Data Subsampling for Bayesian Neural Networks
This addresses scalability for Bayesian inference in neural networks, but it is an incremental improvement over existing MCMC methods.
The paper tackles the scalability issue of MCMC for Bayesian Neural Networks on large datasets by proposing Penalty Bayesian Neural Networks (PBNNs), which use subsampled data with a penalty term to avoid bias, achieving good predictive performance on MNIST and reducing overconfidence.
Markov Chain Monte Carlo (MCMC) algorithms do not scale well for large datasets leading to difficulties in Neural Network posterior sampling. In this paper, we propose Penalty Bayesian Neural Networks - PBNNs, as a new algorithm that allows the evaluation of the likelihood using subsampled batch data (mini-batches) in a Bayesian inference context towards addressing scalability. PBNN avoids the biases inherent in other naive subsampling techniques by incorporating a penalty term as part of a generalization of the Metropolis Hastings algorithm. We show that it is straightforward to integrate PBNN with existing MCMC frameworks, as the variance of the loss function merely reduces the acceptance probability. By comparing with alternative sampling strategies on both synthetic data and the MNIST dataset, we demonstrate that PBNN achieves good predictive performance even for small mini-batch sizes of data. We show that PBNN provides a novel approach for calibrating the predictive distribution by varying the mini-batch size, significantly reducing predictive overconfidence.