Rong Ma

Rong Ma, Eric D. Sun, David Donoho et al.

Single-cell data integration can provide a comprehensive molecular view of cells, and many algorithms have been developed to remove unwanted technical or biological variations and integrate heterogeneous single-cell datasets. Despite their wide usage, existing methods suffer from several fundamental limitations. In particular, we lack a rigorous statistical test for whether two high-dimensional single-cell datasets are alignable (and therefore should even be aligned). Moreover, popular methods can substantially distort the data during alignment, making the aligned data and downstream analysis difficult to interpret. To overcome these limitations, we present a spectral manifold alignment and inference (SMAI) framework, which enables principled and interpretable alignability testing and structure-preserving integration of single-cell data with the same type of features. SMAI provides a statistical test to robustly assess the alignability between datasets to avoid misleading inference, and is justified by high-dimensional statistical theory. On a diverse range of real and simulated benchmark datasets, it outperforms commonly used alignment methods. Moreover, we show that SMAI improves various downstream analyses such as identification of differentially expressed genes and imputation of single-cell spatial transcriptomics, providing further biological insights. SMAI's interpretability also enables quantification and a deeper understanding of the sources of technical confounders in single-cell data.

Rong Ma, Eric D. Sun, James Zou

Dimension reduction and data visualization aim to project a high-dimensional dataset to a low-dimensional space while capturing the intrinsic structures in the data. It is an indispensable part of modern data science, and many dimensional reduction and visualization algorithms have been developed. However, different algorithms have their own strengths and weaknesses, making it critically important to evaluate their relative performance for a given dataset, and to leverage and combine their individual strengths. In this paper, we propose an efficient spectral method for assessing and combining multiple visualizations of a given dataset produced by diverse algorithms. The proposed method provides a quantitative measure -- the visualization eigenscore -- of the relative performance of the visualizations for preserving the structure around each data point. Then it leverages the eigenscores to obtain a consensus visualization, which has much improved { quality over the individual visualizations in capturing the underlying true data structure.} Our approach is flexible and works as a wrapper around any visualizations. We analyze multiple simulated and real-world datasets from diverse applications to demonstrate the effectiveness of the eigenscores for evaluating visualizations and the superiority of the proposed consensus visualization. Furthermore, we establish rigorous theoretical justification of our method based on a general statistical framework, yielding fundamental principles behind the empirical success of consensus visualization along with practical guidance.

Boris Landa, Yuval Kluger, Rong Ma

Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis. In numerous applications, it is necessary to align and jointly embed multiple datasets from different studies or experimental conditions. Such datasets may share underlying structures of interest but exhibit individual distortions, resulting in misaligned embeddings using traditional techniques. In this work, we propose \textit{Entropic Optimal Transport (EOT) eigenmaps}, a principled approach for aligning and jointly embedding a pair of datasets with theoretical guarantees. Our approach leverages the leading singular vectors of the EOT plan matrix between two datasets to extract their shared underlying structure and align the datasets accordingly in a common embedding space. We interpret our approach as an inter-data variant of the classical Laplacian eigenmaps and diffusion maps embeddings, showing that it enjoys many favorable analogous properties. We then analyze a data-generative model where two observed high-dimensional datasets share latent variables on a common low-dimensional manifold, but each dataset is subject to data-specific translation, scaling, nuisance structures, and noise. We show that in a high-dimensional asymptotic regime, the EOT plan recovers the shared manifold structure by approximating a kernel function evaluated at the locations of the latent variables. Subsequently, we provide a geometric interpretation of our embedding by relating it to the eigenfunctions of population-level operators encoding the density and geometry of the shared manifold. Finally, we showcase the performance of our approach for data integration and embedding through simulations and analyses of real-world biological data, demonstrating its advantages over alternative methods in challenging scenarios.

