# Optimal Explanations of Linear Models

arXiv: https://arxiv.org/abs/1907.04669 · HTML: https://mlsanity.com/paper/1907.04669/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [Improving Accuracy Without Losing Interpretability: A ML Approach for Time Series Forecasting](https://mlsanity.com/paper/2212.06620/) (2022)

## Abstract (arXiv)

When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at interpreting models are often ad hoc and application-specific, and the concept of interpretability itself is not well-defined. We propose a general optimization framework to create explanations for linear models. Our methodology decomposes a linear model into a sequence of models of increasing complexity using coordinate updates on the coefficients. Computing this decomposition optimally is a difficult optimization problem for which we propose exact algorithms and scalable heuristics. By solving this problem, we can derive a parametrized family of interpretability metrics for linear models that generalizes typical proxies, and study the tradeoff between interpretability and predictive accuracy.