Sha Cao

Pengtao Dang, Tingbo Guo, Melissa Fishel et al.

A physics-informed neural network (PINN) models the dynamics of a system by integrating the governing physical laws into the architecture of a neural network. By enforcing physical laws as constraints, PINN overcomes challenges with data scarsity and potentially high dimensionality. Existing PINN frameworks rely on fully observed time-course data, the acquisition of which could be prohibitive for many systems. In this study, we developed a new PINN learning paradigm, namely Constrained Learning, that enables the approximation of first-order derivatives or motions using non-time course or partially observed data. Computational principles and a general mathematical formulation of Constrained Learning were developed. We further introduced MPOCtrL (Message Passing Optimization-based Constrained Learning) an optimization approach tailored for the Constrained Learning framework that strives to balance the fitting of physical models and observed data. Its code is available at github link: https://github.com/ptdang1001/MPOCtrL Experiments on synthetic and real-world data demonstrated that MPOCtrL can effectively detect the nonlinear dependency between observed data and the underlying physical properties of the system. In particular, on the task of metabolic flux analysis, MPOCtrL outperforms all existing data-driven flux estimators.

Xiao Wang, Jia Wang, Yijie Wang et al.

Large language models (LLMs) have achieved impressive results in natural language understanding, yet their reasoning capabilities remain limited when operating as single agents. Multi-Agent Debate (MAD) has been proposed to address this limitation by enabling collaborative reasoning among multiple models in a round-table debate manner. While effective, MAD introduces substantial computational overhead due to the number of agents involved and the frequent communication required. In this paper, we propose MARS (Multi-Agent Review System), a role-based collaboration framework inspired by the review process. In MARS, an author agent generates an initial solution, reviewer agents provide decisions and comments independently, and a meta-reviewer integrates the feedback to make the final decision and guide further revision. This design enhances reasoning quality while avoiding costly reviewer-to-reviewer interactions, thereby controlling token consumption and inference time. We compared MARS with both MAD and other state-of-the-art reasoning strategies across multiple benchmarks. Extensive experiments with different LLMs show that MARS matches the accuracy of MAD while reducing both token usage and inference time by approximately 50\%. Code is available at https://github.com/xwang97/MARS.

Pengtao Dang, Tingbo Guo, Sha Cao et al.

Few-shot learning (FSL) is a machine learning paradigm that aims to generalize models from a small number of labeled examples, typically fewer than 10 per class. FSL is particularly crucial in biomedical, environmental, materials, and mechanical sciences, where samples are limited and data collection is often prohibitively costly, time-consuming, or ethically constrained. In this study, we present an innovative approach to FSL by demonstrating that a Large Multi-Modal Model (LMMM), trained on a set of independent tasks spanning diverse domains, task types, and input modalities, can substantially improve the generalization of FSL models, outperforming models based on conventional meta-learning on tasks of the same type. To support this, we first constructed a Multi-Modal Model Few-shot Dataset (M3FD, over 10K+ few-shot samples), which includes 2D RGB images, 2D/3D medical scans, tabular and time-course datasets, from which we manually curated FSL tasks such as classification. We further introduced M3F (Multi-Modal Model for Few-shot learning framework), a novel Large Multi-Modal Model framework tailored for data-constrained scientific applications. M3F supports a wide range of scientific data types through a modular pipeline. By fine-tuning the model on M3FD, M3F improves model performance, making LMMM feasible for real-world FSL deployment. The source code is located at https://github.com/ptdang1001/M3F. To democratize access to complex FSL data and promote reproducibility for public usage, M3FD is paired with a flexible and user-friendly tool that enables efficient querying, task-specific sampling, and preprocessing. Together, our dataset and framework offer a unified, scalable solution that significantly lowers the barrier to applying LMMMs in data-scarce scientific domains.

Wennan Chang, Pengtao Dang, Changlin Wan et al.

In this paper, we propose a Spatial Robust Mixture Regression model to investigate the relationship between a response variable and a set of explanatory variables over the spatial domain, assuming that the relationships may exhibit complex spatially dynamic patterns that cannot be captured by constant regression coefficients. Our method integrates the robust finite mixture Gaussian regression model with spatial constraints, to simultaneously handle the spatial nonstationarity, local homogeneity, and outlier contaminations. Compared with existing spatial regression models, our proposed model assumes the existence a few distinct regression models that are estimated based on observations that exhibit similar response-predictor relationships. As such, the proposed model not only accounts for nonstationarity in the spatial trend, but also clusters observations into a few distinct and homogenous groups. This provides an advantage on interpretation with a few stationary sub-processes identified that capture the predominant relationships between response and predictor variables. Moreover, the proposed method incorporates robust procedures to handle contaminations from both regression outliers and spatial outliers. By doing so, we robustly segment the spatial domain into distinct local regions with similar regression coefficients, and sporadic locations that are purely outliers. Rigorous statistical hypothesis testing procedure has been designed to test the significance of such segmentation. Experimental results on many synthetic and real-world datasets demonstrate the robustness, accuracy, and effectiveness of our proposed method, compared with other robust finite mixture regression, spatial regression and spatial segmentation methods.

