# Rethinking Log Odds: Linear Probability Modelling and Expert Advice in Interpretable Machine Learning

arXiv: https://arxiv.org/abs/2211.06360 · HTML: https://mlsanity.com/paper/2211.06360/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 80 references that are in the map.
- First posted on arXiv 11 Nov 2022.

## Builds on (most cited first, 13 of 13)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [Should we really use post-hoc tests based on mean-ranks?](https://mlsanity.com/paper/1505.02288/) (2015)
- [Boolean Decision Rules via Column Generation](https://mlsanity.com/paper/1805.09901/) (2018)
- [Born-Again Tree Ensembles](https://mlsanity.com/paper/2003.11132/) (2020)
- [Explainable Neural Networks based on Additive Index Models](https://mlsanity.com/paper/1806.01933/) (2018)
- [Enhancing Explainability of Neural Networks through Architecture Constraints](https://mlsanity.com/paper/1901.03838/) (2019)
- [Enforcing Interpretability and its Statistical Impacts: Trade-offs between Accuracy and Interpretability](https://mlsanity.com/paper/2010.13764/) (2020)
- [A Holistic Approach to Interpretability in Financial Lending: Models, Visualizations, and Summary-Explanations](https://mlsanity.com/paper/2106.02605/) (2021)
- [Forecasting remaining useful life: Interpretable deep learning approach via variational Bayesian inferences](https://mlsanity.com/paper/1907.05146/) (2019)
- [Sample size calculations for the experimental comparison of multiple algorithms on multiple problem instances](https://mlsanity.com/paper/1908.01720/) (2019)
- [FEAMOE: Fair, Explainable and Adaptive Mixture of Experts](https://mlsanity.com/paper/2210.04995/) (2022)

## Abstract (arXiv)

We introduce a family of interpretable machine learning models, with two broad additions: Linearised Additive Models (LAMs) which replace the ubiquitous logistic link function in General Additive Models (GAMs); and SubscaleHedge, an expert advice algorithm for combining base models trained on subsets of features called subscales. LAMs can augment any additive binary classification model equipped with a sigmoid link function. Moreover, they afford direct global and local attributions of additive components to the model output in probability space. We argue that LAMs and SubscaleHedge improve the interpretability of their base algorithms. Using rigorous null-hypothesis significance testing on a broad suite of financial modelling data, we show that our algorithms do not suffer from large performance penalties in terms of ROC-AUC and calibration.