Tianxi Cai

Yucong Lin, Keming Lu, Sheng Yu et al.

Objective: Disease knowledge graphs are a way to connect, organize, and access disparate information about diseases with numerous benefits for artificial intelligence (AI). To create knowledge graphs, it is necessary to extract knowledge from multimodal datasets in the form of relationships between disease concepts and normalize both concepts and relationship types. Methods: We introduce REMAP, a multimodal approach for disease relation extraction and classification. The REMAP machine learning approach jointly embeds a partial, incomplete knowledge graph and a medical language dataset into a compact latent vector space, followed by aligning the multimodal embeddings for optimal disease relation extraction. Results: We apply REMAP approach to a disease knowledge graph with 96,913 relations and a text dataset of 1.24 million sentences. On a dataset annotated by human experts, REMAP improves text-based disease relation extraction by 10.0% (accuracy) and 17.2% (F1-score) by fusing disease knowledge graphs with text information. Further, REMAP leverages text information to recommend new relationships in the knowledge graph, outperforming graph-based methods by 8.4% (accuracy) and 10.4% (F1-score). Conclusion: REMAP is a multimodal approach for extracting and classifying disease relationships by fusing structured knowledge and text information. REMAP provides a flexible neural architecture to easily find, access, and validate AI-driven relationships between disease concepts.

Doudou Zhou, Yufeng Zhang, Aaron Sonabend-W et al.

Evidence-based or data-driven dynamic treatment regimes are essential for personalized medicine, which can benefit from offline reinforcement learning (RL). Although massive healthcare data are available across medical institutions, they are prohibited from sharing due to privacy constraints. Besides, heterogeneity exists in different sites. As a result, federated offline RL algorithms are necessary and promising to deal with the problems. In this paper, we propose a multi-site Markov decision process model that allows for both homogeneous and heterogeneous effects across sites. The proposed model makes the analysis of the site-level features possible. We design the first federated policy optimization algorithm for offline RL with sample complexity. The proposed algorithm is communication-efficient, which requires only a single round of communication interaction by exchanging summary statistics. We give a theoretical guarantee for the proposed algorithm, where the suboptimality for the learned policies is comparable to the rate as if data is not distributed. Extensive simulations demonstrate the effectiveness of the proposed algorithm. The method is applied to a sepsis dataset in multiple sites to illustrate its use in clinical settings.

Xin Xiong, Zijian Guo, Tianxi Cai

Many existing transfer learning methods rely on leveraging information from source data that closely resembles the target data. However, this approach often overlooks valuable knowledge that may be present in different yet potentially related auxiliary samples. When dealing with a limited amount of target data and a diverse range of source models, our paper introduces a novel approach, Distributionally Robust Optimization for Transfer Learning (TransDRO), that breaks free from strict similarity constraints. TransDRO is designed to optimize the most adversarial loss within an uncertainty set, defined as a collection of target populations generated as a convex combination of source distributions that guarantee excellent prediction performances for the target data. TransDRO effectively bridges the realms of transfer learning and distributional robustness prediction models. We establish the identifiability of TransDRO and its interpretation as a weighted average of source models closest to the baseline model. We also show that TransDRO achieves a faster convergence rate than the model fitted with the target data. Our comprehensive numerical studies and analysis of multi-institutional electronic health records data using TransDRO further substantiate the robustness and accuracy of TransDRO, highlighting its potential as a powerful tool in transfer learning applications.

Tianxi Cai, Dong Xia, Luwan Zhang et al.

Network analysis has been a powerful tool to unveil relationships and interactions among a large number of objects. Yet its effectiveness in accurately identifying important node-node interactions is challenged by the rapidly growing network size, with data being collected at an unprecedented granularity and scale. Common wisdom to overcome such high dimensionality is collapsing nodes into smaller groups and conducting connectivity analysis on the group level. Dividing efforts into two phases inevitably opens a gap in consistency and drives down efficiency. Consensus learning emerges as a new normal for common knowledge discovery with multiple data sources available. In this paper, we propose a unified multi-view sparse low-rank block model (msLBM) framework, which enables simultaneous grouping and connectivity analysis by combining multiple data sources. The msLBM framework efficiently represents overlapping information across large scale concepts and accommodates different types of heterogeneity across sources. Both features are desirable when analyzing high dimensional electronic health record (EHR) datasets from multiple health systems. An estimating procedure based on the alternating minimization algorithm is proposed. Our theoretical results demonstrate that a consensus knowledge graph can be more accurately learned by leveraging multi-source datasets, and statistically optimal rates can be achieved under mild conditions. Applications to the real world EHR data suggest that our proposed msLBM algorithm can more reliably reveal network structure among clinical concepts by effectively combining summary level EHR data from multiple health systems.

