SNP-heritability is a fundamental quantity in the study of complex traits. Recent works have shown that existing methods to estimate genome-wide SNP-heritability yield biases when their assumptions are violated. While various approaches have been proposed to account for frequency- and LD-dependent genetic architectures, it remains unclear which estimates reported in the literature are reliable. Here we show that genome-wide SNP-heritability can be accurately estimated from biobank-scale data irrespective of genetic architecture, without specifying a heritability model or partitioning SNPs by allele frequency and/or LD. We show analytically and through extensive simulations starting from real genotypes (UK Biobank, N = 337K) that, unlike existing methods, our closed-form estimator is robust across a wide range of architectures. We provide estimates of SNP-heritability for 22 complex traits in the UK Biobank and show that, consistent with our results in simulations, existing biobank-scale methods yield estimates up to 30% different from our theoretically-justified approach.

The proportion of phenotypic variance attributable to the additive effects of a given set of genotyped SNPs (i.e. SNP-heritability) is a fundamental quantity in the study of complex traits.Recent works have shown that existing methods to estimate genome-wide SNP-heritability often yield biases when their assumptions are violated. While various approaches have been proposed to account for frequency-and LD-dependent genetic architectures, it remains unclear which estimates of SNP-heritability reported in the literature are reliable. Here we show that genome-wide SNP-heritability can be accurately estimated from biobank-scale data irrespective of the underlying genetic architecture of the trait, without specifying a heritability model or partitioning SNPs by minor allele frequency and/or LD. We use theoretical justifications coupled with extensive simulations starting from real genotypes from the UK Biobank (N=337K) to show that, unlike existing methods, our closed-form estimator for SNP-heritability is highly accurate across a wide range of architectures. We provide estimates of SNP-heritability for 22 complex traits and diseases in the UK Biobank and show that, consistent with our results in simulations, existing biobank-scale methods yield estimates up to 30% different from our theoretically-justified approach.

MotivationHeritability, the proportion of variation in a trait that can be explained by genetic variation, is an important parameter in efforts to understand the genetic architecture of complex phenotypes as well as in the design and interpretation of genome-wide association studies. Attempts to understand the heritability of complex phenotypes attributable to genome-wide single nucleotide polymorphism (SNP) variation data has motivated the analysis of large datasets as well as the development of sophisticated tools to estimate heritability in these datasets. Linear mixed models (LMMs) have emerged as a key tool for heritability estimation where the parameters of the LMMs, i.e. the variance components, are related to the heritability attributable to the SNPs analyzed. Likelihood-based inference in LMMs, however, poses serious computational burdens.ResultsWe propose a scalable randomized algorithm for estimating variance components in LMMs. Our method is based on a method-of-moment estimator that has a runtime complexity O(NMB) for N individuals and M SNPs (where B is a parameter that controls the number of random matrix-vector multiplications). Further, by leveraging the structure of the genotype matrix, we can reduce the time complexity to O(NMBmax( log⁡3N, log⁡3M)).We demonstrate the scalability and accuracy of our method on simulated as well as on empirical data. On standard hardware, our method computes heritability on a dataset of 500 000 individuals and 100 000 SNPs in 38 min.Availability and implementationThe RHE-reg software is made freely available to the research community at: https://github.com/sriramlab/RHE-reg.

Actor-critic (AC) methods have exhibited great empirical success compared with other reinforcement learning algorithms, where the actor uses the policy gradient to improve the learning policy and the critic uses temporal difference learning to estimate the policy gradient. Under the two time-scale learning rate schedule, the asymptotic convergence of AC has been well studied in the literature. However, the non-asymptotic convergence and finite sample complexity of actor-critic methods are largely open. In this work, we provide a non-asymptotic analysis for two time-scale actor-critic methods under non-i.i.d. setting. We prove that the actor-critic method is guaranteed to find a first-order stationary point (i.e., ∇J(θ) 2 2 ≤ ) of the non-concave performance function J(θ), with O( −2.5 ) sample complexity. To the best of our knowledge, this is the first work providing finite-time analysis and sample complexity bound for two time-scale actor-critic methods.

Background: Parkinson's disease (PD) is an irreversible neurodegenerative disease. The diagnosis of PD based on neuroimaging is usually with low-level or deep learning features, which results in difficulties in achieving precision classification or interpreting the clinical significance. Herein, we aimed to extract highorder features by using radiomics approach and achieve acceptable diagnosis accuracy in PD. Methods: In this retrospective multicohort study, we collected 18 F-fluorodeoxyglucose positron emission tomography ( 18 F-FDG PET) images and clinical scale [the Unified Parkinson's Disease Rating Scale (UPDRS) and Hoehn & Yahr scale (H&Y)] from two cohorts. One cohort from Huashan Hospital had 91 normal controls (NC) and 91 PD patients (UPDRS: 22.7±11.7, H&Y: 1.8±0.8), and the other cohort from Wuxi 904 Hospital had 26 NC and 22 PD patients (UPDRS: 20.9±11.6, H&Y: 1.7±0.9). The Huashan cohort was used as the training and test sets by 5-fold cross-validation and the Wuxi cohort was used as another separate testset. After identifying regions of interests (ROIs) based on the atlas-based method, radiomic features were extracted and selected by using autocorrelation and fisher score algorithm. A support vector machine (SVM) was trained to classify PD and NC based on selected radiomic features. In the comparative experiment, we compared our method with the traditional voxel values method. To guarantee the robustness, above processes were repeated in 500 times.Results: Twenty-six brain ROIs were identified. Six thousand one hundred and ten radiomic features were extracted in total. Among them 30 features were remained after feature selection. The accuracies of the proposed method achieved 90.97%±4.66% and 88.08%±5.27% in Huashan and Wuxi test sets, respectively.Conclusions: This study showed that radiomic features and SVM could be used to distinguish between PD and NC based on 18F-FDG PET images.