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On the consistency of top-k surrogate losses
Forest Yang · Sanmi Koyejo

Wed Jul 15 09:00 AM -- 09:45 AM & Wed Jul 15 08:00 PM -- 08:45 PM (PDT) @
The top-$k$ error is often employed to evaluate performance for challenging classification tasks in computer vision as it is designed to compensate for ambiguity in ground truth labels. This practical success motivates our theoretical analysis of consistent top-$k$ classification. To this end, we provide a characterization of Bayes optimality by defining a top-$k$ preserving property, which is new and fixes a non-uniqueness gap in prior work. Then, we define top-$k$ calibration and show it is necessary and sufficient for consistency. Based on the top-$k$ calibration analysis, we propose a rich class of top-$k$ calibrated Bregman divergence surrogates. Our analysis continues by showing previously proposed hinge-like top-$k$ surrogate losses are not top-$k$ calibrated and thus inconsistent. On the other hand, we propose two new hinge-like losses, one which is similarly inconsistent, and one which is consistent. Our empirical results highlight theoretical claims, confirming our analysis of the consistency of these losses.

Author Information

Forest Yang (Google Brain)
Sanmi Koyejo (Illinois / Google)
Sanmi Koyejo

Sanmi (Oluwasanmi) Koyejo is an Assistant Professor in the Department of Computer Science at Stanford University. Koyejo was previously an Associate Professor in the Department of Computer Science at the University of Illinois at Urbana-Champaign. Koyejo's research interests are in developing the principles and practice of trustworthy machine learning, focusing on applications to neuroscience and healthcare. Koyejo completed a Ph.D. in Electrical Engineering at the University of Texas at Austin, advised by Joydeep Ghosh, and postdoctoral research at Stanford University with Russell A. Poldrack and Pradeep Ravikumar. Koyejo has been the recipient of several awards, including a best paper award from the conference on uncertainty in artificial intelligence, a Skip Ellis Early Career Award, a Sloan Fellowship, a Terman faculty fellowship, an NSF CAREER award, a Kavli Fellowship, an IJCAI early career spotlight, and a trainee award from the Organization for Human Brain Mapping. Koyejo spends time at Google as a part of the Brain team, serves on the Neural Information Processing Systems Foundation Board, the Association for Health Learning and Inference Board, and as president of the Black in AI organization.

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