A Locally Adaptive Interpretable Regression

TL;DR

LoAIR introduces a neural network-based method that adaptively predicts regression coefficients for linear models, enhancing predictive accuracy while maintaining interpretability, and uncovers meaningful relationships in data.

Contribution

The paper presents LoAIR, a novel locally adaptive interpretable regression model that combines neural networks with linear regression to improve predictability without losing interpretability.

Findings

Achieves comparable or better predictive performance than state-of-the-art models.

Discovers meaningful relationships such as a parabolic link between CO2 emissions and GNP.

Bridges gap between econometrics, statistics, and machine learning.

Abstract

Machine learning models with both good predictability and high interpretability are crucial for decision support systems. Linear regression is one of the most interpretable prediction models. However, the linearity in a simple linear regression worsens its predictability. In this work, we introduce a locally adaptive interpretable regression (LoAIR). In LoAIR, a metamodel parameterized by neural networks predicts percentile of a Gaussian distribution for the regression coefficients for a rapid adaptation. Our experimental results on public benchmark datasets show that our model not only achieves comparable or better predictive performance than the other state-of-the-art baselines but also discovers some interesting relationships between input and target variables such as a parabolic relationship between CO2 emissions and Gross National Product (GNP). Therefore, LoAIR is a step towards bridging the gap between econometrics, statistics, and machine learning by improving the predictive ability of linear regression without depreciating its interpretability.