Annie Qu

Hanjia Gao, Hanwen Ye, Qing Nie et al.

Dynamic topic modeling is widely used to analyze evolving trends in scientific literature, medical records, and social media. Traditional topic models represent each topic through a single probability vector on the multinomial simplex and implicitly couple word occurrence and repetition within one probabilistic mechanism. However, this formulation restricts the dependence structure among words and overlooks informative higher-order interactions, particularly in dynamic corpora with overlapping semantics. To address these limitations, we introduce a hypergraph representation of text where each document is modeled as a hyperedge connecting all co-occurring words, with repetition intensities encoded as node weights. This representation naturally separates word occurrence from repetition and induces a novel hypergraph-based multinomial distribution with a nonlinear normalization depending on the observed word set of each document. Building on this likelihood, we develop a dynamic topic modeling framework via structured low-rank factorizations with explicit temporal regularization on topic-word profiles. Moreover, we establish local convergence guarantees and derive non-asymptotic error bounds despite the intrinsic nonconvexity induced by bilinear factorization and document-specific nonlinear normalization. Numerical experiments on synthetic data and an application to the International Conference on Learning Representations (ICLR) corpus demonstrate consistent improvements over existing multinomial-based topic models.

Wenzhuo Zhou, Annie Qu, Keiland W. Cooper et al.

Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, however, existing GNNs suffer from two significant limitations: a lack of interpretability in their 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 effectively 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 node features. Theoretically, we establish the generalization error bound for MaGNet via empirical Rademacher complexity, and demonstrate 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.

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.

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.

Yuanpeng Li, Gefei Lin, Annie Qu et al.

Soft Actor-Critic (SAC) and its variants dominate Multi-Task Reinforcement Learning (MTRL) due to their off-policy sample efficiency, while on-policy methods such as Proximal Policy Optimization (PPO) remain underexplored. We diagnose that PPO in MTRL suffers from a previously overlooked issue: critic-side gradient ill-conditioning, which may cause tail tasks to stall while easy tasks dominate the value function's updates. To address this, we propose TOPPO (Tail-Optimized PPO), a reformulation of PPO via Critic Balancing -- a set of modules that improve gradient conditioning and balance learning dynamics across tasks. Unlike prior approaches that rely on modular architectures or large models, TOPPO targets the optimization bottleneck within PPO itself. Empirically, TOPPO achieves stronger mean and tail-task performance than published SAC-family and ARS-family baselines while using substantially fewer parameters and environment steps on Meta-World+ benchmark. Notably, TOPPO matches or surpasses strong SAC baselines early in training and maintains superior performance at full budget. Ablations confirm the effectiveness of each module in TOPPO and provide insights into their interactions. Our results demonstrate that, with proper optimization, on-policy methods can rival or exceed off-policy approaches in MTRL, challenging the prevailing reliance on SAC and highlighting critic-side gradient conditioning as the central bottleneck.

Wenzhuo Zhou, Annie Qu

Batch reinforcement learning (RL) defines the task of learning from a fixed batch of data lacking exhaustive exploration. Worst-case optimality algorithms, which calibrate a value-function model class from logged experience and perform some type of pessimistic evaluation under the learned model, have emerged as a promising paradigm for batch RL. However, contemporary works on this stream have commonly overlooked the hierarchical decision-making structure hidden in the optimization landscape. In this paper, we adopt a game-theoretical viewpoint and model the policy learning diagram as a two-player general-sum game with a leader-follower structure. We propose a novel stochastic gradient-based learning algorithm: StackelbergLearner, in which the leader player updates according to the total derivative of its objective instead of the usual individual gradient, and the follower player makes individual updates and ensures transition-consistent pessimistic reasoning. The derived learning dynamic naturally lends StackelbergLearner to a game-theoretic interpretation and provides a convergence guarantee to differentiable Stackelberg equilibria. From a theoretical standpoint, we provide instance-dependent regret bounds with general function approximation, which shows that our algorithm can learn a best-effort policy that is able to compete against any comparator policy that is covered by batch data. Notably, our theoretical regret guarantees only require realizability without any data coverage and strong function approximation conditions, e.g., Bellman closedness, which is in contrast to prior works lacking such guarantees. Through comprehensive experiments, we find that our algorithm consistently performs as well or better as compared to state-of-the-art methods in batch RL benchmark and real-world datasets.

Yang Sui, Qi Xu, Yang Bai et al.

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.

Qi Xu, Annie Qu

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.

Ruqian Zhang, Yijiao Zhang, Annie Qu et al.

