Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHigh-dimensional single-index Bayesian modeling of brain atrophy
109
0
0.0
(
0
)
Added by
Arkaprava Roy
Publication date
2017
fields
Mathematical Statistics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We propose a model of brain atrophy as a function of high-dimensional genetic information and low dimensional covariates such as gender, age, APOE gene, and disease status. A nonparametric single-index Bayesian model of high dimension is proposed to model the relationship with B-spline series prior on the unknown functions and Dirichlet process scale mixture of centered normal prior on the distributions of the random effects. The posterior rate of contraction without the random effect is established for a fixed number of regions and time points with increasing sample size. We implement an efficient computation algorithm through a Hamiltonian Monte Carlo (HMC) algorithm. The performance of the proposed Bayesian method is compared with the corresponding least square estimator in the linear model with horseshoe prior, LASSO and SCAD penalization on the high-dimensional covariates. The proposed Bayesian method is applied to a dataset on volumes of brain regions recorded over multiple visits of 748 individuals using 620,901 SNPs and 6 other covariates for each individual, to identify factors associated with brain atrophy.
rate research
Read More
In the era of big data, variable selection is a key technology for handling high-dimensional problems with a small sample size but a large number of covariables. Different variable selection methods were proposed for different models, such as linear model, logistic model and generalized linear model. However, fewer works focused on variable selection for single index models, especially, for single index logistic model, due to the difficulty arose from the unknown link function and the slow mixing rate of MCMC algorithm for traditional logistic model. In this paper, we proposed a Bayesian variable selection procedure for single index logistic model by taking the advantage of Gaussian process and data augmentation. Numerical results from simulations and real data analysis show the advantage of our method over the state of arts.
Variable selection in ultra-high dimensional linear regression is often preceded by a screening step to significantly reduce the dimension. Here a Bayesian variable screening method (BITS) is developed. BITS can successfully integrate prior knowledge, if any, on effect sizes, and the number of true variables. BITS iteratively includes potential variables with the highest posterior probability accounting for the already selected variables. It is implemented by a fast Cholesky update algorithm and is shown to have the screening consistency property. BITS is built based on a model with Gaussian errors, yet, the screening consistency is proved to hold under more general tail conditions. The notion of posterior screening consistency allows the resulting model to provide a good starting point for further Bayesian variable selection methods. A new screening consistent stopping rule based on posterior probability is developed. Simulation studies and real data examples are used to demonstrate scalability and fine screening performance.
It has become increasingly common to collect high-dimensional binary data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for inferences. However, algorithms for fitting such models face issues in scaling up to high dimensions due to the intractability of the likelihood, involving an integral over a multivariate normal distribution having no analytic form. Although a variety of algorithms have been proposed to approximate this intractable integral, these approaches are difficult to implement and/or inaccurate in high dimensions. We propose a two-stage Bayesian approach for inference on model parameters while taking care of the uncertainty propagation between the stages. We use the special structure of latent Gaussian models to reduce the highly expensive computation involved in joint parameter estimation to focus inference on marginal distributions of model parameters. This essentially makes the method embarrassingly parallel for both stages. We illustrate performance in simulations and applications to joint species distribution modeling in ecology.
Early and accurate diagnosis of Alzheimers disease (AD) and its prodromal period mild cognitive impairment (MCI) is essential for the delayed disease progression and the improved quality of patientslife. The emerging computer-aided diagnostic methods that combine deep learning with structural magnetic resonance imaging (sMRI) have achieved encouraging results, but some of them are limit of issues such as data leakage and unexplainable diagnosis. In this research, we propose a novel end-to-end deep learning approach for automated diagnosis of AD and localization of important brain regions related to the disease from sMRI data. This approach is based on a 2D single model strategy and has the following differences from the current approaches: 1) Convolutional Neural Network (CNN) models of different structures and capacities are evaluated systemically and the most suitable model is adopted for AD diagnosis; 2) a data augmentation strategy named Two-stage Random RandAugment (TRRA) is proposed to alleviate the overfitting issue caused by limited training data and to improve the classification performance in AD diagnosis; 3) an explainable method of Grad-CAM++ is introduced to generate the visually explainable heatmaps that localize and highlight the brain regions that our model focuses on and to make our model more transparent. Our approach has been evaluated on two publicly accessible datasets for two classification tasks of AD vs. cognitively normal (CN) and progressive MCI (pMCI) vs. stable MCI (sMCI). The experimental results indicate that our approach outperforms the state-of-the-art approaches, including those using multi-model and 3D CNN methods. The resultant localization heatmaps from our approach also highlight the lateral ventricle and some disease-relevant regions of cortex, coincident with the commonly affected regions during the development of AD.
Single index models provide an effective dimension reduction tool in regression, especially for high dimensional data, by projecting a general multivariate predictor onto a direction vector. We propose a novel single-index model for regression models where metric space-valued random object responses are coupled with multivariate Euclidean predictors. The responses in this regression model include complex, non-Euclidean data, including covariance matrices, graph Laplacians of networks, and univariate probability distribution functions among other complex objects that lie in abstract metric spaces. Frechet regression has provided an approach for modeling the conditional mean of such random objects given multivariate Euclidean vectors, but it does not provide for regression parameters such as slopes or intercepts, since the metric space-valued responses are not amenable to linear operations. We show here that for the case of multivariate Euclidean predictors, the parameters that define a single index and associated projection vector can be used to substitute for the inherent absence of parameters in Frechet regression. Specifically, we derive the asymptotic consistency of suitable estimates of these parameters subject to an identifiability condition. Consistent estimation of the link function of the single index Frechet regression model is obtained through local Frechet regression. We demonstrate the finite sample performance of estimation for the proposed single index Frechet regression model through simulation studies, including the special cases of probability distributions and graph adjacency matrices. The method is also illustrated for resting-state functional Magnetic Resonance Imaging (fMRI) data from the ADNI study.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
