joint work with Wolfram Wiesemann
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data, which makes them susceptible to estimation errors that are preserved or even amplified by the likelihood estimation. To alleviate this issue, we propose to replace the nominal distributions with ambiguity sets containing all distributions that are sufficiently close to the nominal distributions. When this proximity is measured by the Fisher-Rao distance or the Kullback-Leibler divergence, the emerging optimistic likelihoods can be calculated efficiently using either geodesic or standard convex optimization techniques. We showcase the advantages of our optimistic likelihoods on a classification problem using artificially generated as well as standard benchmark instances.
joint work with Dimitris Bertsimas
We discuss prescribing optimal decisions in a framework where their cost depends on uncertain problem parameters that need to be learned from supervised data. Any naive use of training data may, however, lead to gullible decisions over-calibrated to one particular data set. In this presentation, we describe an intriguing relationship between distributional robust decision making and a bagging learning method by Breiman.
joint work with Zhenyu Hu, Qinshen Tang
We consider the cost sharing problem where a coalition of agents, each endowed with an input, shares the output cost incurred from the total coalitional input. Inventory pooling under ambiguous demand with known mean and covariance is a typical example of this problem. We bridge two important allocations-average cost pricing and the Shapley value-from the angle of allocation inequality. We use the concept of majorization to characterize allocation inequality and we derive simple conditions under which one allocation majorizes the other.