Leveraged Weighted Loss For Partial Label Learning

Hongwei Wen, Hanyuan Hang, Jiabin Liu, Zhouchen Lin

Keywords: weakly supervised learning, loss function, risk consistency

Abstract: As an important branch of weakly supervised learning, partial label learning deals with data where each instance is assigned with a set of candidate labels, whereas only one of them is true. In this paper, we propose a family of loss functions named Leveraged Weighted (LW) loss function, which for the first time introduces the leverage parameter $\beta$ to partial loss functions to leverage between losses on partial labels and residual labels (non-partial labels). Under mild assumptions, we achieve the relationship between the partial loss function and its corresponding ordinary loss that leads to the consistency in risk. Compared to the existing literatures, our result applies to both deterministic and stochastic scenarios, considers the loss functions of a more general form, and takes milder assumptions on the distribution of the partial label set. As special cases, with $\beta = 1$ and $\beta = 2$, the corresponding ordinary losses of our LW loss respectively match the binary classification loss and the \textit{one-versus-all} (OVA) loss function. In this way, our theorems successfully explain the experimental results on parameter analysis, where $\beta = 1$ and especially $\beta = 2$ are considered as preferred choices for the leverage parameter $\beta$. Last but not least, real data comparisons show the high effectiveness of our LW loss over other state-of-the-art partial label learning algorithms.

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One-sentence Summary: This paper proposes a family of loss functions named Leveraged Weighted (LW) loss function, which introduces the leverage parameter, with both theoretical and experimental properties examined.

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