Structured Prediction with Partial Labelling through the Infimum Loss

Fully supervised learning demands tight supervision of large amounts of data, a supervision that can be quite costly to acquire and constrains the scope of applications. To overcome this bottleneck, the machine learning community is seeking to incorporate weaker sources of information in the learning framework. In this paper, we address those limitations through partial labelling: e.g., giving only partial ordering when learning user preferences over items, or providing the label "flower" for a picture of Arum Lilies 1, instead of spending a consequent amount of time to find the exact taxonomy. Partial labelling has been studied in the context of classification Cour et al. (2011); Nguyen and Caruana (2008), multilabelling Yu et al. (2014), ranking Hüllermeier et al. (2008); Korba et al. (2018), as well as segmentation Verbeek and Triggs (2008); Papandreou et al. (2015), however a generic framework is still missing. Such a framework is a crucial step towards understanding how to learn from weaker sources of information, and widening the spectrum of machine learning beyond rigid applications of supervised learning. Some interesting directions are provided by Cid-Sueiro et al. (2014); van Rooyen and Williamson (2017), to recover the information lost in a corrupt acquisition of labels. Yet, they assume that the corruption process is known, which is a strong requirement that we want to relax. In this paper, we make the following contributions: - We provide a principled framework to solve the problem of learning with partial labelling, via structured prediction. This approach naturally leads to a variational framework built on the infimum loss.