Didong Li

Buxin Su, Jiayao Zhang, Natalie Collina et al. · princeton

We conducted an experiment during the review process of the 2023 International Conference on Machine Learning (ICML), asking authors with multiple submissions to rank their papers based on perceived quality. In total, we received 1,342 rankings, each from a different author, covering 2,592 submissions. In this paper, we present an empirical analysis of how author-provided rankings could be leveraged to improve peer review processes at machine learning conferences. We focus on the Isotonic Mechanism, which calibrates raw review scores using the author-provided rankings. Our analysis shows that these ranking-calibrated scores outperform the raw review scores in estimating the ground truth ``expected review scores'' in terms of both squared and absolute error metrics. Furthermore, we propose several cautious, low-risk applications of the Isotonic Mechanism and author-provided rankings in peer review, including supporting senior area chairs in overseeing area chairs' recommendations, assisting in the selection of paper awards, and guiding the recruitment of emergency reviewers.

Buxin Su, Jiayao Zhang, Natalie Collina et al.

This article is the rejoinder to ``The ICML 2023 Ranking Experiment: Examining Author Self-Assessment in ML/AI Peer Review,'' to appear in the Journal of the American Statistical Association with discussion. To address the practical and theoretical points raised by the discussants, we organize our response around four core themes: (i) formulating peer review as a statistical estimation problem; (ii) mitigating equity and strategic concerns in the deployment of the Isotonic Mechanism; (iii) incorporating complementary signals such as reviewer rankings and structured metadata; and (iv) exploring a human-centered framework for peer review in the era of generative AI.

Hengrui Luo, Jeremy E. Purvis, Didong Li

Modern datasets often exhibit high dimensionality, yet the data reside in low-dimensional manifolds that can reveal underlying geometric structures critical for data analysis. A prime example of such a dataset is a collection of cell cycle measurements, where the inherently cyclical nature of the process can be represented as a circle or sphere. Motivated by the need to analyze these types of datasets, we propose a nonlinear dimension reduction method, Spherical Rotation Component Analysis (SRCA), that incorporates geometric information to better approximate low-dimensional manifolds. SRCA is a versatile method designed to work in both high-dimensional and small sample size settings. By employing spheres or ellipsoids, SRCA provides a low-rank spherical representation of the data with general theoretic guarantees, effectively retaining the geometric structure of the dataset during dimensionality reduction. A comprehensive simulation study, along with a successful application to human cell cycle data, further highlights the advantages of SRCA compared to state-of-the-art alternatives, demonstrating its superior performance in approximating the manifold while preserving inherent geometric structures.

Jiawen Chen, Wancen Mu, Yun Li et al.

In this paper, we critically examine the prevalent practice of using additive mixtures of Matérn kernels in single-output Gaussian process (GP) models and explore the properties of multiplicative mixtures of Matérn kernels for multi-output GP models. For the single-output case, we derive a series of theoretical results showing that the smoothness of a mixture of Matérn kernels is determined by the least smooth component and that a GP with such a kernel is effectively equivalent to the least smooth kernel component. Furthermore, we demonstrate that none of the mixing weights or parameters within individual kernel components are identifiable. We then turn our attention to multi-output GP models and analyze the identifiability of the covariance matrix $A$ in the multiplicative kernel $K(x,y) = AK_0(x,y)$, where $K_0$ is a standard single output kernel such as Matérn. We show that $A$ is identifiable up to a multiplicative constant, suggesting that multiplicative mixtures are well suited for multi-output tasks. Our findings are supported by extensive simulations and real applications for both single- and multi-output settings. This work provides insight into kernel selection and interpretation for GP models, emphasizing the importance of choosing appropriate kernel structures for different tasks.

Hongqian Niu, Jordan Bryan, Xihao Li et al.

