On the benefits of Maximum Likelihood Estimation for Regression and Forecasting

We propose a practical maximum-likelihood-estimation framework for regression as an alternative to the typical approach of Empirical Risk Minimization (ERM) over a specific loss metric. Our approach is better suited to capture inductive biases in datasets, and can output post-hoc estimators at inference time that can optimize different types of loss metrics. We present theoretical evidence (in the fixed design setting) to demonstrate that our approach is always competitive with using ERM over the loss metric, and in many practical scenarios can be much superior to ERM. For time series forecasting, we propose an end-to-end MLE based training and inference approach that can flexibly capture various inductive biases, and optimize prediction accuracy for a variety of typical loss metrics, without having to choose a specific loss metric at training time. We demonstrate empirically that our method instantiated with a well-designed general purpose likelihood can obtain superior performance over ERM for a variety of time-series forecasting and regression datasets with different inductive biases and data distributions.

• Machine Intelligence