We study a class of decision-making problems with one-sided feedback, where outcomes are only observable for specific actions. A typical example is bank loans, where the repayment status is known only if a loan is approved and remains undefined if rejected. In such scenarios, conventional approaches to causal decision evaluation and learning from observational data are not directly applicable. In this paper, we introduce a novel value function to evaluate decision rules that addresses the issue of undefined counterfactual outcomes. Without assuming no unmeasured confounders, we establish the identification of the value function using shadow variables. Furthermore, leveraging semiparametric theory, we derive the efficiency bound for the proposed value function and develop efficient methods for decision evaluation and learning. Numerical experiments and a real-world data application demonstrate the empirical performance of our proposed methods.

Interference, a key concept in causal inference, extends the reward modeling process by accounting for the impact of one unit’s actions on the rewards of others. In contextual bandit (CB) settings where multiple units are present in the same round, interference can significantly affect the estimation of expected rewards for different arms, thereby influencing the decision-making process. Although some prior work has explored multi-agent and adversarial bandits in interference-aware settings, how to model interference in CB remains significantly underexplored. In this paper, we introduce a systematic framework to address interference in Linear CB (LinCB), bridging the gap between causal inference and online decision-making. We propose a series of algorithms that explicitly quantify the interference effect in the reward modeling process and provide comprehensive theoretical guarantees, including sublinear regret bounds, finite sample upper bounds, and asymptotic properties. The effectiveness of our approach is demonstrated through simulations and a synthetic data generated based on MovieLens data.

Off-Policy Evaluation (OPE) aims to estimate the value of a target policy using offline data collected from potentially different policies. In real-world applications, however, logged data often suffers from missingness. While OPE has been extensively studied in the literature, a theoretical understanding of how missing data affects OPE results remains unclear. In this paper, we investigate OPE in the presence of monotone missingness and theoretically demonstrate that the value estimates remain unbiased under ignorable missingness but can be biased under nonignorable (informative) missingness. To retain the consistency of value estimation, we propose an inverse probability weighting value estimator and conduct statistical inference to quantify the uncertainty of the estimates. Through a series of numerical experiments, we empirically demonstrate that our proposed estimator yields a more reliable value inference under missing data.

Neural operator is considered a popular data-driven alternative to traditional partial differential equation (PDE) solvers. However, most current solutions, whether fulfilling computations in frequency, Laplacian, and wavelet domains, all deviate far from the intrinsic PDE space. While with meticulous network architecture elaborated, the deviation often leads to biased accuracy. To address the issue, we open a new avenue that pioneers leveraging Radon transform to decompose the input space, finalizing a novel Radon neural operator (RNO) to solve PDEs in infinite-dimensional function space. Distinct from previous solutions, we project the input data into the sinogram domain, shrinking the multi-dimensional transformations to a reduced-dimensional counterpart and fitting compactly with the PDE space. Theoretically, we prove that RNO obeys a property of bilipschitz strongly monotonicity under diffeomorphism, providing deeper insights to guarantee the desired accuracy than typical discrete invariance or continuous-discrete equivalence. Within the sinogram domain, we further evidence that different angles contribute unequally to the overall space, thus engineering a reweighting technique to enable more effective PDE solutions. On that basis, a sinogram-domain convolutional layer is crafted, which operates on a fixed $\theta$-grid that is decoupled from the PDE space, further enjoying a natural guarantee of discrete invariance. Extensive experiments demonstrate that RNO sets new state-of-the-art (SOTA) scores across massive standard benchmarks, with superior generalization performance enjoyed. Code is available at <https://github.com/wenbin-lu/Radon-Neural-Operator>.

Truncation by death, a prevalent challenge in critical care, renders traditional dynamic treatment regime (DTR) evaluation inapplicable due to ill-defined potential outcomes. We introduce a principal stratification-based method, focusing on the always-survivor value function. We derive a semiparametrically efficient, multiply robust estimator for multi-stage DTRs, demonstrating its robustness and efficiency. Empirical validation and an application to electronic health records showcase its utility for personalized treatment optimization.