Recent advances in large language model (LLM) embeddings have enabled powerful representations for biological data, but most applications to date focus only on gene-level information. We present one of the first systematic frameworks to generate variant-level embeddings across the entire human genome. Using curated annotations from FAVOR, ClinVar, and the GWAS Catalog, we constructed semantic text descriptions for 8.9 billion possible variants and generated embeddings at three scales: 1.5 million HapMap3+MEGA variants, ~90 million imputed UK Biobank variants, and ~9 billion all possible variants. Embeddings were produced with both OpenAI's text-embedding-3-large and the open-source Qwen3-Embedding-0.6B models. Baseline experiments demonstrate high predictive accuracy for variant properties, validating the embeddings as structured representations of genomic variation. We outline two downstream applications: embedding-informed hypothesis testing by extending the Frequentist And Bayesian framework to genome-wide association studies, and embedding-augmented genetic risk prediction that enhances standard polygenic risk scores. These resources, publicly available on Hugging Face, provide a foundation for advancing large-scale genomic discovery and precision medicine.

Aishwarya Mandyam, Didong Li, Jiayu Yao et al.

Inverse reinforcement learning (IRL) methods infer an agent's reward function using demonstrations of expert behavior. A Bayesian IRL approach models a distribution over candidate reward functions, capturing a degree of uncertainty in the inferred reward function. This is critical in some applications, such as those involving clinical data. Typically, Bayesian IRL algorithms require large demonstration datasets, which may not be available in practice. In this work, we incorporate existing domain-specific data to achieve better posterior concentration rates. We study a common setting in clinical and biological applications where we have access to expert demonstrations and known reward functions for a set of training tasks. Our aim is to learn the reward function of a new test task given limited expert demonstrations. Existing Bayesian IRL methods impose restrictions on the form of input data, thus limiting the incorporation of training task data. To better leverage information from training tasks, we introduce kernel density Bayesian inverse reinforcement learning (KD-BIRL). Our approach employs a conditional kernel density estimator, which uses the known reward functions of the training tasks to improve the likelihood estimation across a range of reward functions and demonstration samples. Our empirical results highlight KD-BIRL's faster concentration rate in comparison to baselines, particularly in low test task expert demonstration data regimes. Additionally, we are the first to provide theoretical guarantees of posterior concentration for a Bayesian IRL algorithm. Taken together, this work introduces a principled and theoretically grounded framework that enables Bayesian IRL to be applied across a variety of domains.

Kevin Wang, Hongqian Niu, Didong Li

Generative Artificial Intelligence (AI), such as large language models (LLMs), has become a transformative force across science, industry, and society. As these systems grow in popularity, web data becomes increasingly interwoven with this AI-generated material and it is increasingly difficult to separate them from naturally generated content. As generative models are updated regularly, later models will inevitably be trained on mixtures of human-generated data and AI-generated data from earlier versions, creating a recursive training process with data contamination. Existing theoretical work has examined only highly simplified settings, where both the real data and the generative model are discrete or Gaussian, where it has been shown that such recursive training leads to model collapse. However, real data distributions are far more complex, and modern generative models are far more flexible than Gaussian and linear mechanisms. To fill this gap, we study recursive training in a general framework with minimal assumptions on the real data distribution and allow the underlying generative model to be a general universal approximator. In this framework, we show that contaminated recursive training still converges, with a convergence rate equal to the minimum of the baseline model's convergence rate and the fraction of real data used in each iteration. To the best of our knowledge, this is the first (positive) theoretical result on recursive training without distributional assumptions on the data. We further extend the analysis to settings where sampling bias is present in data collection and support all theoretical results with empirical studies.

Cuiran Shi, Shuying Han, Shreya Kusumanchi et al.