Tal Einav, Rong Ma

A central challenge in every field of biology is to use existing measurements to predict the outcomes of future experiments. In this work, we consider the wealth of antibody inhibition data against variants of the influenza virus. Due to this viru's genetic diversity and evolvability, the variants examined in one study will often have little-to-no overlap with other studies, making it difficult to discern common patterns or unify datasets for further analysis. To that end, we develop a computational framework that predicts how an antibody or serum would inhibit any variant from any other study. We use this framework to greatly expand seven influenza datasets utilizing hemagglutination inhibition, validating our method upon 200,000 existing measurements and predicting 2,000,000 new values along with their uncertainties. With these new values, we quantify the transferability between seven vaccination and infection studies in humans and ferrets, show that the serum potency is negatively correlated with breadth, and present a tool for pandemic preparedness. This data-driven approach does not require any information beyond each virus's name and measurements, and even datasets with as few as 5 viruses can be expanded, making this approach widely applicable. Future influenza studies using hemagglutination inhibition can directly utilize our curated datasets to predict newly measured antibody responses against ~80 H3N2 influenza viruses from 1968-2011, whereas immunological studies utilizing other viruses or a different assay only need a single partially-overlapping dataset to extend their work. In essence, this approach enables a shift in perspective when analyzing data from "what you see is what you get" into "what anyone sees is what everyone gets."

Rong Ma, Jie Chen, Xiangyang Xue et al.

Deep supervised models possess significant capability to assimilate extensive training data, thereby presenting an opportunity to enhance model performance through training on multiple datasets. However, conflicts arising from different label spaces among datasets may adversely affect model performance. In this paper, we propose a novel approach to automatically construct a unified label space across multiple datasets using graph neural networks. This enables semantic segmentation models to be trained simultaneously on multiple datasets, resulting in performance improvements. Unlike existing methods, our approach facilitates seamless training without the need for additional manual reannotation or taxonomy reconciliation. This significantly enhances the efficiency and effectiveness of multi-dataset segmentation model training. The results demonstrate that our method significantly outperforms other multi-dataset training methods when trained on seven datasets simultaneously, and achieves state-of-the-art performance on the WildDash 2 benchmark.

Yaoming Zhu, Junxin Wang, Yiyang Li et al.

As models become increasingly sophisticated, conventional algorithm benchmarks are increasingly saturated, underscoring the need for more challenging benchmarks to guide future improvements in algorithmic reasoning. This paper introduces OIBench, a high-quality, private, and challenging olympiad-level informatics dataset comprising 250 carefully curated original problems. We detail the construction methodology of the benchmark, ensuring a comprehensive assessment across various programming paradigms and complexities, and we demonstrate its contamination-resistant properties via experiments. We propose Time/Space Completion Curves for finer-grained efficiency analysis and enable direct human-model comparisons through high-level participant evaluations. Our experiments reveal that while open-source models lag behind closed-source counterparts, current SOTA models already outperform most human participants in both correctness and efficiency, while still being suboptimal compared to the canonical solutions. By releasing OIBench as a fully open-source resource (https://huggingface.co/datasets/AGI-Eval/OIBench), we hope this benchmark will contribute to advancing code reasoning capabilities for future LLMs.

Jibai Lin, Bo Ma, Yating Yang et al.

Subject-driven image generation (SDIG) aims to manipulate specific subjects within images while adhering to textual instructions, a task crucial for advancing text-to-image diffusion models. SDIG requires reconciling the tension between maintaining subject identity and complying with dynamic edit instructions, a challenge inadequately addressed by existing methods. In this paper, we introduce the Target-Instructed Diffusion Enhancing (TIDE) framework, which resolves this tension through target supervision and preference learning without test-time fine-tuning. TIDE pioneers target-supervised triplet alignment, modelling subject adaptation dynamics using a (reference image, instruction, target images) triplet. This approach leverages the Direct Subject Diffusion (DSD) objective, training the model with paired "winning" (balanced preservation-compliance) and "losing" (distorted) targets, systematically generated and evaluated via quantitative metrics. This enables implicit reward modelling for optimal preservation-compliance balance. Experimental results on standard benchmarks demonstrate TIDE's superior performance in generating subject-faithful outputs while maintaining instruction compliance, outperforming baseline methods across multiple quantitative metrics. TIDE's versatility is further evidenced by its successful application to diverse tasks, including structural-conditioned generation, image-to-image generation, and text-image interpolation. Our code is available at https://github.com/KomJay520/TIDE.

Zhexuan Liu, Rong Ma, Yiqiao Zhong

Visualizing high-dimensional data is essential for understanding biomedical data and deep learning models. Neighbor embedding methods, such as t-SNE and UMAP, are widely used but can introduce misleading visual artifacts. We find that the manifold learning interpretations from many prior works are inaccurate and that the misuse stems from a lack of data-independent notions of embedding maps, which project high-dimensional data into a lower-dimensional space. Leveraging the leave-one-out principle, we introduce LOO-map, a framework that extends embedding maps beyond discrete points to the entire input space. We identify two forms of map discontinuity that distort visualizations: one exaggerates cluster separation and the other creates spurious local structures. As a remedy, we develop two types of point-wise diagnostic scores to detect unreliable embedding points and improve hyperparameter selection, which are validated on datasets from computer vision and single-cell omics.

