Shixin Xu

Jiaqi Luo, Yuedong Quan, Shixin Xu

Dealing with label noise in tabular classification tasks poses a persistent challenge in machine learning. While robust boosting methods have shown promise in binary classification, their effectiveness in complex, multi-class scenarios is often limited. Additionally, issues like imbalanced datasets, missing values, and computational inefficiencies further complicate their practical utility. This study introduces Robust-GBDT, a groundbreaking approach that combines the power of Gradient Boosted Decision Trees (GBDT) with the resilience of nonconvex loss functions against label noise. By leveraging local convexity within specific regions, Robust-GBDT demonstrates unprecedented robustness, challenging conventional wisdom. Through seamless integration of advanced GBDT with a novel Robust Focal Loss tailored for class imbalance, Robust-GBDT significantly enhances generalization capabilities, particularly in noisy and imbalanced datasets. Notably, its user-friendly design facilitates integration with existing open-source code, enhancing computational efficiency and scalability. Extensive experiments validate Robust-GBDT's superiority over other noise-robust methods, establishing a new standard for accurate classification amidst label noise. This research heralds a paradigm shift in machine learning, paving the way for a new era of robust and precise classification across diverse real-world applications.

Minxin Chen, Chun Liu, Shixin Xu et al.

In this paper, we focus on numerical methods for the genetic drift problems, which is governed by a degenerated convection-dominated parabolic equation. Due to the degeneration and convection, Dirac singularities will always be developed at boundary points as time evolves. In order to find a \emph{complete solution} which should keep the conservation of total probability and expectation, three different schemes based on finite volume methods are used to solve the equation numerically: one is a upwind scheme, the other two are different central schemes. We observed that all the methods are stable and can keep the total probability, but have totally different long-time behaviors concerning with the conservation of expectation. We prove that any extra infinitesimal diffusion leads to a same artificial steady state. So upwind scheme does not work due to its intrinsic numerical viscosity. We find one of the central schemes introduces a numerical viscosity term too, which is beyond the common understanding in the convection-diffusion community. Careful analysis is presented to prove that the other central scheme does work. Our study shows that the numerical methods should be carefully chosen and any method with intrinsic numerical viscosity must be avoided.

Jiaqi Luo, Yuan Yuan, Shixin Xu

Class imbalance remains a significant challenge in machine learning, particularly for tabular data classification tasks. While Gradient Boosting Decision Trees (GBDT) models have proven highly effective for such tasks, their performance can be compromised when dealing with imbalanced datasets. This paper presents the first comprehensive study on adapting class-balanced loss functions to three GBDT algorithms across various tabular classification tasks, including binary, multi-class, and multi-label classification. We conduct extensive experiments on multiple datasets to evaluate the impact of class-balanced losses on different GBDT models, establishing a valuable benchmark. Our results demonstrate the potential of class-balanced loss functions to enhance GBDT performance on imbalanced datasets, offering a robust approach for practitioners facing class imbalance challenges in real-world applications. Additionally, we introduce a Python package that facilitates the integration of class-balanced loss functions into GBDT workflows, making these advanced techniques accessible to a wider audience.

Jiaqi Luo, Shixin Xu

Deep learning models have become popular in the analysis of tabular data, as they address the limitations of decision trees and enable valuable applications like semi-supervised learning, online learning, and transfer learning. However, these deep-learning approaches often encounter a trade-off. On one hand, they can be computationally expensive when dealing with large-scale or high-dimensional datasets. On the other hand, they may lack interpretability and may not be suitable for small-scale datasets. In this study, we propose a novel interpretable neural network called Neural Classification and Regression Tree (NCART) to overcome these challenges. NCART is a modified version of Residual Networks that replaces fully-connected layers with multiple differentiable oblivious decision trees. By integrating decision trees into the architecture, NCART maintains its interpretability while benefiting from the end-to-end capabilities of neural networks. The simplicity of the NCART architecture makes it well-suited for datasets of varying sizes and reduces computational costs compared to state-of-the-art deep learning models. Extensive numerical experiments demonstrate the superior performance of NCART compared to existing deep learning models, establishing it as a strong competitor to tree-based models.

Jiaqi Luo, Zihao Wei, Junkai Man et al.

Gradient Boosting Machines (GBMs) have demonstrated remarkable success in solving diverse problems by utilizing Taylor expansions in functional space. However, achieving a balance between performance and generality has posed a challenge for GBMs. In particular, gradient descent-based GBMs employ the first-order Taylor expansion to ensure applicability to all loss functions, while Newton's method-based GBMs use positive Hessian information to achieve superior performance at the expense of generality. To address this issue, this study proposes a new generic Gradient Boosting Machine called Trust-region Boosting (TRBoost). In each iteration, TRBoost uses a constrained quadratic model to approximate the objective and applies the Trust-region algorithm to solve it and obtain a new learner. Unlike Newton's method-based GBMs, TRBoost does not require the Hessian to be positive definite, thereby allowing it to be applied to arbitrary loss functions while still maintaining competitive performance similar to second-order algorithms. The convergence analysis and numerical experiments conducted in this study confirm that TRBoost is as general as first-order GBMs and yields competitive results compared to second-order GBMs. Overall, TRBoost is a promising approach that balances performance and generality, making it a valuable addition to the toolkit of machine learning practitioners.

