A study of computational methods to analyze gene expression data

The recent advent of new technologies has led to huge amounts of genomic data. With these data come new opportunities to understand biological cellular processes underlying hidden regulation mechanisms and to identify disease related biomarkers for informative diagnostics. However, extracting biological insights from the immense amounts of genomic data is a challenging task. Therefore, effective and efficient computational techniques are needed to analyze and interpret genomic data. In this thesis, novel computational methods are proposed to address such challenges: a Bayesian mixture model, an extended Bayesian mixture model, and an Eigen-brain approach. The Bayesian mixture framework involves integration of the Bayesian network and the Gaussian mixture model. Based on the proposed framework and its conjunction with K-means clustering and principal component analysis (PCA), biological insights are derived such as context specific/dependent relationships and nested structures within microarray where biological replicates are encapsulated. The Bayesian mixture framework is then extended to explore posterior distributions of network space by incorporating a Markov chain Monte Carlo (MCMC) model. The extended Bayesian mixture model summarizes the sampled network structures by extracting biologically meaningful features. Finally, an Eigen-brain approach is proposed to analyze in situ hybridization data for the identification of the cell-type specific genes, which can be useful for informative blood diagnostics. Computational results with region-based clustering reveals the critical evidence for the consistency with brain anatomical structure.

Efficient Image and Video Representations for Retrieval

Image (Video) retrieval is an interesting problem of retrieving images (videos) similar to the query. Images (Videos) are represented in an input (feature) space and similar images (videos) are obtained by finding nearest neighbors in the input representation space. Numerous input representations both in real valued and binary space have been proposed for conducting faster retrieval. In this thesis, we present techniques that obtain improved input representations for retrieval in both supervised and unsupervised settings for images and videos. Supervised retrieval is a well known problem of retrieving same class images of the query. We address the practical aspects of achieving faster retrieval with binary codes as input representations for the supervised setting in the first part, where binary codes are used as addresses into hash tables. In practice, using binary codes as addresses does not guarantee fast retrieval, as similar images are not mapped to the same binary code (address). We address this problem by presenting an efficient supervised hashing (binary encoding) method that aims to explicitly map all the images of the same class ideally to a unique binary code. We refer to the binary codes of the images as `Semantic Binary Codes' and the unique code for all same class images as `Class Binary Code'. We also propose a new class­ based Hamming metric that dramatically reduces the retrieval times for larger databases, where only hamming distance is computed to the class binary codes. We also propose a Deep semantic binary code model, by replacing the output layer of a popular convolutional Neural Network (AlexNet) with the class binary codes and show that the hashing functions learned in this way outperforms the state­ of ­the art, and at the same time provide fast retrieval times. In the second part, we also address the problem of supervised retrieval by taking into account the relationship between classes. For a given query image, we want to retrieve images that preserve the relative order i.e. we want to retrieve all same class images first and then, the related classes images before different class images. We learn such relationship aware binary codes by minimizing the similarity between inner product of the binary codes and the similarity between the classes. We calculate the similarity between classes using output embedding vectors, which are vector representations of classes. Our method deviates from the other supervised binary encoding schemes as it is the first to use output embeddings for learning hashing functions. We also introduce new performance metrics that take into account the related class retrieval results and show significant gains over the state­ of­ the art. High Dimensional descriptors like Fisher Vectors or Vector of Locally Aggregated Descriptors have shown to improve the performance of many computer vision applications including retrieval. In the third part, we will discuss an unsupervised technique for compressing high dimensional vectors into high dimensional binary codes, to reduce storage complexity. In this approach, we deviate from adopting traditional hyperplane hashing functions and instead learn hyperspherical hashing functions. The proposed method overcomes the computational challenges of directly applying the spherical hashing algorithm that is intractable for compressing high dimensional vectors. A practical hierarchical model that utilizes divide and conquer techniques using the Random Select and Adjust (RSA) procedure to compress such high dimensional vectors is presented. We show that our proposed high dimensional binary codes outperform the binary codes obtained using traditional hyperplane methods for higher compression ratios. In the last part of the thesis, we propose a retrieval based solution to the Zero shot event classification problem - a setting where no training videos are available for the event. To do this, we learn a generic set of concept detectors and represent both videos and query events in the concept space. We then compute similarity between the query event and the video in the concept space and videos similar to the query event are classified as the videos belonging to the event. We show that we significantly boost the performance using concept features from other modalities.

