From Predictive to Prescriptive Analytics

Predictive analyses taking advantage of the recent explosion in the availability and accessibility of data have been made possible through flexible machine learning methodologies that are often well-suited to the variety and velocity of today’s data collection. This can be witnessed in recent works studying the predictive power of social media data and in the transformation of business practices around data. It is not clear, however, how to go from expected-value predictions based on predictive observations to decisions that yield high profits and carry low risk. As classical problems of portfolio allocation and inventory management show, decisions based on mean-field analysis are suboptimal and high in risk. In this paper we endeavor to refit existing machine learning predictive methodology and theory to the purpose of prescribing optimal decisions based directly on data and predictive observations. We study the convergence as more data becomes available of such methods to the omniscient optimal decision, that which exploits these predictive observations to their fullest extent by using the unknown distribution of parameters. Incredibly, the data-driven prescriptions developed converge to the omniscient optimum for almost all realizations of data and for almost any given predictive observation and even when data is not IID, which is generally the case in practice. We consider an example of portfolio allocation to illustrate the power of these methods.