Learning Optimized Risk Scores

By Berk Ustun, Cynthia Rudin. 2016

108 citations recorded by the source corpus.

Risk scores are simple classification models that let users make quick risk predictions by adding and subtracting a few small numbers. These models are widely used in medicine and criminal justice, but are difficult to learn from data because they need to be calibrated, sparse, use small integer coefficients, and obey application-specific operational constraints. In this paper, we present a new machine learning approach to learn risk scores. We formulate the risk score problem as a mixed integer nonlinear program, and present a cutting plane algorithm for non-convex settings to efficiently recover its optimal solution. We improve our algorithm with specialized techniques to generate feasible solutions, narrow the optimality gap, and reduce data-related computation. Our approach can fit risk scores in a way that scales linearly in the number of samples, provides a certificate of optimality, and obeys real-world constraints without parameter tuning or post-processing. We benchmark the performance benefits of this approach through an extensive set of numerical experiments, comparing to risk scores built using heuristic approaches. We also discuss its practical benefits through a real-world application where we build a customized risk score for ICU seizure prediction in collaboration with the Massachusetts General Hospital.

Subfields: Economics and Econometrics, Management Science and Operations Research, Statistics and Probability, Optimization & Training

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Cynthia Rudin

In Management Science and Operations Research

1. Chudi Zhong
2. Lesia Semenova
3. Zhi Chen
4. Haiyang Huang
5. Cynthia Rudin

In Statistics and Probability

1. Lesia Semenova
2. Chudi Zhong
3. Zhi Chen
4. Haiyang Huang
5. Cynthia Rudin
6. Berk Ustun
7. Alexander Volfovsky
8. Kush R. Varshney

In Optimization & Training

1. Lesia Semenova
2. Chudi Zhong
3. Zhi Chen
4. Haiyang Huang
5. Cynthia Rudin

Citations in the corpus

• Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges (2021, methodology): “There are several methods that can solve (3) directly (Ustun et al., 2013; Ustun and Rudin, 2016, 2017, 2019; Rudin and Ustun, 2018).”
• Interpretable Optimal Stopping (2018, unknown): “A stream of research has considered interpretable scoring rules for classification and risk prediction; recent examples include Ustun and Rudin (2015, 2016) and Zeng et al. (2017).”