This study presents a large-scale network dataset, NIH-MPINet, curated from NIH RePORTER and PubMed, characterizing collaboration among multiple Principal Investigators (multi-PIs) on NIH R01-equivalent grants from 2006 to 2023. The network characterizes 30,127 PIs as nodes and their collaborations on 86,743 NIH R01-equivalent grants as edges, spanning 888 recipient organizations and supported by 40 NIH Institutes and Centers. We also curated comprehensive metadata, including node-level features such as PI affiliation, alongside edge-level features comprising grant years, titles, and abstracts. Using these data, we constructed a PI collaboration network and identified 19 communities as well as 20 major research topics. Several collaboration communities showed distinct thematic profiles, such as cardiovascular health, cancer immunotherapy, neuroscience, and microbiome research, while genetics and genomics were broadly represented across communities. By incorporating temporal analysis, we observed shifts in research topics and collaboration patterns over time. Topics like healthcare and outcomes research, cognitive health, and Alzheimer's disease have become more prominent in recent years, whereas molecular and cellular biology has seen a relative decline. Overall, this work provides a high-fidelity, feature-rich resource for advancing statistical learning methods and network analysis-based discoveries in the study of long-term biomedical collaboration.

Kevin Wang, Hongqian Niu, Yixin Wang et al.

Generative networks have shown remarkable success in learning complex data distributions, particularly in generating high-dimensional data from lower-dimensional inputs. While this capability is well-documented empirically, its theoretical underpinning remains unclear. One common theoretical explanation appeals to the widely accepted manifold hypothesis, which suggests that many real-world datasets, such as images and signals, often possess intrinsic low-dimensional geometric structures. Under this manifold hypothesis, it is widely believed that to approximate a distribution on a $d$-dimensional Riemannian manifold, the latent dimension needs to be at least $d$ or $d+1$. In this work, we show that this requirement on the latent dimension is not necessary by demonstrating that generative networks can approximate distributions on $d$-dimensional Riemannian manifolds from inputs of any arbitrary dimension, even lower than $d$, taking inspiration from the concept of space-filling curves. This approach, in turn, leads to a super-exponential complexity bound of the deep neural networks through expanded neurons. Our findings thus challenge the conventional belief on the relationship between input dimensionality and the ability of generative networks to model data distributions. This novel insight not only corroborates the practical effectiveness of generative networks in handling complex data structures, but also underscores a critical trade-off between approximation error, dimensionality, and model complexity.

Yixiang Qu, Yifan Dai, Shilin Yu et al.

Large Language Models (LLMs) have demonstrated remarkable proficiency in natural language processing; however, their application in sensitive domains such as healthcare, especially in processing Electronic Health Records (EHRs), is constrained by limited computational resources and privacy concerns. This paper introduces a compact LLM framework optimized for local deployment in environments with stringent privacy requirements and restricted access to high-performance GPUs. Our approach leverages simple yet powerful preprocessing techniques, including regular expressions (regex) and Retrieval-Augmented Generation (RAG), to extract and highlight critical information from clinical notes. By pre-filtering long, unstructured text, we enhance the performance of smaller LLMs on EHR-related tasks. Our framework is evaluated using zero-shot and few-shot learning paradigms on both private and publicly available datasets (MIMIC-IV), with additional comparisons against fine-tuned LLMs on MIMIC-IV. Experimental results demonstrate that our preprocessing strategy significantly supercharges the performance of smaller LLMs, making them well-suited for privacy-sensitive and resource-constrained applications. This study offers valuable insights into optimizing LLM performance for local, secure, and efficient healthcare applications. It provides practical guidance for real-world deployment for LLMs while tackling challenges related to privacy, computational feasibility, and clinical applicability.

Yin Liu, Jianwen Cai, Didong Li

Classical statistical learning theory predicts a U-shaped relationship between test loss and model capacity, driven by the bias-variance trade-off. Recent advances in modern machine learning have revealed a more complex pattern, \textit{double-descent}, in which test loss, after peaking near the interpolation threshold, decreases again as model capacity continues to grow. While this behavior has been extensively analyzed in regression and classification, its manifestation in survival analysis remains unexplored. This study investigates overparametrization in four representative survival models: DeepSurv, PC-Hazard, Nnet-Survival, and N-MTLR. We rigorously define \textit{interpolation} and \textit{finite-norm interpolation}, two key characteristics of loss-based models to understand \textit{double-descent}. We then show the existence (or absence) of \textit{(finite-norm) interpolation} of all four models. Our findings clarify how likelihood-based losses and model implementation jointly determine the feasibility of \textit{interpolation} and show that overparametrization should not be regarded as benign for survival models. All theoretical results are supported by numerical experiments that highlight the distinct generalization behaviors of survival models.

