Supersparse Linear Integer Models for Predictive Scoring Systems

By Berk Ustun, Stefano Tracà, Cynthia Rudin. 2013

20 citations recorded by the source corpus.

Scoring systems are classification models that make predictions using a sparse linear combination of variables with integer coefficients. Such systems are frequently used in medicine because they are interpretable; that is, they only require users to add, subtract and multiply a few meaningful numbers in order to make a prediction. See, for instance, these commonly used scoring systems: (Gage et al. 2001; Le Gall et al. 1984; Le Gall, Lemeshow, and Saulnier 1993; Knaus et al. 1985). Scoring systems strike a delicate balance between accuracy and interpretability that is difficult to replicate with existing machine learning algorithms. Current linear methods such as the lasso, elastic net and LARS are not designed to create scoring systems, since regularization is primarily used to improve accuracy as opposed to sparsity and interpretability (Tibshirani 1996; Zou and Hastie 2005; Efron et al. 2004). These methods can produce very sparse models through heavy regularization or feature selection methods (Guyon and Elisseeff 2003); however, feature selection often relies on greedy optimization and cannot guarantee an optimal balance between sparsity and accuracy. Moreover, the interpretability of scoring systems requires integer coefficients, which these methods do not produce. Existing approaches to interpretable modeling include decision trees and lists (Ruping 2006; Quinlan 1986; Rivest 1987; Letham et al. 2013). We introduce a formal approach for creating scoring systems, called Supersparse Linear Integer Models (SLIM). SLIM produces scoring systems that are accurate and interpretable using a mixed-integer program (MIP) whose objective penalizes the training error, L0-norm and L1-norm of its coefficients. SLIM can create scoring systems for datasets with thousands of training examples and tens to hundreds of features - larger than the sizes of most studies in medicine, where scoring systems are often used.

Subfields: Mathematical Optimization

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In Mathematical Optimization

1. Cynthia Rudin
2. Berk Ustun
3. Ş. Ertekin
4. Chudi Zhong
5. Lesia Semenova
6. Zhi Chen
7. Haiyang Huang
8. Jiaming Zeng

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 classification models for recidivism prediction (2015, methodology): “To this end, we use a powerful new machine learning method known as a Supersparse Linear Integer Model (SLIM, see Ustun et al. 2013, Ustun and Rudin 2014, 2015).”
• Learning Optimized Risk Scores (2016, background): “RiskSLIM risk scores are the risk assessment counterpart to SLIM scoring systems (Ustun et al., 2013; Ustun and Rudin, 2016; Zeng et al., 2016; Ustun et al., 2016).”
• Learning Classification Models of Cognitive Conditions from Subtle Behaviors in the Digital Clock Drawing Test (2015, methodology): “Weuse a recently developed framework, SupersparseLinear IntegerModels (SLIM) (Ustun and Rudin 2015; Ustun et al. 2013), and introduce a simple metric to prioritize more understandable features, enabling us to build interpretable linear models.”
• Machine learning for science and society (2013, background): “…et al. 2013b; McCormick et al. 2012), information retrieval (Letham et al. 2013a), interpretable models (Letham et al. 2013b; McCormick et al. 2012; Ustun et al. 2013), robotic space exploration (Castano et al. 2007; Wagstaff and Born-stein 2009; Wagstaff et al. 2013b), and scientific discovery…”
• Trading Interpretability for Accuracy: Oblique Treed Sparse Additive Models (2015, unknown): “LITERATURE REVIEW This section focuses mainly on”
• Legal requirements on explainability in machine learning (2020, methodology): “As developed in the literature on interpretability and explainability, this requires to use transparent models such as decision trees or linear models, to create new ones (e.g. supersparse linear integer models (SLIM) Ustun et al. 2013a, b; Ustun and Rudin 2016) or to create ways to explain black-bo”
• A Bayesian Approach to Learning Scoring Systems (2015, methodology): “The work of Ustun and Rudin(27) and Ustun et al.(28,29) uses mixed-integer linear programming to exactly optimize the accuracy of the scoring system.”
• Interval Coded Scoring extensions for larger problems (2017, background): “[8], but ICS goes beyond a linear model.”