Rui Duan, Xin Xiong, Jueyi Liu et al.

Cluster analysis across multiple institutions poses significant challenges due to data-sharing restrictions. To overcome these limitations, we introduce the Federated One-shot Ensemble Clustering (FONT) algorithm, a novel solution tailored for multi-site analyses under such constraints. FONT requires only a single round of communication between sites and ensures privacy by exchanging only fitted model parameters and class labels. The algorithm combines locally fitted clustering models into a data-adaptive ensemble, making it broadly applicable to various clustering techniques and robust to differences in cluster proportions across sites. Our theoretical analysis validates the effectiveness of the data-adaptive weights learned by FONT, and simulation studies demonstrate its superior performance compared to existing benchmark methods. We applied FONT to identify subgroups of patients with rheumatoid arthritis across two health systems, revealing improved consistency of patient clusters across sites, while locally fitted clusters proved less transferable. FONT is particularly well-suited for real-world applications with stringent communication and privacy constraints, offering a scalable and practical solution for multi-site clustering.

Doudou Zhou, Han Tong, Linshanshan Wang et al.

The adoption of EHRs has expanded opportunities to leverage data-driven algorithms in clinical care and research. A major bottleneck in effectively conducting multi-institutional EHR studies is the data heterogeneity across systems with numerous codes that either do not exist or represent different clinical concepts across institutions. The need for data privacy further limits the feasibility of including multi-institutional patient-level data required to study similarities and differences across patient subgroups. To address these challenges, we developed the GAME algorithm. Tested and validated across 7 institutions and 2 languages, GAME integrates data in several levels: (1) at the institutional level with knowledge graphs to establish relationships between codes and existing knowledge sources, providing the medical context for standard codes and their relationship to each other; (2) between institutions, leveraging language models to determine the relationships between institution-specific codes with established standard codes; and (3) quantifying the strength of the relationships between codes using a graph attention network. Jointly trained embeddings are created using transfer and federated learning to preserve data privacy. In this study, we demonstrate the applicability of GAME in selecting relevant features as inputs for AI-driven algorithms in a range of conditions, e.g., heart failure, rheumatoid arthritis. We then highlight the application of GAME harmonized multi-institutional EHR data in a study of Alzheimer's disease outcomes and suicide risk among patients with mental health disorders, without sharing patient-level data outside individual institutions.

Huaiyuan Ying, Hongyi Yuan, Jinsen Lu et al.

Electronic Health Records (EHRs) hold immense potential for advancing healthcare, offering rich, longitudinal data that combines structured information with valuable insights from unstructured clinical notes. However, the unstructured nature of clinical text poses significant challenges for secondary applications. Traditional methods for structuring EHR free-text data, such as rule-based systems and multi-stage pipelines, are often limited by their time-consuming configurations and inability to adapt across clinical notes from diverse healthcare settings. Few systems provide a comprehensive attribute extraction for terminologies. While giant large language models (LLMs) like GPT-4 and LLaMA 405B excel at structuring tasks, they are slow, costly, and impractical for large-scale use. To overcome these limitations, we introduce GENIE, a Generative Note Information Extraction system that leverages LLMs to streamline the structuring of unstructured clinical text into usable data with standardized format. GENIE processes entire paragraphs in a single pass, extracting entities, assertion statuses, locations, modifiers, values, and purposes with high accuracy. Its unified, end-to-end approach simplifies workflows, reduces errors, and eliminates the need for extensive manual intervention. Using a robust data preparation pipeline and fine-tuned small scale LLMs, GENIE achieves competitive performance across multiple information extraction tasks, outperforming traditional tools like cTAKES and MetaMap and can handle extra attributes to be extracted. GENIE strongly enhances real-world applicability and scalability in healthcare systems. By open-sourcing the model and test data, we aim to encourage collaboration and drive further advancements in EHR structurization.

Tianxi Cai, Feiqing Huang, Ryumei Nakada et al.

Electronic health record (EHR) systems contain a wealth of multimodal clinical data including structured data like clinical codes and unstructured data such as clinical notes. However, many existing EHR-focused studies has traditionally either concentrated on an individual modality or merged different modalities in a rather rudimentary fashion. This approach often results in the perception of structured and unstructured data as separate entities, neglecting the inherent synergy between them. Specifically, the two important modalities contain clinically relevant, inextricably linked and complementary health information. A more complete picture of a patient's medical history is captured by the joint analysis of the two modalities of data. Despite the great success of multimodal contrastive learning on vision-language, its potential remains under-explored in the realm of multimodal EHR, particularly in terms of its theoretical understanding. To accommodate the statistical analysis of multimodal EHR data, in this paper, we propose a novel multimodal feature embedding generative model and design a multimodal contrastive loss to obtain the multimodal EHR feature representation. Our theoretical analysis demonstrates the effectiveness of multimodal learning compared to single-modality learning and connects the solution of the loss function to the singular value decomposition of a pointwise mutual information matrix. This connection paves the way for a privacy-preserving algorithm tailored for multimodal EHR feature representation learning. Simulation studies show that the proposed algorithm performs well under a variety of configurations. We further validate the clinical utility of the proposed algorithm in real-world EHR data.

