A Multi-level Model for Analysing Whole Genome Sequencing Family Data with Longitudinal Traits

Compared to microarray-based genotyping, next-generation whole genome-sequencing (WGS) studies have the strength to provide greater information for the identification of rare variants, which likely account for a significant portion of missing heritability of common human diseases. In WGS, family-based studies are important because they are likely enriched for rare disease variants that segregate with the disease in relatives. We propose a multilevel model to detect disease variants using family-based WGS data with longitudinal measures. This model incorporates the correlation structure from family pedigrees and that from repeated measures. The iterative generalized least squares (IGLS) algorithm was applied to estimation of parameters and test of associations. The model was applied to the data of Genetic Analysis Workshop 18 and compared with existing linear mixed effect (LME) models. The multilevel model shows higher power at practical p-value levels and a better type I error control than LME model. Both multilevel and LME models, which utilize the longitudinal repeated information, have higher power than the method that only utilize data collected at one time point

Numerical Model of OTRC Wave Basin Based on Linear Hydrodynamics

This thesis presents a numerical model of the Offshore Technology Research Center (OTRC) wave basin based on linear hydrodynamics. WAMIT program is used for hydrodynamic analysis. Two methods are explored in simulating the wave basin: (a) build the wave basin model in WAMIT program with tank walls and the pit as a fixed body; (b) simulate the reflection from tank walls using the method of images. In both methods, the wave maker motion is modeled using generalized modes and the higher order panel method is applied. On each panel, the momentum flux is calculated based on third-order Gauss quadratures. The numerical wave basin contains 48 wave maker flaps, side walls, a floor and the wave absorber is modeled as an open boundary. Regular wave response, including the spatial uniformity of the wave field, has been studied. Evanescent modes from the wavemaker, the effect of reflection from a test model and the side walls, and oblique wave generation have also been investigated. It was found that reasonable results cannot be achieved using method (a) of direct side wall modeling despite numerous modifications to the tank geometry and its discretization; most noticeably, spatial uniformity cannot be achieved in long-crested wave generation. On the other hand, method (b) does yield spatial uniformity in long-crested wave generation, to numerical accuracy. Therefore method (b) is adopted for investigation of wave basin responses

A Generative Model For Zero Shot Learning Using Conditional Variational Autoencoders

Zero shot learning in Image Classification refers to the setting where images from some novel classes are absent in the training data but other information such as natural language descriptions or attribute vectors of the classes are available. This setting is important in the real world since one may not be able to obtain images of all the possible classes at training. While previous approaches have tried to model the relationship between the class attribute space and the image space via some kind of a transfer function in order to model the image space correspondingly to an unseen class, we take a different approach and try to generate the samples from the given attributes, using a conditional variational autoencoder, and use the generated samples for classification of the unseen classes. By extensive testing on four benchmark datasets, we show that our model outperforms the state of the art, particularly in the more realistic generalized setting, where the training classes can also appear at the test time along with the novel classes

Generalized Zero-Shot Learning via Synthesized Examples

We present a generative framework for generalized zero-shot learning where the training and test classes are not necessarily disjoint. Built upon a variational autoencoder based architecture, consisting of a probabilistic encoder and a probabilistic conditional decoder, our model can generate novel exemplars from seen/unseen classes, given their respective class attributes. These exemplars can subsequently be used to train any off-the-shelf classification model. One of the key aspects of our encoder-decoder architecture is a feedback-driven mechanism in which a discriminator (a multivariate regressor) learns to map the generated exemplars to the corresponding class attribute vectors, leading to an improved generator. Our model's ability to generate and leverage examples from unseen classes to train the classification model naturally helps to mitigate the bias towards predicting seen classes in generalized zero-shot learning settings. Through a comprehensive set of experiments, we show that our model outperforms several state-of-the-art methods, on several benchmark datasets, for both standard as well as generalized zero-shot learning.Comment: Accepted in CVPR'1

Estimating Mean and Covariance Structure with Reweighted Least Squares

Does Reweighted Least Squares (RLS) perform better in small samples than maximum likelihood (ML) for mean and covariance structure? ML statistics in covariance structure analysis are based on the asymptotic normality assumption; however, actual applications of structural equation modeling (SEM) in social and behavioral science research usually involve small samples. It has been found that chi-square tests often incorrectly over-reject the null hypothesis: Σ=Σ(θ), because when sample is small the sample covariance matrix becomes ill-conditioned and entails unstable estimates. In certain SEM models, the vector of parameter must contain both means, variances and covariances. Yet, whether RLS also works in mean and covariance structure remains unexamined. This research is an extended examination of reweighted least squares in mean and covariance structure. Specifically, we replace biased covariance matrix in traditional GLS function (Browne, 1974) with the unbiased sample covariance matrix that derives from ML estimation. Moreover, under the assumption of multivariate normality, a Monte Carlo simulation study was carried out to examine the statistical performance as compared with ML methods in different sample sizes. Based on empirical rejection frequencies and empirical averages of test statistic, this study shows that RLS performs much better than ML in mean and covariance structure models when sample sizes are small

An Algebraic Framework for the Real-Time Solution of Inverse Problems on Embedded Systems

This article presents a new approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the data from an array of sensors forms the forcing function. The solution of the equation is formulated as a least squares (LS) problem with linear constraints. The LS approach makes the method suitable for the explicit solution of inverse problems where the forcing function is perturbed by noise. The algebraic computation is partitioned into a initial preparatory step, which precomputes the matrices required for the run-time computation; and the cyclic run-time computation, which is repeated with each acquisition of sensor data. The cyclic computation consists of a single matrix-vector multiplication, in this manner computation complexity is known a-priori, fulfilling the definition of a real-time computation. Numerical testing of the new method is presented on perturbed as well as unperturbed problems; the results are compared with known analytic solutions and solutions acquired from state-of-the-art implicit solvers. The solution is implemented with model based design and uses only fundamental linear algebra; consequently, this approach supports automatic code generation for deployment on embedded systems. The targeting concept was tested via software- and processor-in-the-loop verification on two systems with different processor architectures. Finally, the method was tested on a laboratory prototype with real measurement data for the monitoring of flexible structures. The problem solved is: the real-time overconstrained reconstruction of a curve from measured gradients. Such systems are commonly encountered in the monitoring of structures and/or ground subsidence.Comment: 24 pages, journal articl