Learning from label proportions (LLP), i.e., a challenging weakly-supervised learning task, aims to train a classifier by using bags of instances and the proportions of classes within bags, rather than annotated labels for each instance. Beyond the traditional bag-level loss, the mainstream methodology of LLP is to incorporate an auxiliary instance-level loss with pseudo-labels formed by predictions. Unfortunately, we empirically observed that the pseudo-labels are are often inaccurate due to over-smoothing, especially for the scenarios with large bag sizes, hurting the classifier induction. To alleviate this problem, we suggest a novel LLP method, namely Learning from Label Proportions with Auxiliary High-confident Instance-level Loss (L2P-AHIL). Specifically, we propose a dual entropy-based weight (DEW) method to adaptively measure the confidences of pseudo-labels. It simultaneously emphasizes accurate predictions at the bag level and avoids overly smoothed predictions. We then form high-confident instance-level loss with DEW, and jointly optimize it with the bag-level loss in a self-training manner. The experimental results on benchmark datasets show that L2P-AHIL can surpass the existing baseline methods, and the performance gain can be more significant as the bag size increases. The implementation of our method is available at https://github.com/TianhaoMa5/LLP-AHIL.

BACKGROUND: Gene regulatory networks (GRNs) can be inferred from both gene expression data and genetic perturbations. Under different conditions, the gene data of the same gene set may be different from each other, which results in different GRNs. Detecting structural difference between GRNs under different conditions is of great significance for understanding gene functions and biological mechanisms. RESULTS: In this paper, we propose a Bayesian Fused algorithm to jointly infer differential structures of GRNs under two different conditions. The algorithm is developed for GRNs modeled with structural equation models (SEMs), which makes it possible to incorporate genetic perturbations into models to improve the inference accuracy, so we name it BFDSEM. Different from the naive approaches that separately infer pair-wise GRNs and identify the difference from the inferred GRNs, we first re-parameterize the two SEMs to form an integrated model that takes full advantage of the two groups of gene data, and then solve the re-parameterized model by developing a novel Bayesian fused prior following the criterion that separate GRNs and differential GRN are both sparse. CONCLUSIONS: Computer simulations are run on synthetic data to compare BFDSEM to two state-of-the-art joint inference algorithms: FSSEM and ReDNet. The results demonstrate that the performance of BFDSEM is comparable to FSSEM, and is generally better than ReDNet. The BFDSEM algorithm is also applied to a real data set of lung cancer and adjacent normal tissues, the yielded normal GRN and differential GRN are consistent with the reported results in previous literatures. An open-source program implementing BFDSEM is freely available in Additional file 1.