Xi Luo, Shixin Xu, Ying Xie et al.

Accurate medical image analysis can greatly assist clinical diagnosis, but its effectiveness relies on high-quality expert annotations Obtaining pixel-level labels for medical images, particularly fundus images, remains costly and time-consuming. Meanwhile, despite the success of deep learning in medical imaging, the lack of interpretability limits its clinical adoption. To address these challenges, we propose TWLR, a two-stage framework for interpretable diabetic retinopathy (DR) assessment. In the first stage, a vision-language model integrates domain-specific ophthalmological knowledge into text embeddings to jointly perform DR grading and lesion classification, effectively linking semantic medical concepts with visual features. The second stage introduces an iterative severity regression framework based on weakly-supervised semantic segmentation. Lesion saliency maps generated through iterative refinement direct a progressive inpainting mechanism that systematically eliminates pathological features, effectively downgrading disease severity toward healthier fundus appearances. Critically, this severity regression approach achieves dual benefits: accurate lesion localization without pixel-level supervision and providing an interpretable visualization of disease-to-healthy transformations. Experimental results on the FGADR, DDR, and a private dataset demonstrate that TWLR achieves competitive performance in both DR classification and lesion segmentation, offering a more explainable and annotation-efficient solution for automated retinal image analysis.

Jiaqi Luo, Yahong Yang, Yuan Yuan et al.

This paper introduces Residual-based Smote (RSmote), an innovative local adaptive sampling technique tailored to improve the performance of Physics-Informed Neural Networks (PINNs) through imbalanced learning strategies. Traditional residual-based adaptive sampling methods, while effective in enhancing PINN accuracy, often struggle with efficiency and high memory consumption, particularly in high-dimensional problems. RSmote addresses these challenges by targeting regions with high residuals and employing oversampling techniques from imbalanced learning to refine the sampling process. Our approach is underpinned by a rigorous theoretical analysis that supports the effectiveness of RSmote in managing computational resources more efficiently. Through extensive evaluations, we benchmark RSmote against the state-of-the-art Residual-based Adaptive Distribution (RAD) method across a variety of dimensions and differential equations. The results demonstrate that RSmote not only achieves or exceeds the accuracy of RAD but also significantly reduces memory usage, making it particularly advantageous in high-dimensional scenarios. These contributions position RSmote as a robust and resource-efficient solution for solving complex partial differential equations, especially when computational constraints are a critical consideration.

Jiaqi Luo, Yuan Yuan, Shixin Xu

Tabular-image multimodal learning, which integrates structured tabular data with imaging data, holds great promise for a variety of tasks, especially in medical applications. Yet, two key challenges remain: (1) the lack of a standardized, pretrained representation for tabular data, as is commonly available in vision and language domains; and (2) the difficulty of handling missing values in the tabular modality, which are common in real-world medical datasets. To address these issues, we propose the TabPFN-Integrated Multimodal Engine (TIME), a novel multimodal framework that builds on the recently introduced tabular foundation model, TabPFN. TIME leverages TabPFN as a frozen tabular encoder to generate robust, strong embeddings that are naturally resilient to missing data, and combines them with image features from pretrained vision backbones. We explore a range of fusion strategies and tabular encoders, and evaluate our approach on both natural and medical datasets. Extensive experiments demonstrate that TIME consistently outperforms competitive baselines across both complete and incomplete tabular inputs, underscoring its practical value in real-world multimodal learning scenarios.

Xiaoyan Li, Shixin Xu, Faisal Habib et al.

This study addresses the challenge of reconstructing unseen ECG signals from PPG signals, a critical task for non-invasive cardiac monitoring. While numerous public ECG-PPG datasets are available, they lack the diversity seen in image datasets, and data collection processes often introduce noise, complicating ECG reconstruction from PPG even with advanced machine learning models. To tackle these challenges, we first introduce a novel synthetic ECG-PPG data generation technique using an ODE model to enhance training diversity. Next, we develop a novel subject-independent PPG-to-ECG reconstruction model that integrates contrastive learning, adversarial learning, and attention gating, achieving results comparable to or even surpassing existing approaches for unseen ECG reconstruction. Finally, we examine factors such as sex and age that impact reconstruction accuracy, emphasizing the importance of considering demographic diversity during model training and dataset augmentation.

