Genomic data are subject to various sources of confounding, such as demographic variables, biological heterogeneity, and batch effects. To identify genomic features associated with a variable of interest in the presence of confounders, the traditional approach involves fitting a confounder-adjusted regression model to each genomic feature, followed by multiplicity correction. This study shows that the traditional approach was sub-optimal and proposes a new two-dimensional false discovery rate control framework (2dFDR+) that provides significant power improvement over the conventional method and applies to a wide range of settings. 2dFDR+ uses marginal independence test statistics as auxiliary information to filter out less promising features, and FDR control is performed based on conditional independence test statistics in the remaining features. 2dFDR+ provides (asymptotically) valid inference from samples in settings where the conditional distribution of the genomic variables given the covariate of interest and the confounders is arbitrary and completely unknown. To achieve this goal, our method requires the conditional distribution of the covariate given the confounders to be known or can be estimated from the data. We develop a new procedure to simultaneously select the two cutoff values for the marginal and conditional independence test statistics. 2dFDR+ is proved to offer asymptotic FDR control and dominate the power of the traditional procedure. Promising finite sample performance is demonstrated via extensive simulations and real data applications.
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Two-stage randomized experiments are becoming an increasingly popular experimental design for causal inference when the outcome of one unit may be affected by the treatment assignments of other units in the same cluster. In this paper, we provide a methodological framework for general tools of statistical inference and power analysis for two-stage randomized experiments. Under the randomization-based framework, we consider the estimation of a new direct effect of interest as well as the average direct and spillover effects studied in the literature. We provide unbiased estimators of these causal quantities and their conservative variance estimators in a general setting. Using these results, we then develop hypothesis testing procedures and derive sample size formulas. We theoretically compare the two-stage randomized design with the completely randomized and cluster randomized designs, which represent two limiting designs. Finally, we conduct simulation studies to evaluate the empirical performance of our sample size formulas. For empirical illustration, the proposed methodology is applied to the randomized evaluation of the Indian national health insurance program. An open-source software package is available for implementing the proposed methodology.
Understanding and modelling children's cognitive processes and their behaviour in the context of their interaction with robots and social artificial intelligence systems is a fundamental prerequisite for meaningful and effective robot interventions. However, children's development involve complex faculties such as exploration, creativity and curiosity which are challenging to model. Also, often children express themselves in a playful way which is different from a typical adult behaviour. Different children also have different needs, and it remains a challenge in the current state of the art that those of neurodiverse children are under-addressed. With this workshop, we aim to promote a common ground among different disciplines such as developmental sciences, artificial intelligence and social robotics and discuss cutting-edge research in the area of user modelling and adaptive systems for children.
We propose a sequential, anytime valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood ratios and allow valid inference at arbitrary stopping times. In accordance with the recently introduced model-X setting, our test depends on the availability of the conditional distribution of $X$ given $Z$, or at least a sufficiently sharp approximation thereof. Within this setting, we derive a full characterization of e-statistics for testing conditional independence, investigate growth-rate optimal e-statistics and their power properties, and show that our method yields tests with asymptotic power one in the special case of a logistic regression model. A simulation study is done to demonstrate that the approach is robust with respect to violations of the model-X assumption and competitive in terms of power when compared to established sequential and non-sequential testing methods.
In this paper, we study unmanned aerial vehicles (UAVs) assisted wireless data aggregation (WDA) in multicluster networks, where multiple UAVs simultaneously perform different WDA tasks via over-the-air computation (AirComp) without terrestrial base stations. This work focuses on maximizing the minimum amount of WDA tasks performed among all clusters by optimizing the UAV's trajectory and transceiver design as well as cluster scheduling and association, while considering the WDA accuracy requirement. Such a joint design is critical for interference management in multi-cluster AirComp networks, via enhancing the signal quality between each UAV and its associated cluster for signal alignment and meanwhile reducing the inter-cluster interference between each UAV and its nonassociated clusters. Although it is generally challenging to optimally solve the formulated non-convex mixed-integer nonlinear programming, an efficient iterative algorithm as a compromise approach is developed by exploiting bisection and block coordinate descent methods, yielding an optimal transceiver solution in each iteration. The optimal binary variables and a suboptimal trajectory are obtained by using the dual method and successive convex approximation, respectively. Simulations show the considerable performance gains of the proposed design over benchmarks and the superiority of deploying multiple UAVs in increasing the number of performed tasks while reducing access delays.
Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More specifically, we propose the first use of such bounds to improve Gaussian process (GP) posterior sampling and Bayesian optimization (BO). That is, we transform a GP model satisfying the given bounds, and then sample and weight functions from its posterior. To further exploit these bounds in BO settings, we present bounded entropy search (BES) to select the point gaining the most information about the underlying function, estimated by the GP samples, while satisfying the output constraints. We characterize the sample variance bounds and show that the decision made by BES is explainable. Our proposed approach is conceptually straightforward and can be used as a plug in extension to existing methods for GP posterior sampling and Bayesian optimization.
Machine learning (ML) formalizes the problem of getting computers to learn from experience as optimization of performance according to some metric(s) on a set of data examples. This is in contrast to requiring behaviour specified in advance (e.g. by hard-coded rules). Formalization of this problem has enabled great progress in many applications with large real-world impact, including translation, speech recognition, self-driving cars, and drug discovery. But practical instantiations of this formalism make many assumptions - for example, that data are i.i.d.: independent and identically distributed - whose soundness is seldom investigated. And in making great progress in such a short time, the field has developed many norms and ad-hoc standards, focused on a relatively small range of problem settings. As applications of ML, particularly in artificial intelligence (AI) systems, become more pervasive in the real world, we need to critically examine these assumptions, norms, and problem settings, as well as the methods that have become de-facto standards. There is much we still do not understand about how and why deep networks trained with stochastic gradient descent are able to generalize as well as they do, why they fail when they do, and how they will perform on out-of-distribution data. In this thesis I cover some of my work towards better understanding deep net generalization, identify several ways assumptions and problem settings fail to generalize to the real world, and propose ways to address those failures in practice.
Considerable debate has been generated in recent literature on whether non-confounding covariates should be adjusted for in the analysis of case-control data through logistic regression, and limited theoretical results are available regarding this problem. Zhang et al. (2018) proposed a constrained maximum likelihood approach that is seemingly more powerful than the approaches with or without adjusting for non-confounding covariates in logistic regression, but no theoretical justification was provided regarding this empirical finding. We provide rigorous justification for the relative performances of the above three approaches through Pitman's asymptotic relative efficiencies. Specifically, the constrained maximum likelihood approach is proved to be uniformly most powerful. On the other hand, the relative performance of the other two approaches heavily depends on disease prevalence, that is, adjust for non-confounding covariates can lead to power loss when the disease prevalence is low, but this is not the case otherwise.
Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear systems to estimate their transition matrices more accurately. To address this problem, the current paper investigates methods for jointly estimating the transition matrices of multiple systems. It is assumed that the transition matrices are unknown linear functions of some unknown shared basis matrices. We establish finite-time estimation error rates that fully reflect the roles of trajectory lengths, dimension, and number of systems under consideration. The presented results are fairly general and show the significant gains that can be achieved by pooling data across systems in comparison to learning each system individually. Further, they are shown to be robust against model misspecifications. To obtain the results, we develop novel techniques that are of interest for addressing similar joint-learning problems. They include tightly bounding estimation errors in terms of the eigen-structures of transition matrices, establishing sharp high probability bounds for singular values of dependent random matrices, and capturing effects of misspecified transition matrices as the systems evolve over time.
Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.
Games and simulators can be a valuable platform to execute complex multi-agent, multiplayer, imperfect information scenarios with significant parallels to military applications: multiple participants manage resources and make decisions that command assets to secure specific areas of a map or neutralize opposing forces. These characteristics have attracted the artificial intelligence (AI) community by supporting development of algorithms with complex benchmarks and the capability to rapidly iterate over new ideas. The success of artificial intelligence algorithms in real-time strategy games such as StarCraft II have also attracted the attention of the military research community aiming to explore similar techniques in military counterpart scenarios. Aiming to bridge the connection between games and military applications, this work discusses past and current efforts on how games and simulators, together with the artificial intelligence algorithms, have been adapted to simulate certain aspects of military missions and how they might impact the future battlefield. This paper also investigates how advances in virtual reality and visual augmentation systems open new possibilities in human interfaces with gaming platforms and their military parallels.
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