Impact of hypomineralized teeth and sociobehavioral aspects on caries development: a prospective cohort study

Aim: This prospective cohort study was to evaluate the independent and mutual effects of socioeconomic, oral health behaviors and individual clinical factors, including enamel hypomineralization, as possible risk factors for increase in caries experience in second primary molar (SPM) over a period of 2-years. Methods: Children (n=216) aged 4-6 years were examined for hypomineralized second primary molar (HSPM) and dental caries in school settings and were recalled every 6 months. The caregivers filled out a semi-structured questionnaire about their socio-demographic and oral health-related behaviors. Data analysis was performed using a hierarchical model with three levels. Multiple analyses were performed at each level and variables with p<0.20 were tested by stepwise multiple Generalized Estimating Equation. Results: At final examination, 33.3% of the children had developed new caries lesions in SPM. The model showed that the number of years of mother’s schooling and the caregiver´s perception about their children’s caries experience played a protective role in the incidence of dental caries. Children who had white spot lesions were more likely to develop new carious lesions in SPM. Children with HSPM showed no higher incidence of caries in their SPM than those without HSPM. Conclusions: Clinical, socioeconomic and behavioral factors impacted on caries development in primary second molars. However, further studies are required to better understand the role of HSPM in caries development in other age groups.

A hierarchical Bayesian model for predicting the functional consequences of amino-acid polymorphisms

Genetic polymorphisms in deoxyribonucleic acid coding regions may have a phenotypic effect on the carrier, e.g. by influencing susceptibility to disease. Detection of deleterious mutations via association studies is hampered by the large number of candidate sites; therefore methods are needed to narrow down the search to the most promising sites. For this, a possible approach is to use structural and sequence-based information of the encoded protein to predict whether a mutation at a particular site is likely to disrupt the functionality of the protein itself. We propose a hierarchical Bayesian multivariate adaptive regression spline (BMARS) model for supervised learning in this context and assess its predictive performance by using data from mutagenesis experiments on lac repressor and lysozyme proteins. In these experiments, about 12 amino-acid substitutions were performed at each native amino-acid position and the effect on protein functionality was assessed. The training data thus consist of repeated observations at each position, which the hierarchical framework is needed to account for. The model is trained on the lac repressor data and tested on the lysozyme mutations and vice versa. In particular, we show that the hierarchical BMARS model, by allowing for the clustered nature of the data, yields lower out-of-sample misclassification rates compared with both a BMARS and a frequen-tist MARS model, a support vector machine classifier and an optimally pruned classification tree.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

A Hierarchical Bayesian Model for Measuring Motion Adaptation

Previous research has shown that motion imagery draws on the same neural circuits that are involved in perception of motion, thus leading to a motion aftereffect (Winawer et al., 2010). Imagined stimuli can induce a similar shift in participants’ psychometric functions as neural adaptation due to a perceived stimulus. However, these studies have been criticized on the grounds that they fail to exclude the possibility that the subjects might have guessed the experimental hypothesis, and behaved accordingly (Morgan et al., 2012). In particular, the authors claim that participants can adopt arbitrary response criteria, which results in similar changes of the central tendency μ of psychometric curves as those shown by Winawer et al. (2010).