Changlin Wan, Muhan Zhang, Wei Hao et al.

Hypergraph offers a framework to depict the multilateral relationships in real-world complex data. Predicting higher-order relationships, i.e hyperedge, becomes a fundamental problem for the full understanding of complicated interactions. The development of graph neural network (GNN) has greatly advanced the analysis of ordinary graphs with pair-wise relations. However, these methods could not be easily extended to the case of hypergraph. In this paper, we generalize the challenges of GNN in representing higher-order data in principle, which are edge- and node-level ambiguities. To overcome the challenges, we present SNALS that utilizes bipartite graph neural network with structural features to collectively tackle the two ambiguity issues. SNALS captures the joint interactions of a hyperedge by its local environment, which is retrieved by collecting the spectrum information of their connections. As a result, SNALS achieves nearly 30% performance increase compared with most recent GNN-based models. In addition, we applied SNALS to predict genetic higher-order interactions on 3D genome organization data. SNALS showed consistently high prediction accuracy across different chromosomes, and generated novel findings on 4-way gene interaction, which is further validated by existing literature.

Changlin Wan, Wennan Chang, Tong Zhao et al.

Boolean tensor has been broadly utilized in representing high dimensional logical data collected on spatial, temporal and/or other relational domains. Boolean Tensor Decomposition (BTD) factorizes a binary tensor into the Boolean sum of multiple rank-1 tensors, which is an NP-hard problem. Existing BTD methods have been limited by their high computational cost, in applications to large scale or higher order tensors. In this work, we presented a computationally efficient BTD algorithm, namely \textit{Geometric Expansion for all-order Tensor Factorization} (GETF), that sequentially identifies the rank-1 basis components for a tensor from a geometric perspective. We conducted rigorous theoretical analysis on the validity as well as algorithemic efficiency of GETF in decomposing all-order tensor. Experiments on both synthetic and real-world data demonstrated that GETF has significantly improved performance in reconstruction accuracy, extraction of latent structures and it is an order of magnitude faster than other state-of-the-art methods.

Changlin Wan, Wennan Chang, Tong Zhao et al.

Low rank representation of binary matrix is powerful in disentangling sparse individual-attribute associations, and has received wide applications. Existing binary matrix factorization (BMF) or co-clustering (CC) methods often assume i.i.d background noise. However, this assumption could be easily violated in real data, where heterogeneous row- or column-wise probability of binary entries results in disparate element-wise background distribution, and paralyzes the rationality of existing methods. We propose a binary data denoising framework, namely BIND, which optimizes the detection of true patterns by estimating the row- or column-wise mixture distribution of patterns and disparate background, and eliminating the binary attributes that are more likely from the background. BIND is supported by thoroughly derived mathematical property of the row- and column-wise mixture distributions. Our experiment on synthetic and real-world data demonstrated BIND effectively removes background noise and drastically increases the fairness and accuracy of state-of-the arts BMF and CC methods.

Wennan Chang, Changlin Wan, Yong Zang et al.

Identifying relationships between molecular variations and their clinical presentations has been challenged by the heterogeneous causes of a disease. It is imperative to unveil the relationship between the high dimensional molecular manifestations and the clinical presentations, while taking into account the possible heterogeneity of the study subjects. We proposed a novel supervised clustering algorithm using penalized mixture regression model, called CSMR, to deal with the challenges in studying the heterogeneous relationships between high dimensional molecular features to a phenotype. The algorithm was adapted from the classification expectation maximization algorithm, which offers a novel supervised solution to the clustering problem, with substantial improvement on both the computational efficiency and biological interpretability. Experimental evaluation on simulated benchmark datasets demonstrated that the CSMR can accurately identify the subspaces on which subset of features are explanatory to the response variables, and it outperformed the baseline methods. Application of CSMR on a drug sensitivity dataset again demonstrated the superior performance of CSMR over the others, where CSMR is powerful in recapitulating the distinct subgroups hidden in the pool of cell lines with regards to their coping mechanisms to different drugs. CSMR represents a big data analysis tool with the potential to resolve the complexity of translating the clinical manifestations of the disease to the real causes underpinning it. We believe that it will bring new understanding to the molecular basis of a disease, and could be of special relevance in the growing field of personalized medicine.