Xiucai Ding, Rong Ma

Integrative analysis of multiple heterogeneous datasets has become standard practice in many research fields, especially in single-cell genomics and medical informatics. Existing approaches oftentimes suffer from limited power in capturing nonlinear structures, insufficient account of noisiness and effects of high-dimensionality, lack of adaptivity to signals and sample sizes imbalance, and their results are sometimes difficult to interpret. To address these limitations, we propose a novel kernel spectral method that achieves joint embeddings of two independently observed high-dimensional noisy datasets. The proposed method automatically captures and leverages possibly shared low-dimensional structures across datasets to enhance embedding quality. The obtained low-dimensional embeddings can be utilized for many downstream tasks such as simultaneous clustering, data visualization, and denoising. The proposed method is justified by rigorous theoretical analysis. Specifically, we show the consistency of our method in recovering the low-dimensional noiseless signals, and characterize the effects of the signal-to-noise ratios on the rates of convergence. Under a joint manifolds model framework, we establish the convergence of ultimate embeddings to the eigenfunctions of some newly introduced integral operators. These operators, referred to as duo-landmark integral operators, are defined by the convolutional kernel maps of some reproducing kernel Hilbert spaces (RKHSs). These RKHSs capture the either partially or entirely shared underlying low-dimensional nonlinear signal structures of the two datasets. Our numerical experiments and analyses of two single-cell omics datasets demonstrate the empirical advantages of the proposed method over existing methods in both embeddings and several downstream tasks.

Rong Ma, Xi Li, Jingyuan Hu et al.

Single-cell sequencing is revolutionizing biology by enabling detailed investigations of cell-state transitions. Many biological processes unfold along continuous trajectories, yet it remains challenging to extract smooth, low-dimensional representations from inherently noisy, high-dimensional single-cell data. Neighbor embedding (NE) algorithms, such as t-SNE and UMAP, are widely used to embed high-dimensional single-cell data into low dimensions. But they often introduce undesirable distortions, resulting in misleading interpretations. Existing evaluation methods for NE algorithms primarily focus on separating discrete cell types rather than capturing continuous cell-state transitions, while dynamic modeling approaches rely on strong assumptions about cellular processes and specialized data. To address these challenges, we build on the Predictability-Computability-Stability (PCS) framework for reliable and reproducible data-driven discoveries. First, we systematically evaluate popular NE algorithms through empirical analysis, simulation, and theory, and reveal their key shortcomings, such as artifacts and instability. We then introduce NESS, a principled and interpretable machine learning approach to improve NE representations by leveraging algorithmic stability and to enable robust inference of smooth biological structures. NESS offers useful concepts, quantitative stability metrics, and efficient computational workflows to uncover developmental trajectories and cell-state transitions in single-cell data. Finally, we apply NESS to six single-cell datasets, spanning pluripotent stem cell differentiation, organoid development, and multiple tissue-specific lineage trajectories. Across these diverse contexts, NESS consistently yields useful biological insights, such as identification of transitional and stable cell states and quantification of transcriptional dynamics during development.

Tavor Z. Baharav, Phillip B. Nicol, Rafael A. Irizarry et al.

Modern data analysis increasingly requires identifying shared latent structure across multiple high-dimensional datasets. A commonly used model assumes that the data matrices are noisy observations of low-rank matrices with a shared singular subspace. In this case, two primary methods have emerged for estimating this shared structure, which vary in how they integrate information across datasets. The first approach, termed Stack-SVD, concatenates all the datasets, and then performs a singular value decomposition (SVD). The second approach, termed SVD-Stack, first performs an SVD separately for each dataset, then aggregates the top singular vectors across these datasets, and finally computes a consensus amongst them. While these methods are widely used, they have not been rigorously studied in the proportional asymptotic regime, which is of great practical relevance in today's world of increasing data size and dimensionality. This lack of theoretical understanding has led to uncertainty about which method to choose and limited the ability to fully exploit their potential. To address these challenges, we derive exact expressions for the asymptotic performance and phase transitions of these two methods and develop optimal weighting schemes to further improve both methods. Our analysis reveals that while neither method uniformly dominates the other in the unweighted case, optimally weighted Stack-SVD dominates optimally weighted SVD-Stack. We extend our analysis to accommodate multiple shared components, and provide practical algorithms for estimating optimal weights from data, offering theoretical guidance for method selection in practical data integration problems. Extensive numerical simulations and semi-synthetic experiments on genomic data corroborate our theoretical findings.