Junhan Yu, Zhunyi Feng, Junwei Lu et al.

Electronic Health Records (EHR) contain valuable clinical information for predicting patient outcomes and guiding healthcare decisions. However, effectively modeling Electronic Health Records (EHRs) requires addressing data heterogeneity and complex temporal patterns. Standard approaches often struggle with irregular time intervals between clinical events. We propose TALE-EHR, a Transformer-based framework featuring a novel time-aware attention mechanism that explicitly models continuous temporal gaps to capture fine-grained sequence dynamics. To complement this temporal modeling with robust semantics, TALE-EHR leverages embeddings derived from standardized code descriptions using a pre-trained Large Language Model (LLM), providing a strong foundation for understanding clinical concepts. Experiments on the MIMIC-IV and PIC dataset demonstrate that our approach outperforms state-of-the-art baselines on tasks such as disease progression forecasting. TALE-EHR underscores the benefit of integrating explicit, continuous temporal modeling with strong semantic representations provides a powerful solution for advancing EHR analysis.

Ryumei Nakada, Wenlong Ji, Tianxi Cai et al.

Prompt engineering has emerged as a powerful technique for guiding large language models (LLMs) toward desired responses, significantly enhancing their performance across diverse tasks. Beyond their role as static predictors, LLMs increasingly function as intelligent agents, capable of reasoning, decision-making, and adapting dynamically to complex environments. However, the theoretical underpinnings of prompt engineering remain largely unexplored. In this paper, we introduce a formal framework demonstrating that transformer models, when provided with carefully designed prompts, can act as a configurable computational system by emulating a ``virtual'' neural network during inference. Specifically, input prompts effectively translate into the corresponding network configuration, enabling LLMs to adjust their internal computations dynamically. Building on this construction, we establish an approximation theory for $β$-times differentiable functions, proving that transformers can approximate such functions with arbitrary precision when guided by appropriately structured prompts. Moreover, our framework provides theoretical justification for several empirically successful prompt engineering techniques, including the use of longer, structured prompts, filtering irrelevant information, enhancing prompt token diversity, and leveraging multi-agent interactions. By framing LLMs as adaptable agents rather than static models, our findings underscore their potential for autonomous reasoning and problem-solving, paving the way for more robust and theoretically grounded advancements in prompt engineering and AI agent design.

Yinjie Wang, Doudou Zhou, Yue Liu et al.

Electronic Health Records (EHRs), comprising diverse clinical data such as diagnoses, medications, and laboratory results, hold great promise for translational research. EHR-derived data have advanced disease prevention, improved clinical trial recruitment, and generated real-world evidence. Synthesizing EHRs across institutions enables large-scale, generalizable studies that capture rare diseases and population diversity, but remains hindered by the heterogeneity of medical codes, institution-specific terminologies, and the absence of standardized data structures. These barriers limit the interpretability, comparability, and scalability of EHR-based analyses, underscoring the need for robust methods to harmonize and extract meaningful insights from distributed, heterogeneous data. To address this, we propose MASH (Multi-source Automated Structured Hierarchy), a fully automated framework that aligns medical codes across institutions using neural optimal transport and constructs hierarchical graphs with learned hyperbolic embeddings. During training, MASH integrates information from pre-trained language models, co-occurrence patterns, textual descriptions, and supervised labels to capture semantic and hierarchical relationships among medical concepts more effectively. Applied to real-world EHR data, including diagnosis, medication, and laboratory codes, MASH produces interpretable hierarchical graphs that facilitate the navigation and understanding of heterogeneous clinical data. Notably, it generates the first automated hierarchies for unstructured local laboratory codes, establishing foundational references for downstream applications.

Kimberly F. Greco, Zongxin Yang, Mengyan Li et al.

