Learning from Label Proportions with Dual-proportion Constraints

Abstract

Learning from Label Proportions (LLP) is a weakly supervised problem in which the training data comprise bags, that is, groups of instances, each annotated only with bag-level class label proportions, and the objective is to learn a classifier that predicts instance-level labels. This setting is widely applicable when privacy constraints limit access to instance-level annotations or when fine-grained labeling is costly or impractical. In this work, we introduce a method that leverages Dual proportion Constraints (LLP-DC) during training, enforcing them at both the bag and instance levels. Specifically, the bag-level training aligns the mean prediction with the given proportion, and the instance-level training aligns hard pseudo-labels that satisfy the proportion constraint, where a minimum-cost maximum-flow algorithm is used to generate hard pseudo-labels. Extensive experimental results across various benchmark datasets empirically validate that LLP-DC consistently improves over previous LLP methods across datasets and bag sizes. The code is publicly available at https://github.com/TianhaoMa5/CV PR2026_Findings_LLP_DC.

Figures (5)

• Figure 1: Training an instance-level classifier from a dataset with only bag-level class proportions.
• Figure 2: A toy example of minimum-cost maximum-flow problem with 3 instances and 2 labels. Given a labeled bag $\{\mathbf{x}_{i1},\mathbf{x}_{i2},\mathbf{x}_{i3},\bm{\alpha}_i\}$ and the current predicted outputs of instances $\{\mathbf{p}_{i1},\mathbf{p}_{i2},\mathbf{p}_{i3}\}$, we can form a corresponding directed multistage graph, and apply any off-the-shelf tool to solve for the optimal flow $\mathbf{g}^*$. It corresponds to the optimal candidate label assignment $\mathbf{\hat{y}}^*$ with the highest probability, indicated by the bold amounts for the bold edges between instance and label nodes. Best viewed in color.
• Figure 3: Overview of Llp-dc: the illustrated pipeline depicts the training process for a single bag. Given weakly augmented instances $(\mathbf{x}_1^{\mathrm{w}},\dots,\mathbf{x}_m^{\mathrm{w}})$ and strongly augmented instances $(\mathbf{x}_1^{\mathrm{s}},\dots,\mathbf{x}_m^{\mathrm{s}})$, the model $g(\cdot)$ predicts on the weak views $g(\mathbf{x}_1^{\mathrm{w}}),\dots,g(\mathbf{x}_m^{\mathrm{w}})$; their average is aligned with the label proportion $\bm{\alpha}$ to compute the bag-level loss $\mathcal{L}_{\mathrm{bag}}$. Using these weak predictions and $\bm{\alpha}$, we build a graph and solve a minimum-cost maximum-flow problem to obtain pseudo-labels $\mathbf{y}^{*}$ that satisfy the proportion constraints. Finally, we compute the instance-level loss $\mathcal{L}_{\mathrm{ins}}$ on the strong views $g(\mathbf{x}_1^{\mathrm{s}}),\dots,g(\mathbf{x}_m^{\mathrm{s}})$ against $\mathbf{y}^{*}$.
• Figure 4: Pseudo-label accuracy (left) and pseudo-label ratio (right) during training on CIFAR-10 (left two panels) and CIFAR-100 (right two panels) under different bag sizes (16, 32, 64, 128).
• Figure 5: Sensitivity analysis of the instance-level loss weight $\lambda$ in $\mathcal{L}_{\mathrm{ins}}$ and the threshold $\tau$ parameter on CIFAR-10 and CIFAR-100. For $\lambda \in \{2, 1, 0.75, 0.5, 0.25, 0\}$, performance remains stable over a moderate range, indicating robustness to the choice of $\lambda$. Similarly, for $\tau$$\{0.95, 0.8, 0.6, 0.3, 0\}$, performance is consistent across a broad range, demonstrating robustness to threshold selection. Setting $\lambda=0$ or the $\tau$ to 1 reduces the method to DLLP.