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TOPIC:
SUPPORT VECTOR DECISION MAKING
ABSTRACT
The paper considers binary decision-making in a utility framework. Given an information set, the decision-maker first predicts a binary outcome and then takes a binary action to maximize her expected utility. The utility function can depend on the binary outcome, the action taken, and some observable covariates. Instead of maximizing the average utility over the training set, this paper takes into consideration the margin of a training point measured by its distance to the decision boundary. It proposes to maximize a criterion function that can be regarded as a surrogate of the average utility, subject to a margin control. The solution gives rise to a set of support vectors that determines the location and orientation of the decision hyperplane. Each of the support vectors contains the threshold function that maximizes the expected utility as an element, and the number of support vectors can be potentially much smaller than the sample size. Under the proposed support vector decision rule, the action for an out-of-sample covariate vector is determined by its similarity to the support vectors. The paper considers both parametric and nonparametric decision boundaries. A finite sample generalization bound is established. A simulation study shows that the proposed method outperforms existing methods under the data generating processes considered in the literature when the conditional probability of the outcome variable is misspecified.
Keywords: Decision-based binary prediction, Maximum margin decision, Maximum utility estimation, Support vector decision, Support vector machine.