Jonas Fischer, Rong Ma

Low-dimensional embeddings (LDEs) of high-dimensional data are ubiquitous in science and engineering. They allow us to quickly understand the main properties of the data, identify outliers and processing errors, and inform the next steps of data analysis. As such, LDEs have to be faithful to the original high-dimensional data, i.e., they should represent the relationships that are encoded in the data, both at a local as well as global scale. The current generation of LDE approaches focus on reconstructing local distances between any pair of samples correctly, often out-performing traditional approaches aiming at all distances. For these approaches, global relationships are, however, usually strongly distorted, often argued to be an inherent trade-off between local and global structure learning for embeddings. We suggest a new perspective on LDE learning, reconstructing angles between data points. We show that this approach, Mercat, yields good reconstruction across a diverse set of experiments and metrics, and preserve structures well across all scales. Compared to existing work, our approach also has a simple formulation, facilitating future theoretical analysis and algorithmic improvements.

Xiucai Ding, Rong Ma

We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and corrupted by high-dimensional noise. The algorithm employs an adaptive bandwidth selection procedure which does not rely on prior knowledge of the underlying manifold. The obtained low-dimensional embeddings can be further utilized for downstream purposes such as data visualization, clustering and prediction. Our method is theoretically justified and practically interpretable. Specifically, we establish the convergence of the final embeddings to their noiseless counterparts when the dimension and size of the samples are comparably large, and characterize the effect of the signal-to-noise ratio on the rate of convergence and phase transition. We also prove convergence of the embeddings to the eigenfunctions of an integral operator defined by the kernel map of some reproducing kernel Hilbert space capturing the underlying nonlinear structures. Numerical simulations and analysis of three real datasets show the superior empirical performance of the proposed method, compared to many existing methods, on learning various manifolds in diverse applications.

Xinggang Hu, Yunzhou Zhang, Zhenzhong Cao et al.

The dynamic factors in the environment will lead to the decline of camera localization accuracy due to the violation of the static environment assumption of SLAM algorithm. Recently, some related works generally use the combination of semantic constraints and geometric constraints to deal with dynamic objects, but problems can still be raised, such as poor real-time performance, easy to treat people as rigid bodies, and poor performance in low dynamic scenes. In this paper, a dynamic scene-oriented visual SLAM algorithm based on object detection and coarse-to-fine static probability named CFP-SLAM is proposed. The algorithm combines semantic constraints and geometric constraints to calculate the static probability of objects, keypoints and map points, and takes them as weights to participate in camera pose estimation. Extensive evaluations show that our approach can achieve almost the best results in high dynamic and low dynamic scenarios compared to the state-of-the-art dynamic SLAM methods, and shows quite high real-time ability.

T. Tony Cai, Rong Ma

Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrix reordering based on a noisy disordered monotone Toeplitz matrix model. We establish the fundamental statistical limit for this problem in a decision-theoretic framework and demonstrate that a constrained least squares estimator achieves the optimal rate. However, due to its computational complexity, we analyze a popular polynomial-time algorithm, spectral seriation, and show that it is suboptimal. To address this, we propose a novel polynomial-time adaptive sorting algorithm with guaranteed performance improvement. Simulations and analyses of two real single-cell RNA sequencing datasets demonstrate the superiority of our algorithm over existing methods.

Fei Xue, Rong Ma, Hongzhe Li

Blockwise missing data occurs frequently when we integrate multisource or multimodality data where different sources or modalities contain complementary information. In this paper, we consider a high-dimensional linear regression model with blockwise missing covariates and a partially observed response variable. Under this framework, we propose a computationally efficient estimator for the regression coefficient vector based on carefully constructed unbiased estimating equations and a blockwise imputation procedure, and obtain its rate of convergence. Furthermore, building upon an innovative projected estimating equation technique that intrinsically achieves bias-correction of the initial estimator, we propose a nearly unbiased estimator for each individual regression coefficient, which is asymptotically normally distributed under mild conditions. Based on these debiased estimators, asymptotically valid confidence intervals and statistical tests about each regression coefficient are constructed. Numerical studies and application analysis of the Alzheimer's Disease Neuroimaging Initiative data show that the proposed method performs better and benefits more from unsupervised samples than existing methods.