Typical off-policy evaluation (OPE) and off-policy learning (OPL) are not well-defined problems under "truncation by death", where the outcome of interest is not defined after some events, such as death. The standard OPE no longer yields consistent estimators, and the standard OPL results in suboptimal policies. In this paper, we formulate OPE and OPL using principal stratification under "truncation by death". We propose a survivor value function for a subpopulation whose outcomes are always defined regardless of treatment conditions. We establish a novel identification strategy under principal ignorability, and derive the semiparametric efficiency bound of an OPE estimator. Then, we propose multiply robust estimators for OPE and OPL. We show that the proposed estimators are consistent and asymptotically normal even with flexible semi/nonparametric models for nuisance functions approximation. Moreover, under mild rate conditions of nuisance functions approximation, the estimators achieve the semiparametric efficiency bound. Finally, we conduct experiments to demonstrate the empirical performance of the proposed estimators.

An individualized decision rule (IDR) is a decision function that assigns each individual a given treatment based on his/her observed characteristics. Most of the existing works in the literature consider settings with binary or finitely many treatment options. In this paper, we focus on the continuous treatment setting and propose a jump interval-learning to develop an individualized interval-valued decision rule (I2DR) that maximizes the expected outcome. Unlike IDRs that recommend a single treatment, the proposed I2DR yields an interval of treatment options for each individual, making it more flexible to implement in practice. To derive an optimal I2DR, our jump interval-learning method estimates the conditional mean of the outcome given the treatment and the covariates via jump penalized regression, and derives the corresponding optimal I2DR based on the estimated outcome regression function. The regressor is allowed to be either linear for clear interpretation or deep neural network to model complex treatment-covariates interactions. To implement jump interval-learning, we develop a searching algorithm based on dynamic programming that efficiently computes the outcome regression function. Statistical properties of the resulting I2DR are established when the outcome regression function is either a piecewise or continuous function over the treatment space. We further develop a procedure to infer the mean outcome under the (estimated) optimal policy. Extensive simulations and a real data application to a Warfarin study are conducted to demonstrate the empirical validity of the proposed I2DR.

In this paper, we present a framework for moving compute and data between processing elements in a distributed heterogeneous system. The implementation of the framework is based on the LLVM compiler toolchain combined with the UCX communication framework. The framework can generate binary machine code or LLVM bitcode for multiple CPU architectures and move the code to remote machines while dynamically optimizing and linking the code on the target platform. The remotely injected code can recursively propagate itself to other remote machines or generate new code. The goal of this paper is threefold: (a) to present an ar-chitecture and implementation of the framework that provides essential infrastructure to program a new class of disaggregated systems wherein heterogeneous programming elements such as compute nodes and data processing units (DPUs) are distributed across the system, (b) to demonstrate how the framework can be integrated with modern, high-level programming languages such as Julia, and (c) to demonstrate and evaluate a new class of eXtended Remote Direct Memory Access (X-RDMA) communication operations that are enabled by this framework. To evaluate the capabilities of the framework, we used a cluster with Fujitsu CPUs and heterogeneous cluster with Intel CPUs and BlueField-2 DPUs interconnected using high-performance RDMA fabric. We demonstrated an X-RDMA pointer chase application that outperforms an RDMA GET-based implementation by 70% and is as fast as Active Messages, but does not require function predeployment on remote platforms.

Online A/B testing plays a critical role in the high-tech industry to guide product development and accelerate innovation. It performs a null hypothesis statistical test to determine which variant is better. However, a typical A/B test presents two problems: (i) a fixed-horizon framework inflates the false-positive errors under continuous monitoring; (ii) the homogeneous effects assumption fails to identify a subgroup with a beneficial treatment effect. In this paper, we propose a sequential test for sub group t reatment effects based on val ue difference, named SUBTLE, to address these two problems simultaneously. The SUBTLE allows the experimenters to “peek” at the results during the experiment without harming the statistical guarantees. It assumes heterogeneous treatment effects and aims to test if some subgroup of the population will benefit from the investigative treatment. If the testing result indicates the existence of such a subgroup, a subgroup will be identified using a readily available estimated optimal treatment rule. We examine the empirical performance of our proposed test on both simulations and a real dataset. The results show that the SUBTLE has high detection power with controlled type I error at any time, is more robust to noise covariates, and can achieve early stopping compared with the corresponding fixed-horizon test.

