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This paper studies the problem of statistical inference for genetic relatedness between binary traits based on individual-level genome-wide association data. Specifically, under the high-dimensional logistic regression model, we define parameters characterizing the cross-trait genetic correlation, the genetic covariance and the trait-specific genetic variance. A novel weighted debiasing method is developed for the logistic Lasso estimator and computationally efficient debiased estimators are proposed. The rates of convergence for these estimators are studied and their asymptotic normality is established under mild conditions. Moreover, we construct confidence intervals and statistical tests for these parameters, and provide theoretical justifications for the methods, including the coverage probability and expected length of the confidence intervals, as well as the size and power of the proposed tests. Numerical studies are conducted under both model generated data and simulated genetic data to show the superiority of the proposed methods and their applicability to the analysis of real genetic data. Finally, by analyzing a real data set on autoimmune diseases, we demonstrate the ability to obtain novel insights about the shared genetic architecture between ten pediatric autoimmune diseases.

The underlying physics of astronomical systems governs the relation between their measurable properties. Consequently, quantifying the statistical relationships between system-level observable properties of a population offers insights into the astrophysical drivers of that class of systems. While purely linear models capture behavior over a limited range of system scale, the fact that astrophysics is ultimately scale-dependent implies the need for a more flexible approach to describing population statistics over a wide dynamic range. For such applications, we introduce and implement a class of Kernel-Localized Linear Regression (KLLR) models. KLLR is a natural extension to the commonly-used linear models that allows the parameters of the linear model -- normalization, slope, and covariance matrix -- to be scale-dependent. KLLR performs inference in two steps: (1) it estimates the mean relation between a set of independent variables and a dependent variable and; (2) it estimates the conditional covariance of the dependent variables given a set of independent variables. We demonstrate the model's performance in a simulated setting and showcase an application of the proposed model in analyzing the baryonic content of dark matter halos. As a part of this work, we publicly release a Python implementation of the KLLR method.

We propose Multi-Level Local SGD, a distributed gradient method for learning a smooth, non-convex objective in a heterogeneous multi-level network. Our network model consists of a set of disjoint sub-networks, with a single hub and multiple worker nodes; further, worker nodes may have different operating rates. The hubs exchange information with one another via a connected, but not necessarily complete communication network. In our algorithm, sub-networks execute a distributed SGD algorithm, using a hub-and-spoke paradigm, and the hubs periodically average their models with neighboring hubs. We first provide a unified mathematical framework that describes the Multi-Level Local SGD algorithm. We then present a theoretical analysis of the algorithm; our analysis shows the dependence of the convergence error on the worker node heterogeneity, hub network topology, and the number of local, sub-network, and global iterations. We back up our theoretical results via simulation-based experiments using both convex and non-convex objectives.

When drawing causal inferences about the effects of multiple treatments on clustered survival outcomes using observational data, we need to address implications of the multilevel data structure, multiple treatments, censoring and unmeasured confounding for causal analyses. Few off-the-shelf causal inference tools are available to simultaneously tackle these issues. We develop a flexible random-intercept accelerated failure time model, in which we use Bayesian additive regression trees to capture arbitrarily complex relationships between censored survival times and pre-treatment covariates and use the random intercepts to capture cluster-specific main effects. We develop an efficient Markov chain Monte Carlo algorithm to draw posterior inferences about the population survival effects of multiple treatments and examine the variability in cluster-level effects. We further propose an interpretable sensitivity analysis approach to evaluate the sensitivity of drawn causal inferences about treatment effect to the potential magnitude of departure from the causal assumption of no unmeasured confounding. Expansive simulations empirically validate and demonstrate good practical operating characteristics of our proposed methods. Applying the proposed methods to a dataset on older high-risk localized prostate cancer patients drawn from the National Cancer Database, we evaluate the comparative effects of three treatment approaches on patient survival, and assess the ramifications of potential unmeasured confounding. The methods developed in this work are readily available in the $\textsf{R}$ package $\textsf{riAFTBART}$.

