Calibrated and Sharp Uncertainties in Deep Learning via Density Estimation
This addresses the need for accurate uncertainty quantification in machine learning, particularly for applications requiring reliable probabilistic predictions, though it is incremental as it builds on existing calibration concepts.
The paper tackles the problem of poor calibration in probabilistic deep learning models, where confidence intervals do not match true outcome frequencies, by introducing a recalibration training procedure based on low-dimensional density estimation. The result is a method that ensures distribution calibration without sacrificing performance, with empirical improvements on linear and deep Bayesian models.
Accurate probabilistic predictions can be characterized by two properties -- calibration and sharpness. However, standard maximum likelihood training yields models that are poorly calibrated and thus inaccurate -- a 90% confidence interval typically does not contain the true outcome 90% of the time. This paper argues that calibration is important in practice and is easy to maintain by performing low-dimensional density estimation. We introduce a simple training procedure based on recalibration that yields calibrated models without sacrificing overall performance; unlike previous approaches, ours ensures the most general property of distribution calibration and applies to any model, including neural networks. We formally prove the correctness of our procedure assuming that we can estimate densities in low dimensions and we establish uniform convergence bounds. Our results yield empirical performance improvements on linear and deep Bayesian models and suggest that calibration should be increasingly leveraged across machine learning. We release a library that implements our methods along with a blog post here: https://shachideshpande.github.io/blog-distribution-calibration/.