Ruoqing Zhu

Yifan Chen, Tianning Xu, Dilek Hakkani-Tur et al.

Multiple sampling-based methods have been developed for approximating and accelerating node embedding aggregation in graph convolutional networks (GCNs) training. Among them, a layer-wise approach recursively performs importance sampling to select neighbors jointly for existing nodes in each layer. This paper revisits the approach from a matrix approximation perspective, and identifies two issues in the existing layer-wise sampling methods: suboptimal sampling probabilities and estimation biases induced by sampling without replacement. To address these issues, we accordingly propose two remedies: a new principle for constructing sampling probabilities and an efficient debiasing algorithm. The improvements are demonstrated by extensive analyses of estimation variance and experiments on common benchmarks. Code and algorithm implementations are publicly available at https://github.com/ychen-stat-ml/GCN-layer-wise-sampling .

Wenzhuo Zhou, Yuhan Li, Ruoqing Zhu et al.

We study high-confidence off-policy evaluation in the context of infinite-horizon Markov decision processes, where the objective is to establish a confidence interval (CI) for the target policy value using only offline data pre-collected from unknown behavior policies. This task faces two primary challenges: providing a comprehensive and rigorous error quantification in CI estimation, and addressing the distributional shift that results from discrepancies between the distribution induced by the target policy and the offline data-generating process. Motivated by an innovative unified error analysis, we jointly quantify the two sources of estimation errors: the misspecification error on modeling marginalized importance weights and the statistical uncertainty due to sampling, within a single interval. This unified framework reveals a previously hidden tradeoff between the errors, which undermines the tightness of the CI. Relying on a carefully designed discriminator function, the proposed estimator achieves a dual purpose: breaking the curse of the tradeoff to attain the tightest possible CI, and adapting the CI to ensure robustness against distributional shifts. Our method is applicable to time-dependent data without assuming any weak dependence conditions via leveraging a local supermartingale/martingale structure. Theoretically, we show that our algorithm is sample-efficient, error-robust, and provably convergent even in non-linear function approximation settings. The numerical performance of the proposed method is examined in synthetic datasets and an OhioT1DM mobile health study.

Yuhan Li, Wenzhuo Zhou, Ruoqing Zhu

Many real-world applications of reinforcement learning (RL) require making decisions in continuous action environments. In particular, determining the optimal dose level plays a vital role in developing medical treatment regimes. One challenge in adapting existing RL algorithms to medical applications, however, is that the popular infinite support stochastic policies, e.g., Gaussian policy, may assign riskily high dosages and harm patients seriously. Hence, it is important to induce a policy class whose support only contains near-optimal actions, and shrink the action-searching area for effectiveness and reliability. To achieve this, we develop a novel \emph{quasi-optimal learning algorithm}, which can be easily optimized in off-policy settings with guaranteed convergence under general function approximations. Theoretically, we analyze the consistency, sample complexity, adaptability, and convergence of the proposed algorithm. We evaluate our algorithm with comprehensive simulated experiments and a dose suggestion real application to Ohio Type 1 diabetes dataset.

Hanwen Ye, Wenzhuo Zhou, Ruoqing Zhu et al.

Recent advances in dynamic treatment regimes (DTRs) facilitate the search for optimal treatments, which are tailored to individuals' specific needs and able to maximize their expected clinical benefits. However, existing algorithms relying on consistent trajectories, such as inverse probability weighting estimators (IPWEs), could suffer from insufficient sample size under optimal treatments and a growing number of decision-making stages, particularly in the context of chronic diseases. To address these challenges, we propose a novel individualized learning method which estimates the DTR with a focus on prioritizing alignment between the observed treatment trajectory and the one obtained by the optimal regime across decision stages. By relaxing the restriction that the observed trajectory must be fully aligned with the optimal treatments, our approach substantially improves the sample efficiency and stability of IPWE-based methods. In particular, the proposed learning scheme builds a more general framework which includes the popular outcome weighted learning framework as a special case of ours. Moreover, we introduce the notion of stage importance scores along with an attention mechanism to explicitly account for heterogeneity among decision stages. We establish the theoretical properties of the proposed approach, including the Fisher consistency and finite-sample performance bound. Empirically, we evaluate the proposed method in extensive simulated environments and a real case study for the COVID-19 pandemic.

Yuhan Li, Hongtao Zhang, Keaven Anderson et al.

