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TITLE: Goal Scoring, Coherent Loss, and Application to Machine Learning
ABSTRACT:
Motivated by the binary classification problem in machine learning, we study a class of decision problems where the decision maker has a list of goals, from which he aims to attain the maximal possible number of goals. In binary classification, this essentially means seeking a prediction rule to achieve the lowest probability of misclassification, and computationally it involves minimizing a (difficult) non-convex, 0-1 loss function. To address the intractability, previous methods consider minimizing the cumulative loss – the sum of convex surrogates of the 0-1 loss of each goal. We revisit this paradigm and develop instead an axiomatic framework by proposing a set of salient properties on functions for goal scoring and then propose the coherent loss approach, which is a tractable upper-bound of the loss over the entire set of goals. We show that the proposed approach yields a strictly tighter approximation to the total loss (i.e., the number of missed goal) than any convex cumulative loss approach while preserving the convexity of the underlying optimization problem. Moreover, this approach, applied to for binary classification, also has a robustness interpretation which builds a connection to robust SVMs.
Bio: Dr. Huan Xu is an assistant professor at the Stewart School of Industrial & Systems Engineering at Georgia Tech. His current research interest focuses on data, learning, and decision making. Specifically, he is interested in machine learning, high-dimensional statistics, robust and stochastic optimization, sequential decision making, and application to large-scale systems.
