Faithful Heteroscedastic Regression with Neural Networks
This addresses the issue of unreliable uncertainty quantification in regression tasks for practitioners in fields like finance or healthcare, though it is incremental as it builds on existing optimization methods.
The paper tackled the problem of suboptimal mean and uncalibrated variance estimates in heteroscedastic regression with neural networks, by introducing two simple modifications to optimization that provably retain mean accuracy comparable to homoscedastic models and achieve best-in-class variance calibration.
Heteroscedastic regression models a Gaussian variable's mean and variance as a function of covariates. Parametric methods that employ neural networks for these parameter maps can capture complex relationships in the data. Yet, optimizing network parameters via log likelihood gradients can yield suboptimal mean and uncalibrated variance estimates. Current solutions side-step this optimization problem with surrogate objectives or Bayesian treatments. Instead, we make two simple modifications to optimization. Notably, their combination produces a heteroscedastic model with mean estimates that are provably as accurate as those from its homoscedastic counterpart (i.e.~fitting the mean under squared error loss). For a wide variety of network and task complexities, we find that mean estimates from existing heteroscedastic solutions can be significantly less accurate than those from an equivalently expressive mean-only model. Our approach provably retains the accuracy of an equally flexible mean-only model while also offering best-in-class variance calibration. Lastly, we show how to leverage our method to recover the underlying heteroscedastic noise variance.