Abstract
This paper studies the integration of predictive and prescriptive analytics framework for deriving decision from data. Traditionally, in predictive analytics, the purpose is to derive prediction of unknown parameters from data using statistics and machine learning, and in prescriptive analytics, the purpose is to derive a decision from known parameters using optimization technology. These have been studied independently, but the effect of the prediction error in predictive analytics on the decision-making in prescriptive analytics has not been clarified. We propose a modeling framework that integrates machine learning and robust optimization. The proposed algorithm utilizes the k-nearest neighbor model to predict the distribution of uncertain parameters based on the observed auxiliary data. The enclosing minimum volume ellipsoid that contains k-nearest neighbors of is used to form the uncertainty set for the robust optimization formulation. We illustrate the data-driven decision-making framework and our novel robustness notion on a two-stage linear stochastic programming under uncertain parameters. The problem can be reduced to a convex programming, and thus can be solved to optimality very efficiently by the off-the-shelf solvers.
Highlights
The term “analytics” was coined in a research report “Competing on Analytics” by Davenport (2006) [1] and has become widespread ever since
Predictive analytics has been studied in the field of statistics and machine learning, and prescription analytics has been studied in the field of mathematical optimization
We propose a framework that integrates machine learning and robust optimization to safeguard against the case when the estimation error yields serious trouble
Summary
The term “analytics” was coined in a research report “Competing on Analytics” by Davenport (2006) [1] and has become widespread ever since. In the integrated framework proposed in this study, it is desirable to use all the samples in the k-nearest neighbor instead of a single prediction value in order to consider the robustness against the prediction error. The novelty of this proposal is that it integrates predictive analytics and prescription analytics, considers prediction errors that could not be considered in the existing studies, and derives decision from data. Another novelty is to develop an algorithm that has few assumptions by analysts, is versatile, and has scalability that can withstand large-scale data.
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