In the pharmaceutical industry, the use of artificial intelligence (AI) has seen consistent growth over the past decade. This rise is attributed to major advancements in statistical machine learning methodologies, computational capabilities and the increased availability of large datasets. AI techniques are applied throughout different stages of drug development, ranging from drug discovery to post-marketing benefit-risk assessment. Kolluri et al. provided a review of several case studies that span these stages, featuring key applications such as protein structure prediction, success probability estimation, subgroup identification, and AI-assisted clinical trial monitoring. From a regulatory standpoint, there was a notable uptick in submissions incorporating AI components in 2021. The most prevalent therapeutic areas leveraging AI were oncology (27%), psychiatry (15%), gastroenterology (12%), and neurology (11%). The paradigm of personalized or precision medicine has gained significant traction in recent research, partly due to advancements in AI techniques \cite{hamburg2010path}. This shift has had a transformative impact on the pharmaceutical industry. Departing from the traditional "one-size-fits-all" model, personalized medicine incorporates various individual factors, such as environmental conditions, lifestyle choices, and health histories, to formulate customized treatment plans. By utilizing sophisticated machine learning algorithms, clinicians and researchers are better equipped to make informed decisions in areas such as disease prevention, diagnosis, and treatment selection, thereby optimizing health outcomes for each individual.

Mehrdad Mohammadi, Qi Zheng, Ruoqing Zhu

We propose an (offline) multi-dimensional distributional reinforcement learning framework (KE-DRL) that leverages Hilbert space mappings to estimate the kernel mean embedding of the multi-dimensional value distribution under a proposed target policy. In our setting, the state-action variables are multi-dimensional and continuous. By mapping probability measures into a reproducing kernel Hilbert space via kernel mean embeddings, our method replaces Wasserstein metrics with an integral probability metric. This enables efficient estimation in multi-dimensional state-action spaces and reward settings, where direct computation of Wasserstein distances is computationally challenging. Theoretically, we establish contraction properties of the distributional Bellman operator under our proposed metric involving the Matern family of kernels and provide uniform convergence guarantees. Simulations and empirical results demonstrate robust off-policy evaluation and recovery of the kernel mean embedding under mild assumptions, namely, Lipschitz continuity and boundedness of the kernels, highlighting the potential of embedding-based approaches in complex real-world decision-making scenarios and risk evaluation.

Yuhan Li, Eugene Han, Yifan Hu et al.

This paper addresses the challenge of offline policy learning in reinforcement learning with continuous action spaces when unmeasured confounders are present. While most existing research focuses on policy evaluation within partially observable Markov decision processes (POMDPs) and assumes discrete action spaces, we advance this field by establishing a novel identification result to enable the nonparametric estimation of policy value for a given target policy under an infinite-horizon framework. Leveraging this identification, we develop a minimax estimator and introduce a policy-gradient-based algorithm to identify the in-class optimal policy that maximizes the estimated policy value. Furthermore, we provide theoretical results regarding the consistency, finite-sample error bound, and regret bound of the resulting optimal policy. Extensive simulations and a real-world application using the German Family Panel data demonstrate the effectiveness of our proposed methodology.

Tianning Xu, Ruoqing Zhu, Xiaofeng Shao

Infinite-order U-statistics (IOUS) has been used extensively on subbagging ensemble learning algorithms such as random forests to quantify its uncertainty. While normality results of IOUS have been studied extensively, its variance estimation approaches and theoretical properties remain mostly unexplored. Existing approaches mainly utilize the leading term dominance property in the Hoeffding decomposition. However, such a view usually leads to biased estimation when the kernel size is large or the sample size is small. On the other hand, while several unbiased estimators exist in the literature, their relationships and theoretical properties, especially the ratio consistency, have never been studied. These limitations lead to unguaranteed performances of constructed confidence intervals. To bridge these gaps in the literature, we propose a new view of the Hoeffding decomposition for variance estimation that leads to an unbiased estimator. Instead of leading term dominance, our view utilizes the dominance of the peak region. Moreover, we establish the connection and equivalence of our estimator with several existing unbiased variance estimators. Theoretically, we are the first to establish the ratio consistency of such a variance estimator, which justifies the coverage rate of confidence intervals constructed from random forests. Numerically, we further propose a local smoothing procedure to improve the estimator's finite sample performance. Extensive simulation studies show that our estimators enjoy lower bias and archive targeted coverage rates.

