Risk Consistent Multi-Class Learning from Label Proportions
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This study addresses a multiclass learning from label proportions (MCLLP) setting in which training instances are provided in bags and only the proportion of each class within the bags is provided. Most existing MCLLP methods impose bag-wise constraints on the prediction of instances or assign them pseudo-labels; however, none of these methods have a theoretical consistency. To solve this problem, a risk-consistent method is proposed for instance classification using the empirical risk minimization framework, and its estimation error bound is derived. An approximation method is proposed for the proposed risk estimator, to apply it to large bags, by diverting the constraints on bags in existing research. The proposed method can be applied to any deep model or loss and is compatible with stochastic optimization. Experiments are conducted on benchmarks to verify the effectiveness of the proposed method.
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