SummaryThe genetic architecture of autism spectrum disorder involves the interplay of common and rare variation and their impact on hundreds of genes. Using exome sequencing, analysis of rare coding variation in 3,871 autism cases and 9,937 ancestry-matched or parental controls implicates 22 autosomal genes at a false discovery rate (FDR) < 0.05, and a set of 107 autosomal genes strongly enriched for those likely to affect risk (FDR < 0.30). These 107 genes, which show unusual evolutionary constraint against mutations, incur de novo loss-of-function mutations in over 5% of autistic subjects. Many of the genes implicated encode proteins for synaptic, transcriptional, and chromatin remodeling pathways. These include voltage-gated ion channels regulating propagation of action potentials, pacemaking, and excitability-transcription coupling, as well as histone-modifying enzymes and chromatin remodelers, prominently histone post-translational modifications involving lysine methylation/demethylation.

SUMMARY Autism spectrum disorder (ASD) is a complex developmental syndrome of unknown etiology. Recent studies employing exome- and genome-wide sequencing have identified nine high-confidence ASD (hcASD) genes. Working from the hypothesis that ASD-associated mutations in these biologically pleiotropic genes will disrupt intersecting developmental processes to contribute to a common phenotype, we have attempted to identify time periods, brain regions, and cell types in which these genes converge. We have constructed coexpression networks based on the hcASD “seed” genes, leveraging a rich expression data set encompassing multiple human brain regions across human development and into adulthood. By assessing enrichment of an independent set of probable ASD (pASD) genes, derived from the same sequencing studies, we demonstrate a key point of convergence in midfetal layer 5/6 cortical projection neurons. This approach informs when, where, and in what cell types mutations in these specific genes may be productively studied to clarify ASD pathophysiology.

We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as log n, with n the number of nodes. This result applies to some popular polynomial time spectral clustering algorithms and is further extended to degree corrected stochastic block models using a spherical k-median spectral clustering method. A key component of our analysis is a combinatorial bound on the spectrum of binary random matrices, which is sharper than the conventional matrix Bernstein inequality and may be of independent interest.

We develop a general framework for distribution-free predictive inference in regression, using conformal inference. The proposed methodology allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preserves the consistency properties of the original estimator under standard assumptions, while guaranteeing finite-sample marginal coverage even when these assumptions do not hold. We analyze and compare, both empirically and theoretically, the two major variants of our conformal framework: full conformal inference and split conformal inference, along with a related jackknife method. These methods offer different tradeoffs between statistical accuracy (length of resulting prediction intervals) and computational efficiency. As extensions, we develop a method for constructing valid in-sample prediction intervals called rank-one-out conformal inference, which has essentially the same computational efficiency as split conformal inference. We also describe an extension of our procedures for producing prediction bands with locally varying length, in order to adapt to heteroskedascity in the data. Finally, we propose a model-free notion of variable importance, called leave-one-covariate-out or LOCO inference. Accompanying this paper is an R package conformalInference that implements all of the proposals we have introduced. In the spirit of reproducibility, all of our empirical results can also be easily (re)generated using this package.

We show by means of several examples that robust statistical estimators present an excellent starting point for differentially private estimators. Our algorithms use a new paradigm for differentially private mechanisms, which we call Propose-Test-Release (PTR), and for which we give a formal definition and general composition theorems.