arXiv subjects

Bochao Jia

Publications and source records attributed to Bochao Jia.

7 recordsLinked to original sources

arXiv2021

A fusion learning method to subgroup analysis of Alzheimer's disease

Uncovering the heterogeneity in the disease progression of Alzheimer's is a key factor to disease understanding and treatment development, so that interventions can be tailored to target the subgroups that will benefit most from the treatment, which is an important goal of precision medicine. However, in practice, one top methodological challenge hindering the heterogeneity investigation is that the true subgroup membership of each individual is often unknown. In this article, we aim to identify latent subgroups of individuals who share a common disorder progress over time, to predict latent subgroup memberships, and to estimate and infer the heterogeneous trajectories among the subgroups. To achieve these goals, we apply a concave fusion learning method proposed in Ma and Huang (2017) and Ma et al. (2019) to conduct subgroup analysis for longitudinal trajectories of the Alzheimer's disease data. The heterogeneous trajectories are represented by subject-specific unknown functions which are approximated by B-splines. The concave fusion method can simultaneously estimate the spline coefficients and merge them together for the subjects belonging to the same subgroup to automatically identify subgroups and recover the heterogeneous trajectories. The resulting estimator of the disease trajectory of each subgroup is supported by an asymptotic distribution. It provides a sound theoretical basis for further conducting statistical inference in subgroup analysis..

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arXiv2020

Markov Neighborhood Regression for High-Dimensional Inference

This paper proposes an innovative method for constructing confidence intervals and assessing p-values in statistical inference for high-dimensional linear models. The proposed method has successfully broken the high-dimensional inference problem into a series of low-dimensional inference problems: For each regression coefficient $β_i$, the confidence interval and $p$-value are computed by regressing on a subset of variables selected according to the conditional independence relations between the corresponding variable $X_i$ and other variables. Since the subset of variables forms a Markov neighborhood of $X_i$ in the Markov network formed by all the variables $X_1,X_2,\ldots,X_p$, the proposed method is coined as Markov neighborhood regression. The proposed method is tested on high-dimensional linear, logistic and Cox regression. The numerical results indicate that the proposed method significantly outperforms the existing ones. Based on the Markov neighborhood regression, a method of learning causal structures for high-dimensional linear models is proposed and applied to identification of drug sensitive genes and cancer driver genes. The idea of using conditional independence relations for dimension reduction is general and potentially can be extended to other high-dimensional or big data problems as well.

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arXiv2018

Fast Bayesian Integrative Learning of Multiple Gene Regulatory Networks for Type 1 Diabetes

Motivated by the need to study the molecular mechanism underlying Type 1 Diabetes (T1D) with the gene expression data collected from both the patients and healthy controls at multiple time points, we propose an innovative method for jointly estimating multiple dependent Gaussian graphical models. Compared to the existing methods, the proposed method has a few significant advantages. First, it includes a meta-analysis procedure to explicitly integrate information across distinct conditions. In contrast, the existing methods often integrate information through prior distributions or penalty function, which is usually less efficient. Second, instead of working on original data, the Bayesian step of the proposed method works on edge-wise scores, through which the proposed method avoids to invert high-dimensional covariance matrices and thus can perform very fast. The edge-wise score forms an equivalent measure of the partial correlation coefficient and thus provides a good summary for the graph structure information contained in the data under each condition. Third, the proposed method can provide an overall uncertainty measure for the edges detected in multiple graphical models, while the existing methods only produce a point estimate or are feasible for very small size problems. We prove consistency of the proposed method under mild conditions and illustrate its performance using simulated and real data examples. The numerical results indicate the superiority of the proposed method over the existing ones in both estimation accuracy and computational efficiency. Extension of the proposed method to joint estimation of multiple mixed graphical models is straightforward.

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arXiv2018

The application of Monte Carlo methods for learning generalized linear model

Monte Carlo method is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other mathematical methods. Basically, many statisticians have been increasingly drawn to Monte Carlo method in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. In this paper, we will introduce the Monte Carlo method for calculating coefficients in Generalized Linear Model(GLM), especially for Logistic Regression. Our main methods are Metropolis Hastings(MH) Algorithms and Stochastic Approximation in Monte Carlo Computation(SAMC). For comparison, we also get results automatically using MLE method in R software.

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arXiv2018

Learning Gene Regulatory Networks with High-Dimensional Heterogeneous Data

The Gaussian graphical model is a widely used tool for learning gene regulatory networks with high-dimensional gene expression data. Most existing methods for Gaussian graphical models assume that the data are homogeneous, i.e., all samples are drawn from a single Gaussian distribution. However, for many real problems, the data are heterogeneous, which may contain some subgroups or come from different resources. This paper proposes to model the heterogeneous data using a mixture Gaussian graphical model, and apply the imputation-consistency algorithm, combining with the $ψ$-learning algorithm, to estimate the parameters of the mixture model and cluster the samples to different subgroups. An integrated Gaussian graphical network is learned across the subgroups along with the iterations of the imputation-consistency algorithm. The proposed method is compared with an existing method for learning mixture Gaussian graphical models as well as a few other methods developed for homogeneous data, such as graphical Lasso, nodewise regression and $ψ$-learning. The numerical results indicate superiority of the proposed method in all aspects of parameter estimation, cluster identification and network construction. The numerical results also indicate generality of the proposed method: it can be applied to homogeneous data without significant harms.

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arXiv2018

Mixture Envelope Model for Heterogeneous Genomics Data Analysis

Envelope model also known as multivariate regression model was proposed to solve the multiple response regression problems. It measures the linear association between predictors and multiple responses by using the minimal reducing subspace of the covariance matrix that accommodates the mean function. However, in many real applications, data may consist many unknown confounding factors or they just come from different resources. Thus, there might be some heterogeneous dependency across the whole population and divide them into different groups. For example, there exists several subtypes across the population with breast cancer with different gene interaction mechanisms for each subtype group. In this setting, constructing a single model using all observations ignores the difference between groups while estimating multiple models for each group is infeasible due to the unknown group classification. To deal with this problem, we proposed a mixture envelope model which construct a groupwise model for heterogeneous data and simultaneously classify them into different groups by an Imputation-Conditional Consistency (ICC) algorithm. Simulation results shows that our proposed method outperforms on both classification and prediction than some existing methods. Finally, we apply our proposed method into breast cancer analysis to identify patients with inflammatory breast cancer subtype and evaluate the associations between micro-RNAs and message RNAs gene expression.

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arXiv2018

An Imputation-Consistency Algorithm for High-Dimensional Missing Data Problems and Beyond

Missing data are frequently encountered in high-dimensional problems, but they are usually difficult to deal with using standard algorithms, such as the expectation-maximization (EM) algorithm and its variants. To tackle this difficulty, some problem-specific algorithms have been developed in the literature, but there still lacks a general algorithm. This work is to fill the gap: we propose a general algorithm for high-dimensional missing data problems. The proposed algorithm works by iterating between an imputation step and a consistency step. At the imputation step, the missing data are imputed conditional on the observed data and the current estimate of parameters; and at the consistency step, a consistent estimate is found for the minimizer of a Kullback-Leibler divergence defined on the pseudo-complete data. For high dimensional problems, the consistent estimate can be found under sparsity constraints. The consistency of the averaged estimate for the true parameter can be established under quite general conditions. The proposed algorithm is illustrated using high-dimensional Gaussian graphical models, high-dimensional variable selection, and a random coefficient model.

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