On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks
This addresses reliability issues in uncertainty estimation for probabilistic deep learning, offering a more robust method for applications requiring accurate uncertainty quantification.
The paper identifies pitfalls in using log-likelihood loss for heteroscedastic uncertainty estimation in neural networks, leading to poor parameter estimates, and proposes a β-NLL alternative that improves predictive RMSE and log-likelihood robustness across tasks.
Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by maximizing the logarithm of the likelihood function under the observed data. In this work, we examine this approach and identify potential hazards associated with the use of log-likelihood in conjunction with gradient-based optimizers. First, we present a synthetic example illustrating how this approach can lead to very poor but stable parameter estimates. Second, we identify the culprit to be the log-likelihood loss, along with certain conditions that exacerbate the issue. Third, we present an alternative formulation, termed $β$-NLL, in which each data point's contribution to the loss is weighted by the $β$-exponentiated variance estimate. We show that using an appropriate $β$ largely mitigates the issue in our illustrative example. Fourth, we evaluate this approach on a range of domains and tasks and show that it achieves considerable improvements and performs more robustly concerning hyperparameters, both in predictive RMSE and log-likelihood criteria.