Multi-task Learning for Heterogeneous Multi-source Block-Wise Missing Data

Multi-task learning (MTL) has emerged as an imperative machine learning tool to solve multiple learning tasks simultaneously and has been successfully applied to healthcare, marketing, and biomedical fields. However, in order to borrow information across different tasks effectively, it is essential to utilize both homogeneous and heterogeneous information. Among the extensive literature on MTL, various forms of heterogeneity are presented in MTL problems, such as block-wise, distribution, and posterior heterogeneity. Existing methods, however, struggle to tackle these forms of heterogeneity simultaneously in a unified framework. In this paper, we propose a two-step learning strategy for MTL which addresses the aforementioned heterogeneity. First, we impute the missing blocks using shared representations extracted from homogeneous source across different tasks. Next, we disentangle the mappings between input features and responses into a shared component and a task-specific component, respectively, thereby enabling information borrowing through the shared component. Our numerical experiments and real-data analysis from the ADNI database demonstrate the superior MTL performance of the proposed method compared to other competing methods.

Multi-task Learning for Heterogeneous Data via Integrating Shared and Task-Specific Encodings

Multi-task learning (MTL) has become an essential machine learning tool for addressing multiple learning tasks simultaneously and has been effectively applied across fields such as healthcare, marketing, and biomedical research. However, to enable efficient information sharing across tasks, it is crucial to leverage both shared and heterogeneous information. Despite extensive research on MTL, various forms of heterogeneity, including distribution and posterior heterogeneity, present significant challenges. Existing methods often fail to address these forms of heterogeneity within a unified framework. In this paper, we propose a dual-encoder framework to construct a heterogeneous latent factor space for each task, incorporating a task-shared encoder to capture common information across tasks and a task-specific encoder to preserve unique task characteristics. Additionally, we explore the intrinsic similarity structure of the coefficients corresponding to learned latent factors, allowing for adaptive integration across tasks to manage posterior heterogeneity. We introduce a unified algorithm that alternately learns the task-specific and task-shared encoders and coefficients. In theory, we investigate the excess risk bound for the proposed MTL method using local Rademacher complexity and apply it to a new but related task. Through simulation studies, we demonstrate that the proposed method outperforms existing data integration methods across various settings. Furthermore, the proposed method achieves superior predictive performance for time to tumor doubling across five distinct cancer types in PDX data.

Reinforcement Learning for Individual Optimal Policy from Heterogeneous Data

Offline reinforcement learning (RL) aims to find optimal policies in dynamic environments in order to maximize the expected total rewards by leveraging pre-collected data. Learning from heterogeneous data is one of the fundamental challenges in offline RL. Traditional methods focus on learning an optimal policy for all individuals with pre-collected data from a single episode or homogeneous batch episodes, and thus, may result in a suboptimal policy for a heterogeneous population. In this paper, we propose an individualized offline policy optimization framework for heterogeneous time-stationary Markov decision processes (MDPs). The proposed heterogeneous model with individual latent variables enables us to efficiently estimate the individual Q-functions, and our Penalized Pessimistic Personalized Policy Learning (P4L) algorithm guarantees a fast rate on the average regret under a weak partial coverage assumption on behavior policies. In addition, our simulation studies and a real data application demonstrate the superior numerical performance of the proposed method compared with existing methods.

Representation Retrieval Learning for Heterogeneous Data Integration

In the era of big data, large-scale, multi-modal datasets are increasingly ubiquitous, offering unprecedented opportunities for predictive modeling and scientific discovery. However, these datasets often exhibit complex heterogeneity, such as covariate shift, posterior drift, and missing modalities, that can hinder the accuracy of existing prediction algorithms. To address these challenges, we propose a novel Representation Retrieval ($R^2$) framework, which integrates a representation learning module (the representer) with a sparsity-induced machine learning model (the learner). Moreover, we introduce the notion of "integrativeness" for representers, characterized by the effective data sources used in learning representers, and propose a Selective Integration Penalty (SIP) to explicitly improve the property. Theoretically, we demonstrate that the $R^2$ framework relaxes the conventional full-sharing assumption in multi-task learning, allowing for partially shared structures, and that SIP can improve the convergence rate of the excess risk bound. Extensive simulation studies validate the empirical performance of our framework, and applications to two real-world datasets further confirm its superiority over existing approaches.

Optimal Transport for Latent Integration with An Application to Heterogeneous Neuronal Activity Data

Detecting dynamic patterns of task-specific responses shared across heterogeneous datasets is an essential and challenging problem in many scientific applications in medical science and neuroscience. In our motivating example of rodent electrophysiological data, identifying the dynamical patterns in neuronal activity associated with ongoing cognitive demands and behavior is key to uncovering the neural mechanisms of memory. One of the greatest challenges in investigating a cross-subject biological process is that the systematic heterogeneity across individuals could significantly undermine the power of existing machine learning methods to identify the underlying biological dynamics. In addition, many technically challenging neurobiological experiments are conducted on only a handful of subjects where rich longitudinal data are available for each subject. The low sample sizes of such experiments could further reduce the power to detect common dynamic patterns among subjects. In this paper, we propose a novel heterogeneous data integration framework based on optimal transport to extract shared patterns in complex biological processes. The key advantages of the proposed method are that it can increase discriminating power in identifying common patterns by reducing heterogeneity unrelated to the signal by aligning the extracted latent spatiotemporal information across subjects. Our approach is effective even with a small number of subjects, and does not require auxiliary matching information for the alignment. In particular, our method can align longitudinal data across heterogeneous subjects in a common latent space to capture the dynamics of shared patterns while utilizing temporal dependency within subjects.

