A Decision-Theoretic Motivation for L1-Regularized Maximum Likelihood Modeling

Financial practitioners must often estimate probabilities. We provide a new decision-theoretic problem formulation for estimating probabilistic models; this formulation naturally leads to certain minimum relative entropy problems that have l1-regularized maximum likelihood duals. In this formulation, a model is estimated to be used in a simple decision scenario, where the decision-maker uses the model to make decisions in an uncertain world. We formulated the model building problem as the search for the model that performs best in the most adverse 'world' among those 'worlds' that are consistent with a set of relaxed feature constraints