Learn More
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(More)
We develop a cyclical blockwise coordinate descent algorithm for the multi-task Lasso that efficiently solves problems with thousands of features and tasks. The main result shows that a closed-form Winsorization operator can be obtained for the sup-norm penalized least squares regression. This allows the algorithm to find solutions to very large-scale(More)
We present a new class of models for high-dimensional nonparametric regression and classification called sparse additive models (SpAM). Our methods combine ideas from sparse linear modeling and additive nonparametric regression. We derive a method for fitting the models that is effective even when the number of covariates is larger than the sample size. A(More)
Recent methods for estimating sparse undirected graphs for real-valued data in high dimensional problems rely heavily on the assumption of normality. We show how to use a semiparametric Gaus-sian copula—or " nonparanormal " —for high dimensional inference. Just as additive models extend linear models by replacing linear functions with a set of(More)
In this paper, we propose a semiparametric approach, named nonparanor-mal skeptic, for efficiently and robustly estimating high dimensional undirected graph-ical models. To achieve modeling flexibility, we consider Gaussian Copula graphical models (or the nonparanormal) as proposed by Liu et al. (2009). To achieve estimation robustness, we exploit(More)
We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to a forest; rather, we form kernel density estimates of the bivariate and univariate marginals, and apply Kruskal's(More)
In this paper, we focus on the application of the Peaceman-Rachford splitting method (PRSM) to a convex minimization model with linear constraints and a separable objective function. Compared to the Douglas-Rachford splitting method (DRSM), another splitting method from which the alternating direction method of multipliers originates, PRSM requires more(More)
We prove a new exponential concentration inequality for a plug-in estimator of the Shannon mutual information. Previous results on mutual information estimation only bounded expected error. The advantage of having the exponential inequality is that, combined with the union bound, we can guarantee accurate estimators of the mutual information for many pairs(More)
A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include K-fold cross-validation (K-CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Though these methods work well for low-dimensional problems, they are not(More)