Solving the Empirical Bayes Normal Means Problem with Correlated Noise

arXiv.org Machine Learning

The Normal Means problem plays a fundamental role in many areas of modern high-dimensional statistics, both in theory and practice. And the Empirical Bayes (EB) approach to solving this problem has been shown to be highly effective, again both in theory and practice. However, almost all EB treatments of the Normal Means problem assume that the observations are independent. In practice correlations are ubiquitous in real-world applications, and these correlations can grossly distort EB estimates. Here, exploiting theory from Schwartzman (2010), we develop new EB methods for solving the Normal Means problem that take account of unknown correlations among observations. We provide practical software implementations of these methods, and illustrate them in the context of large-scale multiple testing problems and False Discovery Rate (FDR) control. In realistic numerical experiments our methods compare favorably with other commonly-used multiple testing methods.


Using Virtual Patients to Train Clinical Interviewing Skills

AAAI Conferences

Virtual patients are viewed as a cost-effective alternative to standardized patients for role-play training of clinical interviewing skills. However, training studies produce mixed results. Students give high ratings to practice with virtual patients and feel more self-confident, but they show little improvement in objective skills. This confidence-competence gap matches a common cognitive illusion, in which students overestimate the effectiveness of training that is too easy. We hypothesize that cost-effective training requires virtual patients that emphasize functional and psychological fidelity over physical fidelity. We discuss 12 design decisions aimed at cost-effective training and their application in virtual patients for practicing brief intervention in alcohol abuse. Our STAR Workshop includes 3 such patients and a virtual coach. A controlled experiment evaluated STAR and compared it to an easier E-Book and no-training Control. E-Book subjects displayed the illusion, giving high ratings to their training and self-confidence, but performing no better than Control subjects on skills. STAR subjects gave high ratings to their training and self-confidence and scored better higher than E-Book or Control subjects on skills. We invite other researchers to use the underlying Imp technology to build virtual patients for their own work.


Bayesian Inference of Spreading Processes on Networks

arXiv.org Machine Learning

Infectious diseases are studied to understand their spreading mechanisms, to evaluate control strategies and to predict the risk and course of future outbreaks. Because people only interact with a small number of individuals, and because the structure of these interactions matters for spreading processes, the pairwise relationships between individuals in a population can be usefully represented by a network. Although the underlying processes of transmission are different, the network approach can be used to study the spread of pathogens in a contact network or the spread of rumors in an online social network. We study simulated simple and complex epidemics on synthetic networks and on two empirical networks, a social / contact network in an Indian village and an online social network in the U.S. Our goal is to learn simultaneously about the spreading process parameters and the source node (first infected node) of the epidemic, given a fixed and known network structure, and observations about state of nodes at several points in time. Our inference scheme is based on approximate Bayesian computation (ABC), an inference technique for complex models with likelihood functions that are either expensive to evaluate or analytically intractable. ABC enables us to adopt a Bayesian approach to the problem despite the posterior distribution being very complex. Our method is agnostic about the topology of the network and the nature of the spreading process. It generally performs well and, somewhat counter-intuitively, the inference problem appears to be easier on more heterogeneous network topologies, which enhances its future applicability to real-world settings where few networks have homogeneous topologies.


A Bayesian Group Sparse Multi-Task Regression Model for Imaging Genetics

arXiv.org Machine Learning

Motivation: Recent advances in technology for brain imaging and high-throughput genotyping have motivated studies examining the influence of genetic variation on brain structure. Wang et al. (Bioinformatics, 2012) have developed an approach for the analysis of imaging genomic studies using penalized multi-task regression with regularization based on a novel group $l_{2,1}$-norm penalty which encourages structured sparsity at both the gene level and SNP level. While incorporating a number of useful features, the proposed method only furnishes a point estimate of the regression coefficients; techniques for conducting statistical inference are not provided. A new Bayesian method is proposed here to overcome this limitation. Results: We develop a Bayesian hierarchical modeling formulation where the posterior mode corresponds to the estimator proposed by Wang et al. (Bioinformatics, 2012), and an approach that allows for full posterior inference including the construction of interval estimates for the regression parameters. We show that the proposed hierarchical model can be expressed as a three-level Gaussian scale mixture and this representation facilitates the use of a Gibbs sampling algorithm for posterior simulation. Simulation studies demonstrate that the interval estimates obtained using our approach achieve adequate coverage probabilities that outperform those obtained from the nonparametric bootstrap. Our proposed methodology is applied to the analysis of neuroimaging and genetic data collected as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI), and this analysis of the ADNI cohort demonstrates clearly the value added of incorporating interval estimation beyond only point estimation when relating SNPs to brain imaging endophenotypes.


Eigen Values Features for the Classification of Brain Signals corresponding to 2D and 3D Educational Contents

arXiv.org Machine Learning

In this paper, we have proposed a brain signal classification method, which uses eigenvalues of the covariance matrix as features to classify images (topomaps) created from the brain signals. The signals are recorded during the answering of 2D and 3D questions. The system is used to classify the correct and incorrect answers for both 2D and 3D questions. Using the classification technique, the impacts of 2D and 3D multimedia educational contents on learning, memory retention and recall will be compared. The subjects learn similar 2D and 3D educational contents. Afterwards, subjects are asked 20 multiple-choice questions (MCQs) associated with the contents after thirty minutes (Short-Term Memory) and two months (Long-Term Memory). Eigenvalues features extracted from topomaps images are given to K-Nearest Neighbor (KNN) and Support Vector Machine (SVM) classifiers, in order to identify the states of the brain related to incorrect and correct answers. Excellent accuracies obtained by both classifiers and by applying statistical analysis on the results, no significant difference is indicated between 2D and 3D multimedia educational contents on learning, memory retention and recall in both STM and LTM.