Wennan Chang, Xinyu Zhou, Yong Zang et al.

Parameter estimation of mixture regression model using the expectation maximization (EM) algorithm is highly sensitive to outliers. Here we propose a fast and efficient robust mixture regression algorithm, called Component-wise Adaptive Trimming (CAT) method. We consider simultaneous outlier detection and robust parameter estimation to minimize the effect of outlier contamination. Robust mixture regression has many important applications including in human cancer genomics data, where the population often displays strong heterogeneity added by unwanted technological perturbations. Existing robust mixture regression methods suffer from outliers as they either conduct parameter estimation in the presence of outliers, or rely on prior knowledge of the level of outlier contamination. CAT was implemented in the framework of classification expectation maximization, under which a natural definition of outliers could be derived. It implements a least trimmed squares (LTS) approach within each exclusive mixing component, where the robustness issue could be transformed from the mixture case to simple linear regression case. The high breakdown point of the LTS approach allows us to avoid the pre-specification of trimming parameter. Compared with multiple existing algorithms, CAT is the most competitive one that can handle and adaptively trim off outliers as well as heavy tailed noise, in different scenarios of simulated data and real genomic data. CAT has been implemented in an R package `RobMixReg' available in CRAN.

Changlin Wan, Wennan Chang, Tong Zhao et al.

Boolean matrix has been used to represent digital information in many fields, including bank transaction, crime records, natural language processing, protein-protein interaction, etc. Boolean matrix factorization (BMF) aims to find an approximation of a binary matrix as the Boolean product of two low rank Boolean matrices, which could generate vast amount of information for the patterns of relationships between the features and samples. Inspired by binary matrix permutation theories and geometric segmentation, we developed a fast and efficient BMF approach called MEBF (Median Expansion for Boolean Factorization). Overall, MEBF adopted a heuristic approach to locate binary patterns presented as submatrices that are dense in 1's. At each iteration, MEBF permutates the rows and columns such that the permutated matrix is approximately Upper Triangular-Like (UTL) with so-called Simultaneous Consecutive-ones Property (SC1P). The largest submatrix dense in 1 would lies on the upper triangular area of the permutated matrix, and its location was determined based on a geometric segmentation of a triangular. We compared MEBF with other state of the art approaches on data scenarios with different sparsity and noise levels. MEBF demonstrated superior performances in lower reconstruction error, and higher computational efficiency, as well as more accurate sparse patterns than popular methods such as ASSO, PANDA and MP. We demonstrated the application of MEBF on both binary and non-binary data sets, and revealed its further potential in knowledge retrieving and data denoising.

Emily E Diller, Sha Cao, Beth Ey et al.

Background and Purpose: Biopsy is the main determinants of glioma clinical management, but require invasive sampling that fail to detect relevant features because of tumor heterogeneity. The purpose of this study was to evaluate the accuracy of a voxel-wise, multiparametric MRI radiomic method to predict features and develop a minimally invasive method to objectively assess neoplasms. Methods: Multiparametric MRI were registered to T1-weighted gadolinium contrast-enhanced data using a 12 degree-of-freedom affine model. The retrospectively collected MRI data included T1-weighted, T1-weighted gadolinium contrast-enhanced, T2-weighted, fluid attenuated inversion recovery, and multi-b-value diffusion-weighted acquired at 1.5T or 3.0T. Clinical experts provided voxel-wise annotations for five disease states on a subset of patients to establish a training feature vector of 611,930 observations. Then, a k-nearest-neighbor (k-NN) classifier was trained using a 25% hold-out design. The trained k-NN model was applied to 13,018,171 observations from seventeen histologically confirmed glioma patients. Linear regression tested overall survival (OS) relationship to predicted disease compositions (PDC) and diagnostic age (alpha = 0.05). Canonical discriminant analysis tested if PDC and diagnostic age could differentiate clinical, genetic, and microscopic factors (alpha = 0.05). Results: The model predicted voxel annotation class with a Dice similarity coefficient of 94.34% +/- 2.98. Linear combinations of PDCs and diagnostic age predicted OS (p = 0.008), grade (p = 0.014), and endothelia proliferation (p = 0.003); but fell short predicting gene mutations for TP53BP1 and IDH1. Conclusions: This voxel-wise, multi-parametric MRI radiomic strategy holds potential as a non-invasive decision-making aid for clinicians managing patients with glioma.