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Optimization and Analysis of the pAp@k Metric for Recommender Systems
Gaurush Hiranandani · Warut Vijitbenjaronk · Sanmi Koyejo · Prateek Jain

Tue Jul 14 11:00 AM -- 11:45 AM & Tue Jul 14 10:00 PM -- 10:45 PM (PDT) @ Virtual

Modern recommendation and notification systems must be robust to data imbalance, limitations on the number of recommendations/notifications, and heterogeneous engagement profiles across users. The pAp@k metric, which combines the partial-AUC and the precision@k metrics, was recently proposed to evaluate such recommendation systems and has been used in real-world deployments. Conceptually, pAp@k measures the probability of correctly ranking a top-ranked positive instance over top-ranked negative instances. Due to the combinatorial aspect surfaced by top-ranked points, little is known about the characteristics and optimization methods of pAp@k. In this paper, we analyze the learning-theoretic properties of pAp@k, particularly its benefits in evaluating modern recommender systems, and propose novel surrogates that are consistent under certain data regularity conditions. We then provide gradient descent based algorithms to optimize the surrogates directly. Our analysis and experimental evaluation suggest that pAp@k indeed exhibits a certain dual behavior with respect to partial-AUC and precision@k. Moreover, the proposed methods outperform all the baselines in various applications. Taken together, our results motivate the use of pAp@k for large-scale recommender systems with heterogeneous user-engagement.

Author Information

Gaurush Hiranandani (UIUC)
Warut Vijitbenjaronk (University of Illinois, Urbana-Champaign)
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.

Prateek Jain (Microsoft Research)

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