Rare diseases affect an estimated 300-400 million people worldwide, yet individual conditions remain underdiagnosed and poorly characterized due to their low prevalence and limited clinician familiarity. Computational phenotyping offers a scalable approach to improving rare disease detection, but algorithm development is hindered by the scarcity of high-quality labeled data for training. Expert-labeled datasets from chart reviews and registries are clinically accurate but limited in scope and availability, whereas labels derived from electronic health records (EHRs) provide broader coverage but are often noisy or incomplete. To address these challenges, we propose WEST (WEakly Supervised Transformer for rare disease phenotyping and subphenotyping from EHRs), a framework that combines routinely collected EHR data with a limited set of expert-validated cases and controls to enable large-scale phenotyping. At its core, WEST employs a weakly supervised transformer model trained on extensive probabilistic silver-standard labels - derived from both structured and unstructured EHR features - that are iteratively refined during training to improve model calibration. We evaluate WEST on two rare pulmonary diseases using EHR data from Boston Children's Hospital and show that it outperforms existing methods in phenotype classification, identification of clinically meaningful subphenotypes, and prediction of disease progression. By reducing reliance on manual annotation, WEST enables data-efficient rare disease phenotyping that improves cohort definition, supports earlier and more accurate diagnosis, and accelerates data-driven discovery for the rare disease community.

Sinian Zhang, Kaicheng Zhang, Ziping Xu et al.

The linear Markov Decision Process (MDP) framework offers a principled foundation for reinforcement learning (RL) with strong theoretical guarantees and sample efficiency. However, its restrictive assumption-that both transition dynamics and reward functions are linear in the same feature space-limits its applicability in real-world domains, where rewards often exhibit nonlinear or discrete structures. Motivated by applications such as healthcare and e-commerce, where data is scarce and reward signals can be binary or count-valued, we propose the Generalized Linear MDP (GLMDP) framework-an extension of the linear MDP framework-that models rewards using generalized linear models (GLMs) while maintaining linear transition dynamics. We establish the Bellman completeness of GLMDPs with respect to a new function class that accommodates nonlinear rewards and develop two offline RL algorithms: Generalized Pessimistic Value Iteration (GPEVI) and a semi-supervised variant (SS-GPEVI) that utilizes both labeled and unlabeled trajectories. Our algorithms achieve theoretical guarantees on policy suboptimality and demonstrate improved sample efficiency in settings where reward labels are expensive or limited.

Hongyi Yuan, Suqi Liu, Kelly Cho et al.

We introduce GENomic Encoding REpresentation with Language Model (GENEREL), a framework designed to bridge genetic and biomedical knowledge bases. What sets GENEREL apart is its ability to fine-tune language models to infuse biological knowledge behind clinical concepts such as diseases and medications. This fine-tuning enables the model to capture complex biomedical relationships more effectively, enriching the understanding of how genomic data connects to clinical outcomes. By constructing a unified embedding space for biomedical concepts and a wide range of common SNPs from sources such as patient-level data, biomedical knowledge graphs, and GWAS summaries, GENEREL aligns the embeddings of SNPs and clinical concepts through multi-task contrastive learning. This allows the model to adapt to diverse natural language representations of biomedical concepts while bypassing the limitations of traditional code mapping systems across different data sources. Our experiments demonstrate GENEREL's ability to effectively capture the nuanced relationships between SNPs and clinical concepts. GENEREL also emerges to discern the degree of relatedness, potentially allowing for a more refined identification of concepts. This pioneering approach in constructing a unified embedding system for both SNPs and biomedical concepts enhances the potential for data integration and discovery in biomedical research.

Jun Wen, Jue Hou, Clara-Lea Bonzel et al.

Electronic health record (EHR) data are increasingly used to support real-world evidence (RWE) studies. Yet its ability to generate reliable RWE is limited by the lack of readily available precise information on the timing of clinical events such as the onset time of heart failure. We propose a LAbel-efficienT incidenT phEnotyping (LATTE) algorithm to accurately annotate the timing of clinical events from longitudinal EHR data. By leveraging the pre-trained semantic embedding vectors from large-scale EHR data as prior knowledge, LATTE selects predictive EHR features in a concept re-weighting module by mining their relationship to the target event and compresses their information into longitudinal visit embeddings through a visit attention learning network. LATTE employs a recurrent neural network to capture the sequential dependency between the target event and visit embeddings before/after it. To improve label efficiency, LATTE constructs highly informative longitudinal silver-standard labels from large-scale unlabeled patients to perform unsupervised pre-training and semi-supervised joint training. Finally, LATTE enhances cross-site portability via contrastive representation learning. LATTE is evaluated on three analyses: the onset of type-2 diabetes, heart failure, and the onset and relapses of multiple sclerosis. We use various evaluation metrics present in the literature including the $ABC_{gain}$, the proportion of reduction in the area between the observed event indicator and the predicted cumulative incidences in reference to the prediction per incident prevalence. LATTE consistently achieves substantial improvement over benchmark methods such as SAMGEP and RETAIN in all settings.

