigo, incluindo a distribuição a posteriori para o índice de concordância e análise de resíduos. A determinação de fatores de risco, baseados em variáveis disponíveis na chegada do paciente ao hospital, é muito importante para a tomada de decisão sobre o curso do tratamento. O modelo identificado se revela fortemente confiável e acurado, com uma taxa de classificação correta de 88% e um índice de concordância de 83%.

Framework for Skew-Probit Links in Binary Regression

We review several asymmetrical links for binary regression models and present a unified approach for two skew-probit links proposed in the literature. Moreover, under skew-probit link, conditions for the existence of the ML estimators and the posterior distribution under improper priors are established. The framework proposed here considers two sets of latent variables which are helpful to implement the Bayesian MCMC approach. A simulation study to criteria for models comparison is conducted and two applications are made. Using different Bayesian criteria we show that, for these data sets, the skew-probit links are better than alternative links proposed in the literature.

Bayesian outlier analysis in binary regression

We propose alternative approaches to analyze residuals in binary regression models based on random effect components. Our preferred model does not depend upon any tuning parameter, being completely automatic. Although the focus is mainly on accommodation of outliers, the proposed methodology is also able to detect them. Our approach consists of evaluating the posterior distribution of random effects included in the linear predictor. The evaluation of the posterior distributions of interest involves cumbersome integration, which is easily dealt with through stochastic simulation methods. We also discuss different specifications of prior distributions for the random effects. The potential of these strategies is compared in a real data set. The main finding is that the inclusion of extra variability accommodates the outliers, improving the adjustment of the model substantially, besides correctly indicating the possible outliers.

A note on model uncertainty in linear regression

We consider model selection uncertainty in linear regression. We study theoretically and by simulation the approach of Buckland and co-workers, who proposed estimating a parameter common to all models under study by taking a weighted average over the models, using weights obtained from information criteria or the bootstrap. This approach is compared with the usual approach in which the 'best' model is used, and with Bayesian model averaging. The weighted predictor behaves similarly to model averaging, with generally more realistic mean-squared errors than the usual model-selection-based estimator.

Latent residual analysis in binary regression with skewed link

Model diagnostics is an integral part of model determination and an important part of the model diagnostics is residual analysis. We adapt and implement residuals considered in the literature for the probit, logistic and skew-probit links under binary regression. New latent residuals for the skew-probit link are proposed here. We have detected the presence of outliers using the residuals proposed here for different models in a simulated dataset and a real medical dataset.

Model Selection in Summary Evaluation

A difficulty in the design of automated text summarization algorithms is in the objective evaluation. Viewing summarization as a tradeoff between length and information content, we introduce a technique based on a hierarchy of classifiers to rank, through model selection, different summarization methods. This summary evaluation technique allows for broader comparison of summarization methods than the traditional techniques of summary evaluation. We present an empirical study of two simple, albeit widely used, summarization methods that shows the different usages of this automated task-based evaluation system and confirms the results obtained with human-based evaluation methods over smaller corpora.

An empirical study of Hoelfding Racing for model selction in K-nearest neighbor classification

Racing algorithms have recently been proposed as a general-purpose method for performing model selection in machine teaming algorithms. In this paper, we present an empirical study of the Hoeffding racing algorithm for selecting the k parameter in a simple k-nearest neighbor classifier. Fifteen widely-used classification datasets from UCI are used and experiments conducted across different confidence levels for racing. The results reveal a significant amount of sensitivity of the k-nn classifier to its model parameter value. The Hoeffding racing algorithm also varies widely in its performance, in terms of the computational savings gained over an exhaustive evaluation. While in some cases the savings gained are quite small, the racing algorithm proved to be highly robust to the possibility of erroneously eliminating the optimal models. All results were strongly dependent on the datasets used.

Meta-learning for informed model searches in Automated Machine Learning

Day by day, machine learning is changing our lives in ways we could not have imagined just 5 years ago. ML expertise is more and more requested and needed, though just a limited number of ML engineers are available on the job market, and their knowledge is always limited by an inherent characteristic of theirs: they are humans. This thesis explores the possibilities offered by meta-learning, a new field in ML that takes learning a level higher: models are trained on other models' training data, starting from features of the dataset they were trained on, inference times, obtained performances, to try to understand the relationship between a good model and the way it was obtained. The so-called metamodel was trained on data collected by OpenML, the largest ML metadata platform that's publicly available today. Datasets were analyzed to obtain meta-features that describe them, which were then tied to model performances in a regression task. The obtained metamodel predicts the expected performances of a given model type (e.g., a random forest) on a given ML task (e.g., classification on the UCI census dataset). This research was then integrated into a custom-made AutoML framework, to show how meta-learning is not an end in itself, but it can be used to further progress our ML research. Encoding ML engineering expertise in a model allows better, faster, and more impactful ML applications across the whole world, while reducing the cost that is inevitably tied to human engineers.

USE OF HIDDEN MARKOV MODELS FOR QTL MAPPING

An important aspect of the QTL mapping problem is the treatment of missing genotype data. If complete genotype data were available, QTL mapping would reduce to the problem of model selection in linear regression. However, in the consideration of loci in the intervals between the available genetic markers, genotype data is inherently missing. Even at the typed genetic markers, genotype data is seldom complete, as a result of failures in the genotyping assays or for the sake of economy (for example, in the case of selective genotyping, where only individuals with extreme phenotypes are genotyped). We discuss the use of algorithms developed for hidden Markov models (HMMs) to deal with the missing genotype data problem.