Buxin Su, Natalie Collina, Garrett Wen et al.

Peer review in academic research aims not only to ensure factual correctness but also to identify work of high scientific potential that can shape future research directions. This task is especially critical in fast-moving fields such as artificial intelligence (AI), yet it has become increasingly difficult given the rapid growth of submissions. In this paper, we investigate an underexplored measure for identifying high-impact research: authors' own rankings of their multiple submissions to the same AI conference. Grounded in game-theoretic reasoning, we hypothesize that self-rankings are informative because authors possess unique understanding of their work's conceptual depth and long-term promise. To test this hypothesis, we conducted a large-scale experiment at a leading AI conference, where 1,342 researchers self-ranked their 2,592 submissions by perceived quality. Tracking outcomes over more than a year, we found that papers ranked highest by their authors received twice as many citations as their lowest-ranked counterparts; self-rankings were especially effective at identifying highly cited papers (those with over 150 citations). Moreover, we showed that self-rankings outperformed peer review scores in predicting future citation counts. Our results remained robust after accounting for confounders such as preprint posting time and self-citations. Together, these findings demonstrate that authors' self-rankings provide a reliable and valuable complement to peer review for identifying and elevating high-impact research in AI.

Shiyi Yang, Can Chen, Didong Li

Networks with higher-order interactions, prevalent in biological, social, and information systems, are naturally represented as hypergraphs, yet their structural complexity poses fundamental challenges for geometric characterization. While curvature-based methods offer powerful insights in graph analysis, existing extensions to hypergraphs suffer from critical trade-offs: combinatorial approaches such as Forman-Ricci curvature capture only coarse features, whereas geometric methods like Ollivier-Ricci curvature offer richer expressivity but demand costly optimal transport computations. To address these challenges, we introduce hypergraph lower Ricci curvature (HLRC), a novel curvature metric defined in closed form that achieves a principled balance between interpretability and efficiency. Evaluated across diverse synthetic and real-world hypergraph datasets, HLRC consistently reveals meaningful higher-order organization, distinguishing intra- from inter-community hyperedges, uncovering latent semantic labels, tracking temporal dynamics, and supporting robust clustering of hypergraphs based on global structure. By unifying geometric sensitivity with algorithmic simplicity, HLRC provides a versatile foundation for hypergraph analytics, with broad implications for tasks including node classification, anomaly detection, and generative modeling in complex systems.

Xuejun Sun, Yiran Song, Xiaochen Zhou et al.

Respiratory viral infections pose a global health burden, yet the cellular immune responses driving protection or pathology remain unclear. Natural infection cohorts often lack pre-exposure baseline data and structured temporal sampling. In contrast, inoculation and vaccination trials generate insightful longitudinal transcriptomic data. However, the scattering of these datasets across platforms, along with inconsistent metadata and preprocessing procedure, hinders AI-driven discovery. To address these challenges, we developed the Human Respiratory Viral Immunization LongitudinAl Gene Expression (HR-VILAGE-3K3M) repository: an AI-ready, rigorously curated dataset that integrates 14,136 RNA-seq profiles from 3,178 subjects across 66 studies encompassing over 2.56 million cells. Spanning vaccination, inoculation, and mixed exposures, the dataset includes microarray, bulk RNA-seq, and single-cell RNA-seq from whole blood, PBMCs, and nasal swabs, sourced from GEO, ImmPort, and ArrayExpress. We harmonized subject-level metadata, standardized outcome measures, applied unified preprocessing pipelines with rigorous quality control, and aligned all data to official gene symbols. To demonstrate the utility of HR-VILAGE-3K3M, we performed predictive modeling of vaccine responders and evaluated batch-effect correction methods. Beyond these initial demonstrations, it supports diverse systems immunology applications and benchmarking of feature selection and transfer learning algorithms. Its scale and heterogeneity also make it ideal for pretraining foundation models of the human immune response and for advancing multimodal learning frameworks. As the largest longitudinal transcriptomic resource for human respiratory viral immunization, it provides an accessible platform for reproducible AI-driven research, accelerating systems immunology and vaccine development against emerging viral threats.

