Tuo Zhao

Patterns and rates of exonic de novo mutations in autism spectrum disorders

Autism spectrum disorders (ASD) are believed to have genetic and environmental origins, yet in only a modest fraction of individuals can specific causes be identified. To identify further genetic risk factors, here we assess the role of de novo mutations in ASD by sequencing the exomes of ASD cases and their parents (n = 175 trios). Fewer than half of the cases (46.3%) carry a missense or nonsense de novo variant, and the overall rate of mutation is only modestly higher than the expected rate. In contrast, the proteins encoded by genes that harboured de novo missense or nonsense mutations showed a higher degree of connectivity among themselves and to previous ASD genes as indexed by protein-protein interaction screens. The small increase in the rate of de novo events, when taken together with the protein interaction results, are consistent with an important but limited role for de novo point mutations in ASD, similar to that documented for de novo copy number variants. Genetic models incorporating these data indicate that most of the observed de novo events are unconnected to ASD; those that do confer risk are distributed across many genes and are incompletely penetrant (that is, not necessarily sufficient for disease). Our results support polygenic models in which spontaneous coding mutations in any of a large number of genes increases risk by 5- to 20-fold. Despite the challenge posed by such models, results from de novo events and a large parallel case–control study provide strong evidence in favour of CHD8 and KATNAL2 as genuine autism risk factors.

Automated diagnoses of attention deficit hyperactive disorder using magnetic resonance imaging

Successful automated diagnoses of attention deficit hyperactive disorder (ADHD) using imaging and functional biomarkers would have fundamental consequences on the public health impact of the disease. In this work, we show results on the predictability of ADHD using imaging biomarkers and discuss the scientific and diagnostic impacts of the research. We created a prediction model using the landmark ADHD 200 data set focusing on resting state functional connectivity (rs-fc) and structural brain imaging. We predicted ADHD status and subtype, obtained by behavioral examination, using imaging data, intelligence quotients and other covariates. The novel contributions of this manuscript include a thorough exploration of prediction and image feature extraction methodology on this form of data, including the use of singular value decompositions (SVDs), CUR decompositions, random forest, gradient boosting, bagging, voxel-based morphometry, and support vector machines as well as important insights into the value, and potentially lack thereof, of imaging biomarkers of disease. The key results include the CUR-based decomposition of the rs-fc-fMRI along with gradient boosting and the prediction algorithm based on a motor network parcellation and random forest algorithm. We conjecture that the CUR decomposition is largely diagnosing common population directions of head motion. Of note, a byproduct of this research is a potential automated method for detecting subtle in-scanner motion. The final prediction algorithm, a weighted combination of several algorithms, had an external test set specificity of 94% with sensitivity of 21%. The most promising imaging biomarker was a correlation graph from a motor network parcellation. In summary, we have undertaken a large-scale statistical exploratory prediction exercise on the unique ADHD 200 data set. The exercise produced several potential leads for future scientific exploration of the neurological basis of ADHD.

Sparse Covariance Matrix Estimation With Eigenvalue Constraints

We propose a new approach for estimating high-dimensional, positive-definite covariance matrices. Our method extends the generalized thresholding operator by adding an explicit eigenvalue constraint. The estimated covariance matrix simultaneously achieves sparsity and positive definiteness. The estimator is rate optimal in the minimax sense and we develop an efficient iterative soft-thresholding and projection algorithm based on the alternating direction method of multipliers. Empirically, we conduct thorough numerical experiments on simulated datasets as well as real data examples to illustrate the usefulness of our method. Supplementary materials for the article are available online.

Positive Semidefinite Rank-Based Correlation Matrix Estimation With Application to Semiparametric Graph Estimation

Many statistical methods gain robustness and flexibility by sacrificing convenient computational structures. In this article, we illustrate this fundamental tradeoff by studying a semiparametric graph estimation problem in high dimensions. We explain how novel computational techniques help to solve this type of problem. In particular, we propose a nonparanormal neighborhood pursuit algorithm to estimate high-dimensional semiparametric graphical models with theoretical guarantees. Moreover, we provide an alternative view to analyze the tradeoff between computational efficiency and statistical error under a smoothing optimization framework. Though this article focuses on the problem of graph estimation, the proposed methodology is widely applicable to other problems with similar structures. We also report thorough experimental results on text, stock, and genomic datasets.

Calibrated Precision Matrix Estimation for High-Dimensional Elliptical Distributions.

We propose a semiparametric method for estimating a precision matrix of high-dimensional elliptical distributions. Unlike most existing methods, our method naturally handles heavy tailness and conducts parameter estimation under a calibration framework, thus achieves improved theoretical rates of convergence and finite sample performance on heavy-tail applications. We further demonstrate the performance of the proposed method using thorough numerical experiments.

Pathwise coordinate optimization for sparse learning: Algorithm and theory

The pathwise coordinate optimization is one of the most important computational frameworks for high dimensional convex and nonconvex sparse learning problems. It differs from the classical coordinate optimization algorithms in three salient features: {\it warm start initialization}, {\it active set updating}, and {\it strong rule for coordinate preselection}. Such a complex algorithmic structure grants superior empirical performance, but also poses significant challenge to theoretical analysis. To tackle this long lasting problem, we develop a new theory showing that these three features play pivotal roles in guaranteeing the outstanding statistical and computational performance of the pathwise coordinate optimization framework. Particularly, we analyze the existing pathwise coordinate optimization algorithms and provide new theoretical insights into them. The obtained insights further motivate the development of several modifications to improve the pathwise coordinate optimization framework, which guarantees linear convergence to a unique sparse local optimum with optimal statistical properties in parameter estimation and support recovery. This is the first result on the computational and statistical guarantees of the pathwise coordinate optimization framework in high dimensions. Thorough numerical experiments are provided to support our theory.

Accelerated Path-Following Iterative Shrinkage Thresholding Algorithm With Application to Semiparametric Graph Estimation

We propose an accelerated path-following iterative shrinkage thresholding algorithm (APISTA) for solving high-dimensional sparse nonconvex learning problems. The main difference between APISTA and the path-following iterative shrinkage thresholding algorithm (PISTA) is that APISTA exploits an additional coordinate descent subroutine to boost the computational performance. Such a modification, though simple, has profound impact: APISTA not only enjoys the same theoretical guarantee as that of PISTA, that is, APISTA attains a linear rate of convergence to a unique sparse local optimum with good statistical properties, but also significantly outperforms PISTA in empirical benchmarks. As an application, we apply APISTA to solve a family of nonconvex optimization problems motivated by estimating sparse semiparametric graphical models. APISTA allows us to obtain new statistical recovery results that do not exist in the existing literature. Thorough numerical results are provided to back up our theory.