Sai Li, Tianxi Cai, Rui Duan

The limited representation of minorities and disadvantaged populations in large-scale clinical and genomics research has become a barrier to translating precision medicine research into practice. Due to heterogeneity across populations, risk prediction models are often found to be underperformed in these underrepresented populations, and therefore may further exacerbate known health disparities. In this paper, we propose a two-way data integration strategy that integrates heterogeneous data from diverse populations and from multiple healthcare institutions via a federated transfer learning approach. The proposed method can handle the challenging setting where sample sizes from different populations are highly unbalanced. With only a small number of communications across participating sites, the proposed method can achieve performance comparable to the pooled analysis where individual-level data are directly pooled together. We show that the proposed method improves the estimation and prediction accuracy in underrepresented populations, and reduces the gap of model performance across populations. Our theoretical analysis reveals how estimation accuracy is influenced by communication budgets, privacy restrictions, and heterogeneity across populations. We demonstrate the feasibility and validity of our methods through numerical experiments and a real application to a multi-center study, in which we construct polygenic risk prediction models for Type II diabetes in AA population.

Doudou Zhou, Tianxi Cai, Junwei Lu

Matrix completion has attracted attention in many fields, including statistics, applied mathematics, and electrical engineering. Most of the works focus on the independent sampling models under which the observed entries are sampled independently. Motivated by applications in the integration of knowledge graphs derived from multi-source biomedical data such as those from Electronic Health Records (EHR) and biomedical text, we propose the {\bf B}lock-wise {\bf O}verlapping {\bf N}oisy {\bf M}atrix {\bf I}ntegration (BONMI) to treat blockwise missingness of symmetric matrices representing relatedness between entity pairs. Our idea is to exploit the orthogonal Procrustes problem to align the eigenspace of the two sub-matrices, then complete the missing blocks by the inner product of the two low-rank components. Besides, we prove the statistical rate for the eigenspace of the underlying matrix, which is comparable to the rate under the independently missing assumption. Simulation studies show that the method performs well under a variety of configurations. In the real data analysis, the method is applied to two tasks: (i) the integrating of several point-wise mutual information matrices built by English EHR and Chinese medical text data, and (ii) the machine translation between English and Chinese medical concepts. Our method shows an advantage over existing methods.

Jue Hou, Zijian Guo, Tianxi Cai

Risk modeling with EHR data is challenging due to a lack of direct observations on the disease outcome, and the high dimensionality of the candidate predictors. In this paper, we develop a surrogate assisted semi-supervised-learning (SAS) approach to risk modeling with high dimensional predictors, leveraging a large unlabeled data on candidate predictors and surrogates of outcome, as well as a small labeled data with annotated outcomes. The SAS procedure borrows information from surrogates along with candidate predictors to impute the unobserved outcomes via a sparse working imputation model with moment conditions to achieve robustness against mis-specification in the imputation model and a one-step bias correction to enable interval estimation for the predicted risk. We demonstrate that the SAS procedure provides valid inference for the predicted risk derived from a high dimensional working model, even when the underlying risk prediction model is dense and the risk model is mis-specified. We present an extensive simulation study to demonstrate the superiority of our SSL approach compared to existing supervised methods. We apply the method to derive genetic risk prediction of type-2 diabetes mellitus using a EHR biobank cohort.

Aaron Sonabend-W, Nilanjana Laha, Ashwin N. Ananthakrishnan et al.

Reinforcement learning (RL) has shown great success in estimating sequential treatment strategies which take into account patient heterogeneity. However, health-outcome information, which is used as the reward for reinforcement learning methods, is often not well coded but rather embedded in clinical notes. Extracting precise outcome information is a resource intensive task, so most of the available well-annotated cohorts are small. To address this issue, we propose a semi-supervised learning (SSL) approach that efficiently leverages a small sized labeled data with true outcome observed, and a large unlabeled data with outcome surrogates. In particular, we propose a semi-supervised, efficient approach to Q-learning and doubly robust off policy value estimation. Generalizing SSL to sequential treatment regimes brings interesting challenges: 1) Feature distribution for Q-learning is unknown as it includes previous outcomes. 2) The surrogate variables we leverage in the modified SSL framework are predictive of the outcome but not informative to the optimal policy or value function. We provide theoretical results for our Q-function and value function estimators to understand to what degree efficiency can be gained from SSL. Our method is at least as efficient as the supervised approach, and moreover safe as it robust to mis-specification of the imputation models.