Jiawen Chen, Muqing Zhou, Wenrong Wu et al.

Recent advances in multi-modal algorithms have driven and been driven by the increasing availability of large image-text datasets, leading to significant strides in various fields, including computational pathology. However, in most existing medical image-text datasets, the text typically provides high-level summaries that may not sufficiently describe sub-tile regions within a large pathology image. For example, an image might cover an extensive tissue area containing cancerous and healthy regions, but the accompanying text might only specify that this image is a cancer slide, lacking the nuanced details needed for in-depth analysis. In this study, we introduce STimage-1K4M, a novel dataset designed to bridge this gap by providing genomic features for sub-tile images. STimage-1K4M contains 1,149 images derived from spatial transcriptomics data, which captures gene expression information at the level of individual spatial spots within a pathology image. Specifically, each image in the dataset is broken down into smaller sub-image tiles, with each tile paired with 15,000-30,000 dimensional gene expressions. With 4,293,195 pairs of sub-tile images and gene expressions, STimage-1K4M offers unprecedented granularity, paving the way for a wide range of advanced research in multi-modal data analysis an innovative applications in computational pathology, and beyond.

Sam Hawke, Hengrui Luo, Didong Li

Supervised dimension reduction (SDR) has been a topic of growing interest in data science, as it enables the reduction of high-dimensional covariates while preserving the functional relation with certain response variables of interest. However, existing SDR methods are not suitable for analyzing datasets collected from case-control studies. In this setting, the goal is to learn and exploit the low-dimensional structure unique to or enriched by the case group, also known as the foreground group. While some unsupervised techniques such as the contrastive latent variable model and its variants have been developed for this purpose, they fail to preserve the functional relationship between the dimension-reduced covariates and the response variable. In this paper, we propose a supervised dimension reduction method called contrastive inverse regression (CIR) specifically designed for the contrastive setting. CIR introduces an optimization problem defined on the Stiefel manifold with a non-standard loss function. We prove the convergence of CIR to a local optimum using a gradient descent-based algorithm, and our numerical study empirically demonstrates the improved performance over competing methods for high-dimensional data.

Tianyu Wang, Yifeng Huang, Didong Li

Over a complete Riemannian manifold of finite dimension, Greene and Wu introduced a convolution, known as Greene-Wu (GW) convolution. In this paper, we study properties of the GW convolution and apply it to non-Euclidean machine learning problems. In particular, we derive a new formula for how the curvature of the space would affect the curvature of the function through the GW convolution. Also, following the study of the GW convolution, a new method for gradient estimation over Riemannian manifolds is introduced.

Didong Li, Andrew Jones, Barbara Engelhardt

Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal component analysis (CPCA) was proposed for this setting. However, the lack of a formal probabilistic model makes it difficult to reason about CPCA and to tune its hyperparameter. In this work, we propose probabilistic contrastive principal component analysis (PCPCA), a model-based alternative to CPCA. We discuss how to set the hyperparameter in theory and in practice, and we show several of PCPCA's advantages over CPCA, including greater interpretability, uncertainty quantification and principled inference, robustness to noise and missing data, and the ability to generate data from the model. We demonstrate PCPCA's performance through a series of simulations and case-control experiments with datasets of gene expression, protein expression, and images.

