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We build a Bayesian contextual classification model using an optimistic scoreratio for robust binary classification when there is limited information on theclass-conditional, or contextual, distribution. The optimistic score searchesfor the distribution that is most plausible to explain the observed outcomes inthe testing sample among all distributions belonging to the contextualambiguity set which is prescribed using a limited structural constraint on themean vector and the covariance matrix of the underlying contextualdistribution. We show that the Bayesian classifier using the optimistic scoreratio is conceptually attractive, delivers solid statistical guarantees and iscomputationally tractable. We showcase the power of the proposed optimisticscore ratio classifier on both synthetic and empirical data.

Robust Bayesian Classification Using an Optimistic Score Ratio