A Locally Adaptive Interpretable Regression

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.