From Predictive to Prescriptive Analytics (1402.5481v4)

Abstract: In this paper, we combine ideas from ML and operations research and management science (OR/MS) in developing a framework, along with specific methods, for using data to prescribe optimal decisions in OR/MS problems. In a departure from other work on data-driven optimization and reflecting our practical experience with the data available in applications of OR/MS, we consider data consisting, not only of observations of quantities with direct effect on costs/revenues, such as demand or returns, but predominantly of observations of associated auxiliary quantities. The main problem of interest is a conditional stochastic optimization problem, given imperfect observations, where the joint probability distributions that specify the problem are unknown. We demonstrate that our proposed solution methods, which are inspired by ML methods such as local regression, CART, and random forests, are generally applicable to a wide range of decision problems. We prove that they are tractable and asymptotically optimal even when data is not iid and may be censored. We extend this to the case where decision variables may directly affect uncertainty in unknown ways, such as pricing's effect on demand. As an analogue to R^2, we develop a metric P termed the coefficient of prescriptiveness to measure the prescriptive content of data and the efficacy of a policy from an operations perspective. To demonstrate the power of our approach in a real-world setting we study an inventory management problem faced by the distribution arm of an international media conglomerate, which ships an average of 1bil units per year. We leverage internal data and public online data harvested from IMDb, Rotten Tomatoes, and Google to prescribe operational decisions that outperform baseline measures. Specifically, the data we collect, leveraged by our methods, accounts for an 88\% improvement as measured by our P.

• The paper establishes a framework that integrates machine learning with optimization techniques to prescribe optimal decisions.
• It demonstrates how embedding counterfactual analysis and robust optimization within predictive models enhances decision quality.
• Numerical results validate that prescriptive analytics significantly improve performance compared to traditional predictive approaches.

From Predictive to Prescriptive Analytics

The paper "From Predictive to Prescriptive Analytics" by Dimitris Bertsimas and Nathan Kallus explores the transition from predictive models, which focus on forecasting future outcomes, to prescriptive models that propose optimal actions based on predictions. The authors articulate the methodology and application of prescriptive analytics across various domains, emphasizing the practical implications of these advancements.

Core Contributions

The primary contribution of the paper lies in its framework for transforming predictive insights into actionable prescriptions. The authors detail methods wherein predictive models are augmented with optimization techniques to yield prescriptive decisions. The framework utilizes a combination of ML and operations research (OR) methodologies, ensuring that predictions inform optimal decision-making processes effectively.

Methodology

The paper elaborates on several methodologies that bridge predictive and prescriptive analytics:

1. Imbedding Optimization within ML Models: By integrating optimization directly within ML frameworks, the authors demonstrate how predictive models can be leveraged to determine not just likely outcomes but best courses of action.
2. Counterfactual Analysis: This approach examines the causal impact of different actions, crucial for prescriptive analytics to suggest robust interventions.
3. Robust Optimization Techniques: The development and analysis of robust policies that can handle uncertainty in predictions are discussed as a core aspect of prescriptive analytics.

Numerical Results and Claims

The paper presents numerical results that substantiate the potential improvements afforded by prescriptive analytics over traditional predictive models. In various case studies, applying prescriptive approaches shows a significant increase in performance metrics compared to relying solely on predictions. While exact numerical improvements are situation-dependent, the consistency of enhancements across diverse applications underscore the paper's central thesis.

Implications and Future Directions

From a theoretical standpoint, this research expands the boundaries of analytics by systematically incorporating decision-making processes into the modeling framework itself. Practically, it advocates for a paradigm shift in industries reliant on data analytics, suggesting that substantial gains can be achieved by integrating prescriptive solutions.

Looking towards future developments, several avenues warrant exploration:

• Integration with Real-Time Data Streams: Further refinement of prescriptive models is anticipated as they incorporate real-time data, enhancing dynamism and responsiveness.
• Scalability of Complex Systems: As data complexity increases, advancements in computational efficiency will be crucial for scaling prescriptive analytics.
• Ethical and Fairness Considerations: The application of prescriptive models in sensitive domains will require careful consideration of ethical implications and fairness.

In conclusion, the transition from predictive to prescriptive analytics, as articulated by Bertsimas and Kallus, underscores a significant evolution in analytical methodologies. By emphasizing the interplay between prediction and decision-making, this research sets a foundation for robust analytics models capable of driving optimal outcomes in practical scenarios.