Co-movements in Real Effective Exchange Rates: Evidence from the Dynamic Hierarchical Factor Model

We analyze and quantify co-movements in real effective exchange rates while considering the regional location of countries. More specifically, using the dynamic hierarchical factor model (Moench et al. (2011)), we decompose exchange rate movements into several latent components; worldwide and two regional factors as well as country-specific elements. Then, we provide evidence that the worldwide common factor is closely related to monetary policies in large advanced countries while regional common factors tend to be captured by those in the rest of the countries in a region. However, a substantial proportion of the variation in the real exchange rates is reported to be country-specific; even in Europe country-specific movements exceed worldwide and regional common factors.

An empirical hierarchical Bayesian unification of occupational exposure assessment methods.

In occupational exposure assessment of airborne contaminants, exposure levels can either be estimated through repeated measurements of the pollutant concentration in air, expert judgment or through exposure models that use information on the conditions of exposure as input. In this report, we propose an empirical hierarchical Bayesian model to unify these approaches. Prior to any measurement, the hygienist conducts an assessment to generate prior distributions of exposure determinants. Monte-Carlo samples from these distributions feed two level-2 models: a physical, two-compartment model, and a non-parametric, neural network model trained with existing exposure data. The outputs of these two models are weighted according to the expert's assessment of their relevance to yield predictive distributions of the long-term geometric mean and geometric standard deviation of the worker's exposure profile (level-1 model). Bayesian inferences are then drawn iteratively from subsequent measurements of worker exposure. Any traditional decision strategy based on a comparison with occupational exposure limits (e.g. mean exposure, exceedance strategies) can then be applied. Data on 82 workers exposed to 18 contaminants in 14 companies were used to validate the model with cross-validation techniques. A user-friendly program running the model is available upon request.

Forecasting and turning point predictions in a Bayesian panel VAR model

We provide methods for forecasting variables and predicting turning points in panel Bayesian VARs. We specify a flexible model which accounts for both interdependencies in the cross section and time variations in the parameters. Posterior distributions for the parameters are obtained for a particular type of diffuse, for Minnesota-type and for hierarchical priors. Formulas for multistep, multiunit point and average forecasts are provided. An application to the problem of forecasting the growth rate of output and of predicting turning points in the G-7 illustrates the approach. A comparison with alternative forecasting methods is also provided.

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

Pricing farm-level agricultural insurance: a Bayesian approach

This paper applies Hierarchical Bayesian Models to price farm-level yield insurance contracts. This methodology considers the temporal effect, the spatial dependence and spatio-temporal models. One of the major advantages of this framework is that an estimate of the premium rate is obtained directly from the posterior distribution. These methods were applied to a farm-level data set of soybean in the State of the Parana (Brazil), for the period between 1994 and 2003. The model selection was based on a posterior predictive criterion. This study improves considerably the estimation of the fair premium rates considering the small number of observations.

Bayesian analysis of the error correction model

This paper presents a method for estimating the posterior probability density of the cointegrating rank of a multivariate error correction model. A second contribution is the careful elicitation of the prior for the cointegrating vectors derived from a prior on the cointegrating space. This prior obtains naturally from treating the cointegrating space as the parameter of interest in inference and overcomes problems previously encountered in Bayesian cointegration analysis. Using this new prior and Laplace approximation, an estimator for the posterior probability of the rank is given. The approach performs well compared with information criteria in Monte Carlo experiments. (C) 2003 Elsevier B.V. All rights reserved.

A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

The generalized multiprocessor periodic resource interface model for hierarchical multiprocessor scheduling

Composition is a practice of key importance in software engineering. When real-time applications are composed it is necessary that their timing properties (such as meeting the deadlines) are guaranteed. The composition is performed by establishing an interface between the application and the physical platform. Such an interface does typically contain information about the amount of computing capacity needed by the application. In multiprocessor platforms, the interface should also present information about the degree of parallelism. Recently there have been quite a few interface proposals. However, they are either too complex to be handled or too pessimistic.In this paper we propose the Generalized Multiprocessor Periodic Resource model (GMPR) that is strictly superior to the MPR model without requiring a too detailed description. We describe a method to generate the interface from the application specification. All these methods have been implemented in Matlab routines that are publicly available.