T. Tony Cai, Rong Ma

This paper investigates the theoretical foundations of the t-distributed stochastic neighbor embedding (t-SNE) algorithm, a popular nonlinear dimension reduction and data visualization method. A novel theoretical framework for the analysis of t-SNE based on the gradient descent approach is presented. For the early exaggeration stage of t-SNE, we show its asymptotic equivalence to power iterations based on the underlying graph Laplacian, characterize its limiting behavior, and uncover its deep connection to Laplacian spectral clustering, and fundamental principles including early stopping as implicit regularization. The results explain the intrinsic mechanism and the empirical benefits of such a computational strategy. For the embedding stage of t-SNE, we characterize the kinematics of the low-dimensional map throughout the iterations, and identify an amplification phase, featuring the intercluster repulsion and the expansive behavior of the low-dimensional map, and a stabilization phase. The general theory explains the fast convergence rate and the exceptional empirical performance of t-SNE for visualizing clustered data, brings forth interpretations of the t-SNE visualizations, and provides theoretical guidance for applying t-SNE and selecting its tuning parameters in various applications.

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.

Hanshu Cai, Yiwen Gao, Shuting Sun et al.

According to the World Health Organization, the number of mental disorder patients, especially depression patients, has grown rapidly and become a leading contributor to the global burden of disease. However, the present common practice of depression diagnosis is based on interviews and clinical scales carried out by doctors, which is not only labor-consuming but also time-consuming. One important reason is due to the lack of physiological indicators for mental disorders. With the rising of tools such as data mining and artificial intelligence, using physiological data to explore new possible physiological indicators of mental disorder and creating new applications for mental disorder diagnosis has become a new research hot topic. However, good quality physiological data for mental disorder patients are hard to acquire. We present a multi-modal open dataset for mental-disorder analysis. The dataset includes EEG and audio data from clinically depressed patients and matching normal controls. All our patients were carefully diagnosed and selected by professional psychiatrists in hospitals. The EEG dataset includes not only data collected using traditional 128-electrodes mounted elastic cap, but also a novel wearable 3-electrode EEG collector for pervasive applications. The 128-electrodes EEG signals of 53 subjects were recorded as both in resting state and under stimulation; the 3-electrode EEG signals of 55 subjects were recorded in resting state; the audio data of 52 subjects were recorded during interviewing, reading, and picture description. We encourage other researchers in the field to use it for testing their methods of mental-disorder analysis.

T. Tony Cai, Hongzhe Li, Rong Ma

Driven by a wide range of applications, many principal subspace estimation problems have been studied individually under different structural constraints. This paper presents a unified framework for the statistical analysis of a general structured principal subspace estimation problem which includes as special cases non-negative PCA/SVD, sparse PCA/SVD, subspace constrained PCA/SVD, and spectral clustering. General minimax lower and upper bounds are established to characterize the interplay between the information-geometric complexity of the structural set for the principal subspaces, the signal-to-noise ratio (SNR), and the dimensionality. The results yield interesting phase transition phenomena concerning the rates of convergence as a function of the SNRs and the fundamental limit for consistent estimation. Applying the general results to the specific settings yields the minimax rates of convergence for those problems, including the previous unknown optimal rates for non-negative PCA/SVD, sparse SVD and subspace constrained PCA/SVD.

Ying Zeng, Yansong Feng, Rong Ma et al.

The task of event extraction has long been investigated in a supervised learning paradigm, which is bound by the number and the quality of the training instances. Existing training data must be manually generated through a combination of expert domain knowledge and extensive human involvement. However, due to drastic efforts required in annotating text, the resultant datasets are usually small, which severally affects the quality of the learned model, making it hard to generalize. Our work develops an automatic approach for generating training data for event extraction. Our approach allows us to scale up event extraction training instances from thousands to hundreds of thousands, and it does this at a much lower cost than a manual approach. We achieve this by employing distant supervision to automatically create event annotations from unlabelled text using existing structured knowledge bases or tables.We then develop a neural network model with post inference to transfer the knowledge extracted from structured knowledge bases to automatically annotate typed events with corresponding arguments in text.We evaluate our approach by using the knowledge extracted from Freebase to label texts from Wikipedia articles. Experimental results show that our approach can generate a large number of high quality training instances. We show that this large volume of training data not only leads to a better event extractor, but also allows us to detect multiple typed events.