Junpeng Li

Miao Zhang, Junpeng Li, ChangChun HUa et al.

Weakly supervised learning often operates with coarse aggregate signals rather than instance labels. We study a setting where each training example is an $n$-tuple containing exactly m positives, while only the count m per tuple is observed. This NTMP (N-tuple with M positives) supervision arises in, e.g., image classification with region proposals and multi-instance measurements. We show that tuple counts admit a trainable unbiased risk estimator (URE) by linking the tuple-generation process to latent instance marginals. Starting from fixed (n,m), we derive a closed-form URE and extend it to variable tuple sizes, variable counts, and their combination. Identification holds whenever the effective mixing rate is separated from the class prior. We establish generalization bounds via Rademacher complexity and prove statistical consistency with standard rates under mild regularity assumptions. To improve finite-sample stability, we introduce simple ReLU corrections to the URE that preserve asymptotic correctness. Across benchmarks converted to NTMP tasks, the approach consistently outperforms representative weak-supervision baselines and yields favorable precision-recall and F1 trade-offs. It remains robust under class-prior imbalance and across diverse tuple configurations, demonstrating that count-only supervision can be exploited effectively through a theoretically grounded and practically stable objective.

Yang Xu, Junpeng Li, Changchun Hua et al.

The Large Margin Distribution Machine (LMDM) is a recent advancement in classifier design that optimizes not just the minimum margin (as in SVM) but the entire margin distribution, thereby improving generalization. However, existing LMDM formulations are limited to vectorized inputs and struggle with high-dimensional tensor data due to the need for flattening, which destroys the data's inherent multi-mode structure and increases computational burden. In this paper, we propose a Structure-Preserving Margin Distribution Learning for High-Order Tensor Data with Low-Rank Decomposition (SPMD-LRT) that operates directly on tensor representations without vectorization. The SPMD-LRT preserves multi-dimensional spatial structure by incorporating first-order and second-order tensor statistics (margin mean and variance) into the objective, and it leverages low-rank tensor decomposition techniques including rank-1(CP), higher-rank CP, and Tucker decomposition to parameterize the weight tensor. An alternating optimization (double-gradient descent) algorithm is developed to efficiently solve the SPMD-LRT, iteratively updating factor matrices and core tensor. This approach enables SPMD-LRT to maintain the structural information of high-order data while optimizing margin distribution for improved classification. Extensive experiments on diverse datasets (including MNIST, images and fMRI neuroimaging) demonstrate that SPMD-LRT achieves superior classification accuracy compared to conventional SVM, vector-based LMDM, and prior tensor-based SVM extensions (Support Tensor Machines and Support Tucker Machines). Notably, SPMD-LRT with Tucker decomposition attains the highest accuracy, highlighting the benefit of structure preservation. These results confirm the effectiveness and robustness of SPMD-LRT in handling high-dimensional tensor data for classification.

Shuying Huang, Junpeng Li, Changchun Hua et al.

To alleviate the annotation burden in supervised learning, N-tuples learning has recently emerged as a powerful weakly-supervised method. While existing N-tuples learning approaches extend pairwise learning to higher-order comparisons and accommodate various real-world scenarios, they often rely on task-specific designs and lack a unified theoretical foundation. In this paper, we propose a general N-tuples learning framework based on empirical risk minimization, which systematically integrates pointwise unlabeled data to enhance learning performance. This paper first unifies the data generation processes of N-tuples and pointwise unlabeled data under a shared probabilistic formulation. Based on this unified view, we derive an unbiased empirical risk estimator that generalizes a broad class of existing N-tuples models. We further establish a generalization error bound for theoretical support. To demonstrate the flexibility of the framework, we instantiate it in four representative weakly supervised scenarios, each recoverable as a special case of our general model. Additionally, to address overfitting issues arising from negative risk terms, we adopt correction functions to adjust the empirical risk. Extensive experiments on benchmark datasets validate the effectiveness of the proposed framework and demonstrate that leveraging pointwise unlabeled data consistently improves generalization across various N-tuples learning tasks.