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Oral
Binary Classification with Karmic, Threshold-Quasi-Concave Metrics
Bowei Yan · Sanmi Koyejo · Kai Zhong · Pradeep Ravikumar

Thu Jul 12 07:50 AM -- 08:00 AM (PDT) @ A6
in Statistical Learning Theory 4 »

Complex performance measures, beyond the popular measure of accuracy, are increasingly being used in the context of binary classification. These complex performance measures are typically not even decomposable, that is, the loss evaluated on a batch of samples cannot typically be expressed as a sum or average of losses evaluated at individual samples, which in turn requires new theoretical and methodological developments beyond standard treatments of supervised learning. In this paper, we advance this understanding of binary classification for complex performance measures by identifying two key properties: a so-called Karmic property, and a more technical threshold-quasi-concavity property, which we show is milder than existing structural assumptions imposed on performance measures. Under these properties, we show that the Bayes optimal classifier is a threshold function of the conditional probability of positive class. We then leverage this result to come up with a computationally practical plug-in classifier, via a novel threshold estimator, and further, provide a novel statistical analysis of classification error with respect to complex performance measures.

Author Information

Bowei Yan (University of Texas at Austin)
Sanmi Koyejo (University of Illinois at Urbana-Champaign)

Sanmi (Oluwasanmi) Koyejo an Assistant Professor in the Department of Computer Science at the University of Illinois at Urbana-Champaign. Koyejo's research interests are in the development and analysis of probabilistic and statistical machine learning techniques motivated by, and applied to various modern big data problems. He is particularly interested in the analysis of large scale neuroimaging data. Koyejo completed his Ph.D in Electrical Engineering at the University of Texas at Austin advised by Joydeep Ghosh, and completed postdoctoral research at Stanford University with a focus on developing Machine learning techniques for neuroimaging data. His postdoctoral research was primarily with Russell A. Poldrack and Pradeep Ravikumar. Koyejo has been the recipient of several awards including the outstanding NCE/ECE student award, a best student paper award from the conference on uncertainty in artificial intelligence (UAI) and a trainee award from the Organization for Human Brain Mapping (OHBM).

Kai Zhong (University of Texas at Austin)
Pradeep Ravikumar (Carnegie Mellon University)

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