We consider off-policy evaluation (OPE) in continuous treatment settings, such as personalized dose-finding. In OPE, one aims to estimate the mean outcome under a new treatment decision rule using historical data generated by a different decision rule. Most existing works on OPE focus on discrete treatment settings. To handle continuous treatments, we develop a novel estimation method for OPE using deep jump learning. The key ingredient of our method lies in adaptively discretizing the treatment space using deep discretization, by leveraging deep learning and multi-scale change point detection. This allows us to apply existing OPE methods in discrete treatments to handle continuous treatments. Our method is further justified by theoretical results, simulations, and a real application to Warfarin Dosing.

MOTIVATION: Facilitated by technological advances and the decrease in costs, it is feasible to gather subject data from several omics platforms. Each platform assesses different molecular events, and the challenge lies in efficiently analyzing these data to discover novel disease genes or mechanisms. A common strategy is to regress the outcomes on all omics variables in a gene set. However, this approach suffers from problems associated with high-dimensional inference. RESULTS: We introduce a tensor-based framework for variable-wise inference in multi-omics analysis. By accounting for the matrix structure of an individual's multi-omics data, the proposed tensor methods incorporate the relationship among omics effects, reduce the number of parameters, and boost the modeling efficiency. We derive the variable-specific tensor test and enhance computational efficiency of tensor modeling. Using simulations and data applications on the Cancer Cell Line Encyclopedia (CCLE), we demonstrate our method performs favorably over baseline methods and will be useful for gaining biological insights in multi-omics analysis. AVAILABILITY AND IMPLEMENTATION: R function and instruction are available from the authors' website: https://www4.stat.ncsu.edu/~jytzeng/Software/TR.omics/TRinstruction.pdf. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We propose a new framework for online testing of heterogeneous treatment effects. The proposed test, named sequential score test (SST), is able to control type I error under continuous monitoring and detect multi-dimensional heterogeneous treatment effects. We provide an online p-value calculation for SST, making it convenient for continuous monitoring, and extend our tests to online multiple testing settings by controlling the false discovery rate. We examine the empirical performance of the proposed tests and compare them with a state-of-art online test, named mSPRT using simulations and a real data. The results show that our proposed test controls type I error at any time, has higher detection power and allows quick inference on online A/B testing.

In the current era of personalized recommendation, one major interest is to develop an optimal individualized decision rule that assigns individuals with the best treatment option according to their covariates. Estimation of optimal decision rules (ODR) has been extensively investigated recently, however, at present, no testing procedure is proposed to verify whether these ODRs are significantly better than the naive decision rule that always assigning individuals to a fixed treatment option. In this paper, we propose a testing procedure for detecting the existence of an ODR that is better than the naive decision rule under the randomized trials. We construct the proposed test based on the difference of estimated value functions using the augmented inverse probability weighted method. The asymptotic distributions of the proposed test statistic under the null and local alternative hypotheses are established. Based on the established asymptotic distributions, we further develop a sample size calculation formula for testing the existence of an ODR in designing A/B tests. Extensive simulations and a real data application to a schizophrenia clinical trial data are conducted to demonstrate the empirical validity of the proposed methods.

The Markov assumption (MA) is fundamental to the empirical validity of reinforcement learning. In this paper, we propose a novel Forward-Backward Learning procedure to test MA in sequential decision making. The proposed test does not assume any parametric form on the joint distribution of the observed data and plays an important role for identifying the optimal policy in high-order Markov decision processes (MDPs) and partially observable MDPs. Theoretically, we establish the validity of our test. Empirically, we apply our test to both synthetic datasets and a real data example from mobile health studies to illustrate its usefulness.