Though remarkable progress has been achieved in various vision tasks, deep neural networks still suffer obvious performance degradation when tested in out-of-distribution scenarios. We argue that the feature statistics (mean and standard deviation), which carry the domain characteristics of the training data, can be properly manipulated to improve the generalization ability of deep learning models. Common methods often consider the feature statistics as deterministic values measured from the learned features and do not explicitly consider the uncertain statistics discrepancy caused by potential domain shifts during testing. In this paper, we improve the network generalization ability by modeling the uncertainty of domain shifts with synthesized feature statistics during training. Specifically, we hypothesize that the feature statistic, after considering the potential uncertainties, follows a multivariate Gaussian distribution. Hence, each feature statistic is no longer a deterministic value, but a probabilistic point with diverse distribution possibilities. With the uncertain feature statistics, the models can be trained to alleviate the domain perturbations and achieve better robustness against potential domain shifts. Our method can be readily integrated into networks without additional parameters. Extensive experiments demonstrate that our proposed method consistently improves the network generalization ability on multiple vision tasks, including image classification, semantic segmentation, and instance retrieval. The code will be released soon at //github.com/lixiaotong97/DSU.

Normalizing flows have recently demonstrated promising results for low-level vision tasks. For image super-resolution (SR), it learns to predict diverse photo-realistic high-resolution (HR) images from the low-resolution (LR) image rather than learning a deterministic mapping. For image rescaling, it achieves high accuracy by jointly modelling the downscaling and upscaling processes. While existing approaches employ specialized techniques for these two tasks, we set out to unify them in a single formulation. In this paper, we propose the hierarchical conditional flow (HCFlow) as a unified framework for image SR and image rescaling. More specifically, HCFlow learns a bijective mapping between HR and LR image pairs by modelling the distribution of the LR image and the rest high-frequency component simultaneously. In particular, the high-frequency component is conditional on the LR image in a hierarchical manner. To further enhance the performance, other losses such as perceptual loss and GAN loss are combined with the commonly used negative log-likelihood loss in training. Extensive experiments on general image SR, face image SR and image rescaling have demonstrated that the proposed HCFlow achieves state-of-the-art performance in terms of both quantitative metrics and visual quality.

Human parsing is for pixel-wise human semantic understanding. As human bodies are underlying hierarchically structured, how to model human structures is the central theme in this task. Focusing on this, we seek to simultaneously exploit the representational capacity of deep graph networks and the hierarchical human structures. In particular, we provide following two contributions. First, three kinds of part relations, i.e., decomposition, composition, and dependency, are, for the first time, completely and precisely described by three distinct relation networks. This is in stark contrast to previous parsers, which only focus on a portion of the relations and adopt a type-agnostic relation modeling strategy. More expressive relation information can be captured by explicitly imposing the parameters in the relation networks to satisfy the specific characteristics of different relations. Second, previous parsers largely ignore the need for an approximation algorithm over the loopy human hierarchy, while we instead address an iterative reasoning process, by assimilating generic message-passing networks with their edge-typed, convolutional counterparts. With these efforts, our parser lays the foundation for more sophisticated and flexible human relation patterns of reasoning. Comprehensive experiments on five datasets demonstrate that our parser sets a new state-of-the-art on each.

Meta learning is a promising solution to few-shot learning problems. However, existing meta learning methods are restricted to the scenarios where training and application tasks share the same out-put structure. To obtain a meta model applicable to the tasks with new structures, it is required to collect new training data and repeat the time-consuming meta training procedure. This makes them inefficient or even inapplicable in learning to solve heterogeneous few-shot learning tasks. We thus develop a novel and principled HierarchicalMeta Learning (HML) method. Different from existing methods that only focus on optimizing the adaptability of a meta model to similar tasks, HML also explicitly optimizes its generalizability across heterogeneous tasks. To this end, HML first factorizes a set of similar training tasks into heterogeneous ones and trains the meta model over them at two levels to maximize adaptation and generalization performance respectively. The resultant model can then directly generalize to new tasks. Extensive experiments on few-shot classification and regression problems clearly demonstrate the superiority of HML over fine-tuning and state-of-the-art meta learning approaches in terms of generalization across heterogeneous tasks.