T. Tony Cai, Yichen Wang, Linjun Zhang

We propose differentially private algorithms for parameter estimation in both low-dimensional and high-dimensional sparse generalized linear models (GLMs) by constructing private versions of projected gradient descent. We show that the proposed algorithms are nearly rate-optimal by characterizing their statistical performance and establishing privacy-constrained minimax lower bounds for GLMs. The lower bounds are obtained via a novel technique, which is based on Stein's Lemma and generalizes the tracing attack technique for privacy-constrained lower bounds. This lower bound argument can be of independent interest as it is applicable to general parametric models. Simulated and real data experiments are conducted to demonstrate the numerical performance of our algorithms.

Linjun Zhang, Rong Ma, T. Tony Cai et al.

This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random covariates. Building upon a high-dimensional EM algorithm, we propose an iterative procedure for estimating the two regression vectors and establish their rates of convergence. Based on the iterative estimators, we further construct debiased estimators and establish their asymptotic normality. For individual coordinates, confidence intervals centered at the debiased estimators are constructed. Furthermore, a large-scale multiple testing procedure is proposed for testing the regression coefficients and is shown to control the false discovery rate (FDR) asymptotically. Simulation studies are carried out to examine the numerical performance of the proposed methods and their superiority over existing methods. The proposed methods are further illustrated through an analysis of a dataset of multiplex image cytometry, which investigates the interaction networks among the cellular phenotypes that include the expression levels of 20 epitopes or combinations of markers.

Jessica Gronsbell, Molei Liu, Lu Tian et al.

In many contemporary applications, large amounts of unlabeled data are readily available while labeled examples are limited. There has been substantial interest in semi-supervised learning (SSL) which aims to leverage unlabeled data to improve estimation or prediction. However, current SSL literature focuses primarily on settings where labeled data is selected randomly from the population of interest. Non-random sampling, while posing additional analytical challenges, is highly applicable to many real world problems. Moreover, no SSL methods currently exist for estimating the prediction performance of a fitted model under non-random sampling. In this paper, we propose a two-step SSL procedure for evaluating a prediction rule derived from a working binary regression model based on the Brier score and overall misclassification rate under stratified sampling. In step I, we impute the missing labels via weighted regression with nonlinear basis functions to account for nonrandom sampling and to improve efficiency. In step II, we augment the initial imputations to ensure the consistency of the resulting estimators regardless of the specification of the prediction model or the imputation model. The final estimator is then obtained with the augmented imputations. We provide asymptotic theory and numerical studies illustrating that our proposals outperform their supervised counterparts in terms of efficiency gain. Our methods are motivated by electronic health records (EHR) research and validated with a real data analysis of an EHR-based study of diabetic neuropathy.

Aaron Sonabend-W, Junwei Lu, Leo A. Celi et al.

Offline Reinforcement Learning (RL) is a promising approach for learning optimal policies in environments where direct exploration is expensive or unfeasible. However, the adoption of such policies in practice is often challenging, as they are hard to interpret within the application context, and lack measures of uncertainty for the learned policy value and its decisions. To overcome these issues, we propose an Expert-Supervised RL (ESRL) framework which uses uncertainty quantification for offline policy learning. In particular, we have three contributions: 1) the method can learn safe and optimal policies through hypothesis testing, 2) ESRL allows for different levels of risk averse implementations tailored to the application context, and finally, 3) we propose a way to interpret ESRL's policy at every state through posterior distributions, and use this framework to compute off-policy value function posteriors. We provide theoretical guarantees for our estimators and regret bounds consistent with Posterior Sampling for RL (PSRL). Sample efficiency of ESRL is independent of the chosen risk aversion threshold and quality of the behavior policy.

T. Tony Cai, Hongji Wei

We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy, are established in both the univariate and multivariate settings. Communication-efficient and statistically optimal procedures are developed. In the univariate case, the optimal rate depends only on the total communication budget, so long as each local machine has at least one bit. However, in the multivariate case, the minimax rate depends on the specific allocations of the communication budgets among the local machines. Although optimal estimation of a Gaussian mean is relatively simple in the conventional setting, it is quite involved under the communication constraints, both in terms of the optimal procedure design and lower bound argument. The techniques developed in this paper can be of independent interest. An essential step is the decomposition of the minimax estimation problem into two stages, localization and refinement. This critical decomposition provides a framework for both the lower bound analysis and optimal procedure design.

Abhishek Chakrabortty, Jiarui Lu, T. Tony Cai et al.