Jiaqi Luo, Shixin Xu, Zhouwang Yang

The accuracy of Physics-Informed Neural Networks (PINNs) critically depends on the placement of collocation points, as the PDE loss is approximated through sampling over the solution domain. Global sampling ensures stability by covering the entire domain but requires many samples and is computationally expensive, whereas local sampling improves efficiency by focusing on high-residual regions but may neglect well-learned areas, reducing robustness. We propose a Global-Local Fusion (GLF) Sampling Strategy that combines the strengths of both approaches. Specifically, new collocation points are generated by perturbing training points with Gaussian noise scaled inversely to the residual, thereby concentrating samples in difficult regions while preserving exploration. To further reduce computational overhead, a lightweight linear surrogate is introduced to approximate the global residual-based distribution, achieving similar effectiveness at a fraction of the cost. Together, these components, residual-adaptive sampling and residual-based approximation, preserve the stability of global methods while retaining the efficiency of local refinement. Extensive experiments on benchmark PDEs demonstrate that GLF consistently improves both accuracy and efficiency compared with global and local sampling strategies. This study provides a practical and scalable framework for enhancing the reliability and efficiency of PINNs in solving complex and high-dimensional PDEs.

Juntang Wang, Hao Wu, Runkun Guo et al.

Humans possess an innate ability to group objects by similarity, a cognitive mechanism that clustering algorithms aim to emulate. Recent advances in community detection have enabled the discovery of configurations -- valid hierarchical clusterings across multiple resolution scales -- without requiring labeled data. In this paper, we formally characterize these configurations and identify similar emergent structures in register tokens within Vision Transformers. Unlike register tokens, configurations exhibit lower redundancy and eliminate the need for ad hoc selection. They can be learned through unsupervised or self-supervised methods, yet their selection or composition remains specific to the downstream task and input. Building on these insights, we introduce GraMixC, a plug-and-play module that extracts configurations, aligns them using our Reverse Merge/Split (RMS) technique, and fuses them via attention heads before forwarding them to any downstream predictor. On the DSN1 16S rRNA cultivation-media prediction task, GraMixC improves the R2 score from 0.6 to 0.9 across multiple methods, setting a new state of the art. We further validate GraMixC on standard tabular benchmarks, where it consistently outperforms single-resolution and static-feature baselines.

Juntang Wang, Yihan Wang, Hao Wu et al.

Infants discover categories, detect novelty, and adapt to new contexts without supervision -- a challenge for current machine learning. We present a brain-inspired perspective on configurations, a finite-resolution clustering framework that uses a single resolution parameter and attraction-repulsion dynamics to yield hierarchical organization, novelty sensitivity, and flexible adaptation. To evaluate these properties, we introduce mheatmap, which provides proportional heatmaps and a reassignment algorithm to fairly assess multi-resolution and dynamic behavior. Across datasets, configurations are competitive on standard clustering metrics, achieve 87% AUC in novelty detection, and show 35% better stability during dynamic category evolution. These results position configurations as a principled computational model of early cognitive categorization and a step toward brain-inspired AI.

Xiaoyan Li, Shixin Xu, Faisal Habib et al.

Reconstructing ECG from PPG is a promising yet challenging task. While recent advancements in generative models have significantly improved ECG reconstruction, accurately capturing fine-grained waveform features remains a key challenge. To address this, we propose a novel PPG-to-ECG reconstruction method that leverages a Vision Transformer (ViT) as the core network. Unlike conventional approaches that rely on single-channel PPG, our method employs a four-channel signal image representation, incorporating the original PPG, its first-order difference, second-order difference, and area under the curve. This multi-channel design enriches feature extraction by preserving both temporal and physiological variations within the PPG. By leveraging the self-attention mechanism in ViT, our approach effectively captures both inter-beat and intra-beat dependencies, leading to more robust and accurate ECG reconstruction. Experimental results demonstrate that our method consistently outperforms existing 1D convolution-based approaches, achieving up to 29% reduction in PRD and 15% reduction in RMSE. The proposed approach also produces improvements in other evaluation metrics, highlighting its robustness and effectiveness in reconstructing ECG signals. Furthermore, to ensure a clinically relevant evaluation, we introduce new performance metrics, including QRS area error, PR interval error, RT interval error, and RT amplitude difference error. Our findings suggest that integrating a four-channel signal image representation with the self-attention mechanism of ViT enables more effective extraction of informative PPG features and improved modeling of beat-to-beat variations for PPG-to-ECG mapping. Beyond demonstrating the potential of PPG as a viable alternative for heart activity monitoring, our approach opens new avenues for cyclic signal analysis and prediction.

Joshua C Chang, Xiangting Li, Shixin Xu et al.