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 partial information is shared. In this paper, we propose a novel Bayesian transfer learning method named ``CONCERT'' to allow robust partial information transfer for high-dimensional data analysis. A 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 partial similarities and integrate source information collaboratively to improve the performance on the target. In contrast to existing work, the CONCERT is a one-step procedure, which achieves variable selection and information transfer simultaneously. We establish variable selection consistency, as well as estimation and prediction error bounds for CONCERT. Our theory demonstrates the covariate-specific benefit of transfer learning. To ensure that our algorithm is scalable, we adopt the variational Bayes framework to facilitate implementation. Extensive experiments and two real data applications showcase the validity and advantage of CONCERT over existing cutting-edge transfer learning methods.

Rui Miao, Babak Shahbaba, Annie Qu

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.

Ruqian Zhang, Yijiao Zhang, Juan Shen et al.

Large language models have made revolutionary progress in generating human-like text, yet their outputs often tend to be generic, exhibiting insufficient structural diversity, which limits personalized expression. Recent advances in diffusion models have opened new opportunities for improving language generation beyond the limitations of autoregressive paradigms. In this work, we propose a syntax-guided diffusion language model that integrates structural supervision and personalized conditioning to enhance text quality, diversity, and controllability. We introduce a cascaded framework that generates syntactic guidance before conditional text generation, and further generalize it to a novel noncascaded architecture for better alignment between structure and content. By incorporating syntactic information in the generating process, the proposed model better captures the lexical and structural characteristics of stylistic sentence construction. To enable fine-grained personalization, we develop a shared representation mechanism that facilitates information integration across users, supporting both faithful stylistic generation and generalizable zero-shot inference. Extensive experiments on multiple tasks demonstrate the superiority of our approach in fluency, diversity, and stylistic fidelity. Further qualitative analyses highlight its interpretability and flexibility in learning personalized patterns.

Ziyi Liang, Annie Qu, Babak Shahbaba

Developing effective multimodal data fusion strategies has become increasingly essential for improving the predictive power of statistical machine learning methods across a wide range of applications, from autonomous driving to medical diagnosis. Traditional fusion methods, including early, intermediate, and late fusion, integrate data at different stages, each offering distinct advantages and limitations. In this paper, we introduce Meta Fusion, a flexible and principled framework that unifies these existing strategies as special cases. Motivated by deep mutual learning and ensemble learning, Meta Fusion constructs a cohort of models based on various combinations of latent representations across modalities, and further boosts predictive performance through soft information sharing within the cohort. Our approach is model-agnostic in learning the latent representations, allowing it to flexibly adapt to the unique characteristics of each modality. Theoretically, our soft information sharing mechanism reduces the generalization error. Empirically, Meta Fusion consistently outperforms conventional fusion strategies in extensive simulation studies. We further validate our approach on real-world applications, including Alzheimer's disease detection and neural decoding.

Yang Sui, Qi Xu, Yang Bai et al.

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.

Yubai Yuan, Babak Shahbaba, Norbert Fortin et al.

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.

Hanwen Ye, Tatiana Moreno, Adrianne Alpern et al.

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 evaluating children's mental status over time. However, few topic models are built for longitudinal settings, and most existing approaches fail to capture temporal trajectories for each document. To address these challenges, we develop a dynamic topic model with consistent 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 a classifier-free 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 children's mental health progression during the pandemic and offers clinicians valuable insights to recognize disparities in children's mental health related to their sexual and gender identities.

Yujia Deng, Yubai Yuan, Haoda Fu et al.

In this paper we propose an active metric learning method for clustering with pairwise constraints. The proposed method actively queries the label of informative instance pairs, while estimating underlying metrics by incorporating unlabeled instance pairs, which leads to a more accurate and efficient clustering process. In particular, we augment the queried constraints by generating more pairwise labels to provide additional information in learning a metric to enhance clustering performance. Furthermore, we increase the robustness of metric learning by updating the learned metric sequentially and penalizing the irrelevant features adaptively. In addition, we propose a novel active query strategy that evaluates the information gain of instance pairs more accurately by incorporating the neighborhood structure, which improves clustering efficiency without extra labeling cost. In theory, we provide a tighter error bound of the proposed metric learning method utilizing augmented queries compared with methods using existing constraints only. Furthermore, we also investigate the improvement using the active query strategy instead of random selection. Numerical studies on simulation settings and real datasets indicate that the proposed method is especially advantageous when the signal-to-noise ratio between significant features and irrelevant features is low.

Yubai Yuan, Annie Qu

Link prediction infers potential links from observed networks, and is one of the essential problems in network analyses. In contrast to traditional graph representation modeling which only predicts two-way pairwise relations, we propose a novel tensor-based joint network embedding approach on simultaneously encoding pairwise links and hyperlinks onto a latent space, which captures the dependency between pairwise and multi-way links in inferring potential unobserved hyperlinks. The major advantage of the proposed embedding procedure is that it incorporates both the pairwise relationships and subgroup-wise structure among nodes to capture richer network information. In addition, the proposed method introduces a hierarchical dependency among links to infer potential hyperlinks, and leads to better link prediction. In theory we establish the estimation consistency for the proposed embedding approach, and provide a faster convergence rate compared to link prediction utilizing pairwise links or hyperlinks only. Numerical studies on both simulation settings and Facebook ego-networks indicate that the proposed method improves both hyperlink and pairwise link prediction accuracy compared to existing link prediction algorithms.