In this article, we propose novel structural nested models to estimate causal effects of continuous treatments based on mobile health data. To find the treatment regime which optimizes the short-term outcomes for the patients, we define the weighted lag K advantage. The optimal treatment regime is then defined to be the one which maximizes this advantage. This method imposes minimal assumptions on the data generating process. Statistical inference can also be provided for the estimated parameters. Simulation studies and an application to the Ohio type 1 diabetes dataset show that our method could provide meaningful insights for dose suggestions with mobile health data.

An individualized dose rule recommends a dose level within a continuous safe dose range based on patient level information such as physical conditions, genetic factors and medication histories. Traditionally, personalized dose finding process requires repeating clinical visits of the patient and frequent adjustments of the dosage. Thus the patient is constantly exposed to the risk of underdosing and overdosing during the process. Statistical methods for finding an optimal individualized dose rule can lower the costs and risks for patients. In this article, we propose a kernel assisted learning method for estimating the optimal individualized dose rule. The proposed methodology can also be applied to all other continuous decision-making problems. Advantages of the proposed method include robustness to model misspecification and capability of providing statistical inference for the estimated parameters. In the simulation studies, we show that this method is capable of identifying the optimal individualized dose rule and produces favorable expected outcomes in the population. Finally, we illustrate our approach using data from a warfarin dosing study for thrombosis patients.

Precision medicine is an emerging medical approach that allows physicians to select the treatment options based on individual patient information. The goal of precision medicine is to identify the optimal treatment regime (OTR) that yields the most favorable clinical outcome. Prior to adopting any OTR in clinical practice, it is crucial to know the impact of implementing such a policy. Although considerable research has been devoted to estimating the OTR in the literature, less attention has been paid to statistical inference of the OTR. Challenges arise in the nonregular cases where the OTR is not uniquely defined. To deal with nonregularity, we develop a novel inference method for the mean outcome under an OTR (the optimal value function) based on subsample aggregating (subagging). The proposed method can be applied to multi-stage studies where treatments are sequentially assigned over time. Bootstrap aggregating (bagging) and subagging have been recognized as effective vari- ance reduction techniques to improve unstable estimators or classifiers (Buhlmann and Yu, 2002). However, it remains unknown whether these approaches can yield valid inference results. We show the proposed confidence interval (CI) for the optimal value function achieves nominal coverage. In addition, due to the variance reduction effect of subagging, our method enjoys certain statistical optimality. Specifically, we show that the mean squared error of the proposed value estimator is strictly smaller than that based on the simple sample-splitting estimator in the nonregular cases. Moreover, under certain conditions, the length of our proposed CI is shown to be on average shorter than CIs constructed based on the existing state-of-the-art method (Luedtke and van der Laan, 2016) and the 'oracle' method which works as well as if an OTR were known. Extensive numerical studies are conducted to back up our theoretical findings.

Copy number variants (CNVs) are the gain or loss of DNA segments in the genome that can vary in dosage and length. CNVs comprise a large proportion of variation in human genomes and impact health conditions. To detect rare CNV associations, kernel-based methods have been shown to be a powerful tool due to their flexibility in modeling the aggregate CNV effects, their ability to capture effects from different CNV features, and their accommodation of effect heterogeneity. To perform a kernel association test, a CNV locus needs to be defined so that locus-specific effects can be retained during aggregation. However, CNV loci are arbitrarily defined and different locus definitions can lead to different performance depending on the underlying effect patterns. In this work, we develop a new kernel-based test called CONCUR (i.e., copy number profile curve-based association test) that is free from a definition of locus and evaluates CNV-phenotype associations by comparing individuals' copy number profiles across the genomic regions. CONCUR is built on the proposed concepts of "copy number profile curves" to describe the CNV profile of an individual, and the "common area under the curve (cAUC) kernel" to model the multi-feature CNV effects. The proposed method captures the effects of CNV dosage and length, accounts for the numerical nature of copy numbers, and accommodates between- and within-locus etiological heterogeneity without the need to define artificial CNV loci as required in current kernel methods. In a variety of simulation settings, CONCUR shows comparable or improved power over existing approaches. Real data analyses suggest that CONCUR is well powered to detect CNV effects in the Swedish Schizophrenia Study and the Taiwan Biobank.

