Rethinking Approximate Gaussian Inference in Classification
This work addresses the computational cost and noise issues in approximate Gaussian inference for classification, offering a more efficient method for uncertainty estimation in machine learning models.
The authors tackled the problem of efficiently capturing epistemic uncertainty in classification by replacing softmax with normCDF or sigmoid activations, enabling sampling-free approximations and improving uncertainty quantification on datasets like ImageNet and CIFAR-100.
In classification tasks, softmax functions are ubiquitously used as output activations to produce predictive probabilities. Such outputs only capture aleatoric uncertainty. To capture epistemic uncertainty, approximate Gaussian inference methods have been proposed. We develop a common formalism to describe such methods, which we view as outputting Gaussian distributions over the logit space. Predictives are then obtained as the expectations of the Gaussian distributions pushed forward through the softmax. However, such softmax Gaussian integrals cannot be solved analytically, and Monte Carlo (MC) approximations can be costly and noisy. We propose to replace the softmax activation by element-wise normCDF or sigmoid, which allows for the accurate sampling-free approximation of predictives. This also enables the approximation of the Gaussian pushforwards by Dirichlet distributions with moment matching. This approach entirely eliminates the runtime and memory overhead associated with MC sampling. We evaluate it combined with several approximate Gaussian inference methods (Laplace, HET, SNGP) on large- and small-scale datasets (ImageNet, CIFAR-100, CIFAR-10), demonstrating improved uncertainty quantification capabilities compared to softmax MC sampling. Our code is available at https://github.com/bmucsanyi/probit.