Rui Qiu, Zhou Yu, Ruoqing Zhu

Statistical analysis is increasingly confronted with complex data from metric spaces. Petersen and Müller (2019) established a general paradigm of Fréchet regression with complex metric space valued responses and Euclidean predictors. However, the local approach therein involves nonparametric kernel smoothing and suffers from the curse of dimensionality. To address this issue, we in this paper propose a novel random forest weighted local Fréchet regression paradigm. The main mechanism of our approach relies on a locally adaptive kernel generated by random forests. Our first method uses these weights as the local average to solve the conditional Fréchet mean, while the second method performs local linear Fréchet regression, both significantly improving existing Fréchet regression methods. Based on the theory of infinite order U-processes and infinite order $M_{m_n}$-estimator, we establish the consistency, rate of convergence, and asymptotic normality for our local constant estimator, which covers the current large sample theory of random forests with Euclidean responses as a special case. Numerical studies show the superiority of our methods with several commonly encountered types of responses such as distribution functions, symmetric positive-definite matrices, and sphere data. The practical merits of our proposals are also demonstrated through the application to New York taxi data and human mortality data.

Wenzhuo Zhou, Ruoqing Zhu, Annie Qu

Recent advances in mobile health (mHealth) technology provide an effective way to monitor individuals' health statuses and deliver just-in-time personalized interventions. However, the practical use of mHealth technology raises unique challenges to existing methodologies on learning an optimal dynamic treatment regime. Many mHealth applications involve decision-making with large numbers of intervention options and under an infinite time horizon setting where the number of decision stages diverges to infinity. In addition, temporary medication shortages may cause optimal treatments to be unavailable, while it is unclear what alternatives can be used. To address these challenges, we propose a Proximal Temporal consistency Learning (pT-Learning) framework to estimate an optimal regime that is adaptively adjusted between deterministic and stochastic sparse policy models. The resulting minimax estimator avoids the double sampling issue in the existing algorithms. It can be further simplified and can easily incorporate off-policy data without mismatched distribution corrections. We study theoretical properties of the sparse policy and establish finite-sample bounds on the excess risk and performance error. The proposed method is provided in our proximalDTR package and is evaluated through extensive simulation studies and the OhioT1DM mHealth dataset.

Yutong Li, Ruoqing Zhu, Annie Qu et al.

Skin cancer, the most commonly found human malignancy, is primarily diagnosed visually via dermoscopic analysis, biopsy, and histopathological examination. However, unlike other types of cancer, automated image classification of skin lesions is deemed more challenging due to the irregularity and variability in the lesions' appearances. In this work, we propose an adaptation of the Neural Style Transfer (NST) as a novel image pre-processing step for skin lesion classification problems. We represent each dermoscopic image as the style image and transfer the style of the lesion onto a homogeneous content image. This transfers the main variability of each lesion onto the same localized region, which allows us to integrate the generated images together and extract latent, low-rank style features via tensor decomposition. We train and cross-validate our model on a dermoscopic data set collected and preprocessed from the International Skin Imaging Collaboration (ISIC) database. We show that the classification performance based on the extracted tensor features using the style-transferred images significantly outperforms that of the raw images by more than 10%, and is also competitive with well-studied, pre-trained CNN models through transfer learning. Additionally, the tensor decomposition further identifies latent style clusters, which may provide clinical interpretation and insights.

Yifan Cui, Michael R. Kosorok, Erik Sverdrup et al.

Forest-based methods have recently gained in popularity for non-parametric treatment effect estimation. Building on this line of work, we introduce causal survival forests, which can be used to estimate heterogeneous treatment effects in a survival and observational setting where outcomes may be right-censored. Our approach relies on orthogonal estimating equations to robustly adjust for both censoring and selection effects under unconfoundedness. In our experiments, we find our approach to perform well relative to a number of baselines.

Jack Yutong Li, Ruoqing Zhu, Annie Qu et al.

Emergency Department (ED) crowding is a worldwide issue that affects the efficiency of hospital management and the quality of patient care. This occurs when the request for an admit ward-bed to receive a patient is delayed until an admission decision is made by a doctor. To reduce the overcrowding and waiting time of ED, we build a classifier to predict the disposition of patients using manually-typed nurse notes collected during triage, thereby allowing hospital staff to begin necessary preparation beforehand. However, these triage notes involve high dimensional, noisy, and also sparse text data which makes model fitting and interpretation difficult. To address this issue, we propose the semi-orthogonal non-negative matrix factorization (SONMF) for both continuous and binary design matrices to first bi-cluster the patients and words into a reduced number of topics. The subjects can then be interpreted as a non-subtractive linear combination of orthogonal basis topic vectors. These generated topic vectors provide the hospital with a direct understanding of the cause of admission. We show that by using a transformation of basis, the classification accuracy can be further increased compared to the conventional bag-of-words model and alternative matrix factorization approaches. Through simulated data experiments, we also demonstrate that the proposed method outperforms other non-negative matrix factorization (NMF) methods in terms of factorization accuracy, rate of convergence, and degree of orthogonality.