Statistical relational learning is primarily concerned with learning and inferring relationships between entities in large-scale knowledge graphs. Nickel et al. (2011) proposed a RESCAL tensor factorization model for statistical relational learning, which achieves better or at least comparable results on common benchmark data sets when compared to other state-of-the-art methods. Given a positive integer $s$, RESCAL computes an $s$-dimensional latent vector for each entity. The latent factors can be further used for solving relational learning tasks, such as collective classification, collective entity resolution and link-based clustering. The focus of this paper is to determine the number of latent factors in the RESCAL model. Due to the structure of the RESCAL model, its log-likelihood function is not concave. As a result, the corresponding maximum likelihood estimators (MLEs) may not be consistent. Nonetheless, we design a specific pseudometric, prove the consistency of the MLEs under this pseudometric and establish its rate of convergence. Based on these results, we propose a general class of information criteria and prove their model selection consistencies when the number of relations is either bounded or diverges at a proper rate of the number of entities. Simulations and real data examples show that our proposed information criteria have good finite sample properties.

Rare variants are of increasing interest to genetic association studies because of their etiological contributions to human complex diseases. Due to the rarity of the mutant events, rare variants are routinely analyzed on an aggregate level. While aggregation analyses improve the detection of global-level signal, they are not able to pinpoint causal variants within a variant set. To perform inference on a localized level, additional information, e.g., biological annotation, is often needed to boost the information content of a rare variant. Following the observation that important variants are likely to cluster together on functional domains, we propose a protein structure guided local test (POINT) to provide variant-specific association information using structure-guided aggregation of signal. Constructed under a kernel machine framework, POINT performs local association testing by borrowing information from neighboring variants in the 3-dimensional protein space in a data-adaptive fashion. Besides merely providing a list of promising variants, POINT assigns each variant a p-value to permit variant ranking and prioritization. We assess the selection performance of POINT using simulations and illustrate how it can be used to prioritize individual rare variants in PCSK9, ANGPTL4 and CETP in the Action to Control Cardiovascular Risk in Diabetes (ACCORD) clinical trial data.

Genetic association analyses of rare variants in next-generation sequencing (NGS) studies are fundamentally challenging due to the presence of a very large number of candidate variants at extremely low minor allele frequencies. Recent developments often focus on pooling multiple variants to provide association analysis at the gene instead of the locus level. Nonetheless, pinpointing individual variants is a critical goal for genomic researches as such information can facilitate the precise delineation of molecular mechanisms and functions of genetic factors on diseases. Due to the extreme rarity of mutations and high-dimensionality, significances of causal variants cannot easily stand out from those of noncausal ones. Consequently, standard false-positive control procedures, such as the Bonferroni and false discovery rate (FDR), are often impractical to apply, as a majority of the causal variants can only be identified along with a few but unknown number of noncausal variants. To provide informative analysis of individual variants in large-scale sequencing studies, we propose the Adaptive False-Negative Control (AFNC) procedure that can include a large proportion of causal variants with high confidence by introducing a novel statistical inquiry to determine those variants that can be confidently dispatched as noncausal. The AFNC provides a general framework that can accommodate for a variety of models and significance tests. The procedure is computationally efficient and can adapt to the underlying proportion of causal variants and quality of significance rankings. Extensive simulation studies across a plethora of scenarios demonstrate that the AFNC is advantageous for identifying individual rare variants, whereas the Bonferroni and FDR are exceedingly over-conservative for rare variants association studies. In the analyses of the CoLaus dataset, AFNC has identified individual variants most responsible for gene-level significances. Moreover, single-variant results using the AFNC have been successfully applied to infer related genes with annotation information.