Debolina Paul, Saptarshi Chakraborty, Didong Li et al.

Even with the rise in popularity of over-parameterized models, simple dimensionality reduction and clustering methods, such as PCA and k-means, are still routinely used in an amazing variety of settings. A primary reason is the combination of simplicity, interpretability and computational efficiency. The focus of this article is on improving upon PCA and k-means, by allowing non-linear relations in the data and more flexible cluster shapes, without sacrificing the key advantages. The key contribution is a new framework for Principal Elliptical Analysis (PEA), defining a simple and computationally efficient alternative to PCA that fits the best elliptical approximation through the data. We provide theoretical guarantees on the proposed PEA algorithm using Vapnik-Chervonenkis (VC) theory to show strong consistency and uniform concentration bounds. Toy experiments illustrate the performance of PEA, and the ability to adapt to non-linear structure and complex cluster shapes. In a rich variety of real data clustering applications, PEA is shown to do as well as k-means for simple datasets, while dramatically improving performance in more complex settings.

Didong Li, David B Dunson

Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately calculate distances. When data points are real-valued vectors, by far the most common choice is the Euclidean distance. This article is focused on the problem of how to better calculate distances taking into account the intrinsic geometry of the data, assuming data are concentrated near an unknown subspace or manifold. The appropriate geometric distance corresponds to the length of the shortest path along the manifold, which is the geodesic distance. When the manifold is unknown, it is challenging to accurately approximate the geodesic distance. Current algorithms are either highly complex, and hence often impractical to implement, or based on simple local linear approximations and shortest path algorithms that may have inadequate accuracy. We propose a simple and general alternative, which uses pieces of spheres, or spherelets, to locally approximate the unknown subspace and thereby estimate the geodesic distance through paths over spheres. Theory is developed showing lower error for many manifolds, with applications in clustering, conditional density estimation and mean regression. The conclusion is supported through multiple simulation examples and real data sets.

Yueqi Cao, Didong Li, Huafei Sun et al.

In this paper, we propose an efficient method to estimate the Weingarten map for point cloud data sampled from manifold embedded in Euclidean space. A statistical model is established to analyze the asymptotic property of the estimator. In particular, we show the convergence rate as the sample size tends to infinity. We verify the convergence rate through simulated data and apply the estimated Weingarten map to curvature estimation and point cloud simplification to multiple real data sets.

Didong Li, David B Dunson

Classifiers label data as belonging to one of a set of groups based on input features. It is challenging to obtain accurate classification performance when the feature distributions in the different classes are complex, with nonlinear, overlapping and intersecting supports. This is particularly true when training data are limited. To address this problem, this article proposes a new type of classifier based on obtaining a local approximation to the support of the data within each class in a neighborhood of the feature to be classified, and assigning the feature to the class having the closest support. This general algorithm is referred to as LOcal Manifold Approximation (LOMA) classification. As a simple and theoretically supported special case having excellent performance in a broad variety of examples, we use spheres for local approximation, obtaining a SPherical Approximation (SPA) classifier. We illustrate substantial gains for SPA over competitors on a variety of challenging simulated and real data examples.

Didong Li, Minerva Mukhopadhyay, David B. Dunson

In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on exploiting such approximations in clustering, data compression, and prediction. Most of the literature relies on linear or locally linear approximations. In this article, we propose a simple and general alternative, which instead uses spheres, an approach we refer to as spherelets. We develop spherical principal components analysis (SPCA), and provide theory on the convergence rate for global and local SPCA, while showing that spherelets can provide lower covering numbers and MSEs for many manifolds. Results relative to state-of-the-art competitors show gains in ability to accurately approximate manifolds with fewer components. Unlike most competitors, which simply output lower-dimensional features, our approach projects data onto the estimated manifold to produce fitted values that can be used for model assessment and cross validation. The methods are illustrated with applications to multiple data sets.