Stochastic Search Variable Selection in Vector Error Correction Models with an Application to a Model of the UK Macroeconomy

This paper develops methods for Stochastic Search Variable Selection (currently popular with regression and Vector Autoregressive models) for Vector Error Correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK macroeconomic model.

Bayesian Model Averaging in the Instrumental Variable Regression Model

This paper considers the instrumental variable regression model when there is uncertainty about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainty can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The algorithm is very exible and can be easily adapted to analyze any of the di¤erent priors that have been proposed in the Bayesian instrumental variables literature. We show how to calculate the probability of any relevant restriction (e.g. the posterior probability that over-identifying restrictions hold) and discuss diagnostic checking using the posterior distribution of discrepancy vectors. We illustrate our methods in a returns-to-schooling application.

A Combinatorial Approach to the Variable Selection in Multiple Linear Regression: Analysis of Selwood et al Data set -A Case Study.

A combinatorial protocol (CP) is introduced here to interface it with the multiple linear regression (MLR) for variable selection. The efficiency of CP-MLR is primarily based on the restriction of entry of correlated variables to the model development stage. It has been used for the analysis of Selwood et al data set [16], and the obtained models are compared with those reported from GFA [8] and MUSEUM [9] approaches. For this data set CP-MLR could identify three highly independent models (27, 28 and 31) with Q2 value in the range of 0.632-0.518. Also, these models are divergent and unique. Even though, the present study does not share any models with GFA [8], and MUSEUM [9] results, there are several descriptors common to all these studies, including the present one. Also a simulation is carried out on the same data set to explain the model formation in CP-MLR. The results demonstrate that the proposed method should be able to offer solutions to data sets with 50 to 60 descriptors in reasonable time frame. By carefully selecting the inter-parameter correlation cutoff values in CP-MLR one can identify divergent models and handle data sets larger than the present one without involving excessive computer time.

Distributed Feature Selection in Large n and Large p Regression Problems

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (in the sample space) or vertically (in the feature space), and the challenge arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. For sample space partitioning, I propose a MEdian Selection Subset AGgregation Estimator ({\em message}) algorithm for solving these issues. The algorithm applies feature selection in parallel for each subset using regularized regression or Bayesian variable selection method, calculates the `median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in sample size, and has theoretical guarantees. I provide extensive experiments to show excellent performance in feature selection, estimation, prediction, and computation time relative to usual competitors.

While sample space partitioning is useful in handling datasets with large sample size, feature space partitioning is more effective when the data dimension is high. Existing methods for partitioning features, however, are either vulnerable to high correlations or inefficient in reducing the model dimension. In the thesis, I propose a new embarrassingly parallel framework named {\em DECO} for distributed variable selection and parameter estimation. In {\em DECO}, variables are first partitioned and allocated to m distributed workers. The decorrelated subset data within each worker are then fitted via any algorithm designed for high-dimensional problems. We show that by incorporating the decorrelation step, DECO can achieve consistent variable selection and parameter estimation on each subset with (almost) no assumptions. In addition, the convergence rate is nearly minimax optimal for both sparse and weakly sparse models and does NOT depend on the partition number m. Extensive numerical experiments are provided to illustrate the performance of the new framework.

For datasets with both large sample sizes and high dimensionality, I propose a new "divided-and-conquer" framework {\em DEME} (DECO-message) by leveraging both the {\em DECO} and the {\em message} algorithm. The new framework first partitions the dataset in the sample space into row cubes using {\em message} and then partition the feature space of the cubes using {\em DECO}. This procedure is equivalent to partitioning the original data matrix into multiple small blocks, each with a feasible size that can be stored and fitted in a computer in parallel. The results are then synthezied via the {\em DECO} and {\em message} algorithm in a reverse order to produce the final output. The whole framework is extremely scalable.

Strategies for genetic model specification in the screening of genome-wide meta-analysis signals for further replication

Background Meta-analysis is increasingly being employed as a screening procedure in large-scale association studies to select promising variants for follow-up studies. However, standard methods for meta-analysis require the assumption of an underlying genetic model, which is typically unknown a priori. This drawback can introduce model misspecifications, causing power to be suboptimal, or the evaluation of multiple genetic models, which augments the number of false-positive associations, ultimately leading to waste of resources with fruitless replication studies. We used simulated meta-analyses of large genetic association studies to investigate naive strategies of genetic model specification to optimize screenings of genome-wide meta-analysis signals for further replication. Methods Different methods, meta-analytical models and strategies were compared in terms of power and type-I error. Simulations were carried out for a binary trait in a wide range of true genetic models, genome-wide thresholds, minor allele frequencies (MAFs), odds ratios and between-study heterogeneity (tau(2)). Results Among the investigated strategies, a simple Bonferroni-corrected approach that fits both multiplicative and recessive models was found to be optimal in most examined scenarios, reducing the likelihood of false discoveries and enhancing power in scenarios with small MAFs either in the presence or in absence of heterogeneity. Nonetheless, this strategy is sensitive to tau(2) whenever the susceptibility allele is common (MAF epsilon 30%), resulting in an increased number of false-positive associations compared with an analysis that considers only the multiplicative model. Conclusion Invoking a simple Bonferroni adjustment and testing for both multiplicative and recessive models is fast and an optimal strategy in large meta-analysis-based screenings. However, care must be taken when examined variants are common, where specification of a multiplicative model alone may be preferable.