We consider high dimensional $M$-estimation in settings where the response $Y$ is possibly missing at random and the covariates $\mathbf{X} \in \mathbb{R}^p$ can be high dimensional compared to the sample size $n$. The parameter of interest $\boldsymbolθ_0 \in \mathbb{R}^d$ is defined as the minimizer of the risk of a convex loss, under a fully non-parametric model, and $\boldsymbolθ_0$ itself is high dimensional which is a key distinction from existing works. Standard high dimensional regression and series estimation with possibly misspecified models and missing $Y$ are included as special cases, as well as their counterparts in causal inference using 'potential outcomes'. Assuming $\boldsymbolθ_0$ is $s$-sparse ($s \ll n$), we propose an $L_1$-regularized debiased and doubly robust (DDR) estimator of $\boldsymbolθ_0$ based on a high dimensional adaptation of the traditional double robust (DR) estimator's construction. Under mild tail assumptions and arbitrarily chosen (working) models for the propensity score (PS) and the outcome regression (OR) estimators, satisfying only some high-level conditions, we establish finite sample performance bounds for the DDR estimator showing its (optimal) $L_2$ error rate to be $\sqrt{s (\log d)/ n}$ when both models are correct, and its consistency and DR properties when only one of them is correct. Further, when both the models are correct, we propose a desparsified version of our DDR estimator that satisfies an asymptotic linear expansion and facilitates inference on low dimensional components of $\boldsymbolθ_0$. Finally, we discuss various of choices of high dimensional parametric/semi-parametric working models for the PS and OR estimators. All results are validated via detailed simulations.

Luwan Zhang, Katherine Liao, Issac Kohane et al.

Despite recent development in methodology, community detection remains a challenging problem. Existing literature largely focuses on the standard setting where a network is learned using an observed adjacency matrix from a single data source. Constructing a shared network from multiple data sources is more challenging due to the heterogeneity across populations. Additionally, no existing method leverages the prior distance knowledge available in many domains to help the discovery of the network structure. To bridge this gap, in this paper we propose a novel spectral clustering method that optimally combines multiple data sources while leveraging the prior distance knowledge. The proposed method combines a banding step guided by the distance knowledge with a subsequent weighting step to maximize consensus across multiple sources. Its statistical performance is thoroughly studied under a multi-view stochastic block model. We also provide a simple yet optimal rule of choosing weights in practice. The efficacy and robustness of the method is fully demonstrated through extensive simulations. Finally, we apply the method to cluster the International classification of diseases, ninth revision (ICD9), codes and yield a very insightful clustering structure by integrating information from a large claim database and two healthcare systems.

Andrew L. Beam, Benjamin Kompa, Allen Schmaltz et al.

Word embeddings are a popular approach to unsupervised learning of word relationships that are widely used in natural language processing. In this article, we present a new set of embeddings for medical concepts learned using an extremely large collection of multimodal medical data. Leaning on recent theoretical insights, we demonstrate how an insurance claims database of 60 million members, a collection of 20 million clinical notes, and 1.7 million full text biomedical journal articles can be combined to embed concepts into a common space, resulting in the largest ever set of embeddings for 108,477 medical concepts. To evaluate our approach, we present a new benchmark methodology based on statistical power specifically designed to test embeddings of medical concepts. Our approach, called cui2vec, attains state-of-the-art performance relative to previous methods in most instances. Finally, we provide a downloadable set of pre-trained embeddings for other researchers to use, as well as an online tool for interactive exploration of the cui2vec embeddings

Abhishek Chakrabortty, Matey Neykov, Raymond Carroll et al.

We consider the recovery of regression coefficients, denoted by $\boldsymbolβ_0$, for a single index model (SIM) relating a binary outcome $Y$ to a set of possibly high dimensional covariates $\boldsymbol{X}$, based on a large but 'unlabeled' dataset $\mathcal{U}$, with $Y$ never observed. On $\mathcal{U}$, we fully observe $\boldsymbol{X}$ and additionally, a surrogate $S$ which, while not being strongly predictive of $Y$ throughout the entirety of its support, can forecast it with high accuracy when it assumes extreme values. Such datasets arise naturally in modern studies involving large databases such as electronic medical records (EMR) where $Y$, unlike $(\boldsymbol{X}, S)$, is difficult and/or expensive to obtain. In EMR studies, an example of $Y$ and $S$ would be the true disease phenotype and the count of the associated diagnostic codes respectively. Assuming another SIM for $S$ given $\boldsymbol{X}$, we show that under sparsity assumptions, we can recover $\boldsymbolβ_0$ proportionally by simply fitting a least squares LASSO estimator to the subset of the observed data on $(\boldsymbol{X}, S)$ restricted to the extreme sets of $S$, with $Y$ imputed using the surrogacy of $S$. We obtain sharp finite sample performance bounds for our estimator, including deterministic deviation bounds and probabilistic guarantees. We demonstrate the effectiveness of our approach through multiple simulation studies, as well as by application to real data from an EMR study conducted at the Partners HealthCare Systems.

