Bayesian Model Selection via a Data-Emphasized Variational Objective

When training large models on limited data, avoiding overfitting is paramount. Common grid search or smarter search methods rely on expensive separate runs at each candidate hyperparameter while carving out a validation set that reduces available training data. In this paper, we study gradient-based learning of hyperparameters on all training data via the evidence lower bound (ELBO) objective from Bayesian variational methods. We focus on scenarios where the model is over-parameterized for flexibility while the approximate posterior is chosen to be Gaussian with isotropic covariance for tractability, even though it cannot match the true posterior. In such scenarios, we find the ELBO prioritizes posteriors that match the prior, leading to severely underfitting the data. Instead, we recommend a data-emphasized ELBO that upweights the likelihood over the prior. In Bayesian transfer learning of image and text classifiers, our method reduces 88+ hour grid searches of past work to under 3 hours while delivering comparable accuracy. We further demonstrate how our approach enables efficient yet accurate approximations of Gaussian processes with learnable length-scale kernels.