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.

Xuan Bi, Gediminas Adomavicius, William Li et al.

Due to accessible big data collections from consumers, products, and stores, advanced sales forecasting capabilities have drawn great attention from many companies especially in the retail business because of its importance in decision making. Improvement of the forecasting accuracy, even by a small percentage, may have a substantial impact on companies' production and financial planning, marketing strategies, inventory controls, supply chain management, and eventually stock prices. Specifically, our research goal is to forecast the sales of each product in each store in the near future. Motivated by tensor factorization methodologies for personalized context-aware recommender systems, we propose a novel approach called the Advanced Temporal Latent-factor Approach to Sales forecasting (ATLAS), which achieves accurate and individualized prediction for sales by building a single tensor-factorization model across multiple stores and products. Our contribution is a combination of: tensor framework (to leverage information across stores and products), a new regularization function (to incorporate demand dynamics), and extrapolation of tensor into future time periods using state-of-the-art statistical (seasonal auto-regressive integrated moving-average models) and machine-learning (recurrent neural networks) models. The advantages of ATLAS are demonstrated on eight product category datasets collected by the Information Resource, Inc., where a total of 165 million weekly sales transactions from more than 1,500 grocery stores over 15,560 products are analyzed.

Fei Xue, Yanqing Zhang, Wenzhuo Zhou et al.

An optimal dynamic treatment regime (DTR) consists of a sequence of decision rules in maximizing long-term benefits, which is applicable for chronic diseases such as HIV infection or cancer. In this paper, we develop a novel angle-based approach to search the optimal DTR under a multicategory treatment framework for survival data. The proposed method targets maximization the conditional survival function of patients following a DTR. In contrast to most existing approaches which are designed to maximize the expected survival time under a binary treatment framework, the proposed method solves the multicategory treatment problem given multiple stages for censored data. Specifically, the proposed method obtains the optimal DTR via integrating estimations of decision rules at multiple stages into a single multicategory classification algorithm without imposing additional constraints, which is also more computationally efficient and robust. In theory, we establish Fisher consistency of the proposed method under regularity conditions. Our numerical studies show that the proposed method outperforms competing methods in terms of maximizing the conditional survival function. We apply the proposed method to two real datasets: Framingham heart study data and acquired immunodeficiency syndrome (AIDS) clinical data.

Xiwei Tang, Xuan Bi, Annie Qu

This work is motivated by multimodality breast cancer imaging data, which is quite challenging in that the signals of discrete tumor-associated microvesicles (TMVs) are randomly distributed with heterogeneous patterns. This imposes a significant challenge for conventional imaging regression and dimension reduction models assuming a homogeneous feature structure. We develop an innovative multilayer tensor learning method to incorporate heterogeneity to a higher-order tensor decomposition and predict disease status effectively through utilizing subject-wise imaging features and multimodality information. Specifically, we construct a multilayer decomposition which leverages an individualized imaging layer in addition to a modality-specific tensor structure. One major advantage of our approach is that we are able to efficiently capture the heterogeneous spatial features of signals that are not characterized by a population structure as well as integrating multimodality information simultaneously. To achieve scalable computing, we develop a new bi-level block improvement algorithm. In theory, we investigate both the algorithm convergence property, tensor signal recovery error bound and asymptotic consistency for prediction model estimation. We also apply the proposed method for simulated and human breast cancer imaging data. Numerical results demonstrate that the proposed method outperforms other existing competing methods.

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.

Xuan Bi, Annie Qu, Xiaotong Shen

Recommender systems have been widely adopted by electronic commerce and entertainment industries for individualized prediction and recommendation, which benefit consumers and improve business intelligence. In this article, we propose an innovative method, namely the recommendation engine of multilayers (REM), for tensor recommender systems. The proposed method utilizes the structure of a tensor response to integrate information from multiple modes, and creates an additional layer of nested latent factors to accommodate between-subjects dependency. One major advantage is that the proposed method is able to address the "cold-start" issue in the absence of information from new customers, new products or new contexts. Specifically, it provides more effective recommendations through sub-group information. To achieve scalable computation, we develop a new algorithm for the proposed method, which incorporates a maximum block improvement strategy into the cyclic blockwise-coordinate-descent algorithm. In theory, we investigate both algorithmic properties for global and local convergence, along with the asymptotic consistency of estimated parameters. Finally, the proposed method is applied in simulations and IRI marketing data with 116 million observations of product sales. Numerical studies demonstrate that the proposed method outperforms existing competitors in the literature.