Importance sampling (IS) allows one to approximate leave one out (LOO) cross-validation for a Bayesian model, without refitting, by inverting the Bayesian update equation to subtract a given data point from a model posterior. For each data point, one computes expectations under the corresponding LOO posterior by weighted averaging over the full data posterior. This task sometimes requires weight stabilization in the form of adapting the posterior distribution via transformation. So long as one is successful in finding a suitable transformation, one avoids refitting. To this end, we motivate the use of bijective perturbative transformations of the form $T(\boldsymbolθ)=\boldsymbolθ + h Q(\boldsymbolθ),$ for $0<h\ll 1,$ and introduce two classes of such transformations: 1) partial moment matching and 2) gradient flow evolution. The former extends prior literature on moment-matching under the recognition that adaptation for LOO is a small perturbation on the full data posterior. The latter class of methods define transformations based on relaxing various statistical objectives: in our case the variance of the IS estimator and the KL divergence between the transformed distribution and the statistics of the LOO fold. Being model-specific, the gradient flow transformations require evaluating Jacobian determinants. While these quantities are generally readily available through auto-differentiation, we derive closed-form expressions in the case of logistic regression and shallow ReLU activated neural networks. We tested the methodology on an $n\ll p$ dataset that is known to produce unstable LOO IS weights.

Jing Ma, Yiyang Sun, Junjie Liu et al.

Stroke is the top leading causes of death in China (Zhou et al. The Lancet 2019). A dataset from Shanxi Province is used to identify the risk of each patient's at four states low/medium/high/attack and provide the state transition tendency through a SHAP DeepExplainer. To improve the accuracy on an imbalance sample set, the Quadratic Interactive Deep Neural Network (QIDNN) model is first proposed by flexible selecting and appending of quadratic interactive features. The experimental results showed that the QIDNN model with 7 interactive features achieve the state-of-art accuracy $83.25\%$. Blood pressure, physical inactivity, smoking, weight and total cholesterol are the top five important features. Then, for the sake of high recall on the most urgent state, attack state, the stroke occurrence prediction is taken as an auxiliary objective to benefit from multi-objective optimization. The prediction accuracy was promoted, meanwhile the recall of the attack state was improved by $24.9\%$ (to $84.83\%$) compared to QIDNN (from $67.93\%$) with same features. The prediction model and analysis tool in this paper not only gave the theoretical optimized prediction method, but also provided the attribution explanation of risk states and transition direction of each patient, which provided a favorable tool for doctors to analyze and diagnose the disease.

Junjie Liu, Yiyang Sun, Jing Ma et al.

In China, stroke is the first leading cause of death in recent years. It is a major cause of long-term physical and cognitive impairment, which bring great pressure on the National Public Health System. Evaluation of the risk of getting stroke is important for the prevention and treatment of stroke in China. A data set with 2000 hospitalized stroke patients in 2018 and 27583 residents during the year 2017 to 2020 is analyzed in this study. Due to data incompleteness, inconsistency, and non-structured formats, missing values in the raw data are filled with -1 as an abnormal class. With the cleaned features, three models on risk levels of getting stroke are built by using machine learning methods. The importance of "8+2" factors from China National Stroke Prevention Project (CSPP) is evaluated via decision tree and random forest models. Except for "8+2" factors the importance of features and SHAP1 values for lifestyle information, demographic information, and medical measurement are evaluated and ranked via a random forest model. Furthermore, a logistic regression model is applied to evaluate the probability of getting stroke for different risk levels. Based on the census data in both communities and hospitals from Shanxi Province, we investigate different risk factors of getting stroke and their ranking with interpretable machine learning models. The results show that Hypertension (Systolic blood pressure, Diastolic blood pressure), Physical Inactivity (Lack of sports), and Overweight (BMI) are ranked as the top three high-risk factors of getting stroke in Shanxi province. The probability of getting stroke for a person can also be predicted via our machine learning model.

Yihao Hu, Tong Zhao, Shixin Xu et al.

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional finite difference and finite elements methods and emerging advancements in machine learning, we propose a sequence deep learning framework called Neural-PDE, which allows to automatically learn governing rules of any time-dependent PDE system from existing data by using a bidirectional LSTM encoder, and predict the next n time steps data. One critical feature of our proposed framework is that the Neural-PDE is able to simultaneously learn and simulate the multiscale variables.We test the Neural-PDE by a range of examples from one-dimensional PDEs to a high-dimensional and nonlinear complex fluids model. The results show that the Neural-PDE is capable of learning the initial conditions, boundary conditions and differential operators without the knowledge of the specific form of a PDE system.In our experiments the Neural-PDE can efficiently extract the dynamics within 20 epochs training, and produces accurate predictions. Furthermore, unlike the traditional machine learning approaches in learning PDE such as CNN and MLP which require vast parameters for model precision, Neural-PDE shares parameters across all time steps, thus considerably reduces the computational complexity and leads to a fast learning algorithm.