CONCERT: Covariate-Elaborated Robust Local Information Transfer with Conditional Spike-and-Slab Prior

The popularity of transfer learning stems from the fact that it can borrow information from useful auxiliary datasets. Existing statistical transfer learning methods usually adopt a global similarity measure between the source data and the target data, which may lead to inefficiency when only local information is shared. In this paper, we propose a novel Bayesian transfer learning method named "CONCERT" to allow robust local information transfer for high-dimensional data analysis. A novel conditional spike-and-slab prior is introduced in the joint distribution of target and source parameters for information transfer. By incorporating covariate-specific priors, we can characterize the local similarities and make the sources work collaboratively to help improve the performance on the target. Distinguished from existing work, CONCERT is a one-step procedure, which achieves variable selection and information transfer simultaneously. Variable selection consistency is established for our CONCERT. To make our algorithm scalable, we adopt the variational Bayes framework to facilitate implementation. Extensive experiments and a genetic data analysis demonstrate the validity and the advantage of CONCERT over existing cutting-edge transfer learning methods. We also extend our CONCERT to the logistical models with numerical studies showing its superiority over other methods.

Dynamic Topic Language Model on Heterogeneous Children's Mental Health Clinical Notes

Mental health diseases affect children's lives and well-beings which have received increased attention since the COVID-19 pandemic. Analyzing psychiatric clinical notes with topic models is critical to evaluate children's mental status over time. However, few topic models are built for longitudinal settings, and they fail to keep consistent topics and capture temporal trajectories for each document. To address these challenges, we develop a longitudinal topic model with time-invariant topics and individualized temporal dependencies on the evolving document metadata. Our model preserves the semantic meaning of discovered topics over time and incorporates heterogeneity among documents. In particular, when documents can be categorized, we propose an unsupervised topics learning approach to maximize topic heterogeneity across different document groups. We also present an efficient variational optimization procedure adapted for the multistage longitudinal setting. In this case study, we apply our method to the psychiatric clinical notes from a large tertiary pediatric hospital in Southern California and achieve a 38% increase in the overall coherence of extracted topics. Our real data analysis reveals that children tend to express more negative emotions during state shutdowns and more positive when schools reopen. Furthermore, it suggests that sexual and gender minority (SGM) children display more pronounced reactions to major COVID-19 events and a greater sensitivity to vaccine-related news than non-SGM children. This study examines the progression of children's mental health during the pandemic and offers clinicians valuable insights to recognize the disparities in children's mental health related to their sexual and gender identities.

Individualized Dynamic Model for Multi-resolutional Data

Mobile health has emerged as a major success in tracking individual health status, due to the popularity and power of smartphones and wearable devices. This has also brought great challenges in handling heterogeneous, multi-resolution data which arise ubiquitously in mobile health due to irregular multivariate measurements collected from individuals. In this paper, we propose an individualized dynamic latent factor model for irregular multi-resolution time series data to interpolate unsampled measurements of time series with low resolution. One major advantage of the proposed method is the capability to integrate multiple irregular time series and multiple subjects by mapping the multi-resolution data to the latent space. In addition, the proposed individualized dynamic latent factor model is applicable to capturing heterogeneous longitudinal information through individualized dynamic latent factors. In theory, we provide the integrated interpolation error bound of the proposed estimator and derive the convergence rate with B-spline approximation methods. Both the simulation studies and the application to smartwatch data demonstrate the superior performance of the proposed method compared to existing methods.

Stage-Aware Learning for Dynamic Treatments

Recent advances in dynamic treatment regimes (DTRs) provide powerful optimal treatment searching algorithms, which are tailored to individuals' specific needs and able to maximize their expected clinical benefits. However, existing algorithms could suffer from insufficient sample size under optimal treatments, especially for chronic diseases involving long stages of decision-making. 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 inverse probability weighted 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 COVID-19 pandemic.

A Model-Agnostic Graph Neural Network for Integrating Local and Global Information

Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, existing GNNs suffer from two significant limitations: a lack of interpretability in results due to their black-box nature, and an inability to learn representations of varying orders. To tackle these issues, we propose a novel Model-agnostic Graph Neural Network (MaGNet) framework, which is able to sequentially integrate information of various orders, extract knowledge from high-order neighbors, and provide meaningful and interpretable results by identifying influential compact graph structures. In particular, MaGNet consists of two components: an estimation model for the latent representation of complex relationships under graph topology, and an interpretation model that identifies influential nodes, edges, and important node features. Theoretically, we establish the generalization error bound for MaGNet via empirical Rademacher complexity, and showcase its power to represent layer-wise neighborhood mixing. We conduct comprehensive numerical studies using simulated data to demonstrate the superior performance of MaGNet in comparison to several state-of-the-art alternatives. Furthermore, we apply MaGNet to a real-world case study aimed at extracting task-critical information from brain activity data, thereby highlighting its effectiveness in advancing scientific research.