Abhishek Chakrabortty, Tianxi Cai

We consider the linear regression problem under semi-supervised settings wherein the available data typically consists of: (i) a small or moderate sized 'labeled' data, and (ii) a much larger sized 'unlabeled' data. Such data arises naturally from settings where the outcome, unlike the covariates, is expensive to obtain, a frequent scenario in modern studies involving large databases like electronic medical records (EMR). Supervised estimators like the ordinary least squares (OLS) estimator utilize only the labeled data. It is often of interest to investigate if and when the unlabeled data can be exploited to improve estimation of the regression parameter in the adopted linear model. In this paper, we propose a class of 'Efficient and Adaptive Semi-Supervised Estimators' (EASE) to improve estimation efficiency. The EASE are two-step estimators adaptive to model mis-specification, leading to improved (optimal in some cases) efficiency under model mis-specification, and equal (optimal) efficiency under a linear model. This adaptive property, often unaddressed in the existing literature, is crucial for advocating 'safe' use of the unlabeled data. The construction of EASE primarily involves a flexible 'semi-non-parametric' imputation, including a smoothing step that works well even when the number of covariates is not small; and a follow up 'refitting' step along with a cross-validation (CV) strategy both of which have useful practical as well as theoretical implications towards addressing two important issues: under-smoothing and over-fitting. We establish asymptotic results including consistency, asymptotic normality and the adaptive properties of EASE. We also provide influence function expansions and a 'double' CV strategy for inference. The results are further validated through extensive simulations, followed by application to an EMR study on auto-immunity.

Anru Zhang, Lawrence D. Brown, T. Tony Cai

We propose a general semi-supervised inference framework focused on the estimation of the population mean. As usual in semi-supervised settings, there exists an unlabeled sample of covariate vectors and a labeled sample consisting of covariate vectors along with real-valued responses ("labels"). Otherwise, the formulation is "assumption-lean" in that no major conditions are imposed on the statistical or functional form of the data. We consider both the ideal semi-supervised setting where infinitely many unlabeled samples are available, as well as the ordinary semi-supervised setting in which only a finite number of unlabeled samples is available. Estimators are proposed along with corresponding confidence intervals for the population mean. Theoretical analysis on both the asymptotic distribution and $\ell_2$-risk for the proposed procedures are given. Surprisingly, the proposed estimators, based on a simple form of the least squares method, outperform the ordinary sample mean. The simple, transparent form of the estimator lends confidence to the perception that its asymptotic improvement over the ordinary sample mean also nearly holds even for moderate size samples. The method is further extended to a nonparametric setting, in which the oracle rate can be achieved asymptotically. The proposed estimators are further illustrated by simulation studies and a real data example involving estimation of the homeless population.

Matey Neykov, Jun S. Liu, Tianxi Cai

It is known that for a certain class of single index models (SIMs) $Y = f(\boldsymbol{X}_{p \times 1}^\intercal\boldsymbolβ_0, \varepsilon)$, support recovery is impossible when $\boldsymbol{X} \sim \mathcal{N}(0, \mathbb{I}_{p \times p})$ and a model complexity adjusted sample size is below a critical threshold. Recently, optimal algorithms based on Sliced Inverse Regression (SIR) were suggested. These algorithms work provably under the assumption that the design $\boldsymbol{X}$ comes from an i.i.d. Gaussian distribution. In the present paper we analyze algorithms based on covariance screening and least squares with $L_1$ penalization (i.e. LASSO) and demonstrate that they can also enjoy optimal (up to a scalar) rescaled sample size in terms of support recovery, albeit under slightly different assumptions on $f$ and $\varepsilon$ compared to the SIR based algorithms. Furthermore, we show more generally, that LASSO succeeds in recovering the signed support of $\boldsymbolβ_0$ if $\boldsymbol{X} \sim \mathcal{N}(0, \boldsymbolΣ)$, and the covariance $\boldsymbolΣ$ satisfies the irrepresentable condition. Our work extends existing results on the support recovery of LASSO for the linear model, to a more general class of SIMs.

Sheng Yu, Tianrun Cai, Tianxi Cai

Objective: Narrative text in Electronic health records (EHR) contain rich information for medical and data science studies. This paper introduces the design and performance of Narrative Information Linear Extraction (NILE), a natural language processing (NLP) package for EHR analysis that we share with the medical informatics community. Methods: NILE uses a modified prefix-tree search algorithm for named entity recognition, which can detect prefix and suffix sharing. The semantic analyses are implemented as rule-based finite state machines. Analyses include negation, location, modification, family history, and ignoring. Result: The processing speed of NILE is hundreds to thousands times faster than existing NLP software for medical text. The accuracy of presence analysis of NILE is on par with the best performing models on the 2010 i2b2/VA NLP challenge data. Conclusion: The speed, accuracy, and being able to operate via API make NILE a valuable addition to the NLP software for medical informatics and data science.