Stochastic Marginal Likelihood Gradients using Neural Tangent Kernels

Autor:	Immer, Alexander, van der Ouderaa, Tycho F. A., van der Wilk, Mark, Rätsch, Gunnar, Schölkopf, Bernhard
Rok vydání:	2023
Předmět:	Statistics - Machine Learning Computer Science - Machine Learning
Druh dokumentu:	Working Paper
Popis:	Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters just like standard neural network parameters using gradients and on the training data. However, estimating a single hyperparameter gradient requires a pass through the entire dataset, limiting the scalability of such algorithms. In this work, we overcome this issue by introducing lower bounds to the linearized Laplace approximation of the marginal likelihood. In contrast to previous estimators, these bounds are amenable to stochastic-gradient-based optimization and allow to trade off estimation accuracy against computational complexity. We derive them using the function-space form of the linearized Laplace, which can be estimated using the neural tangent kernel. Experimentally, we show that the estimators can significantly accelerate gradient-based hyperparameter optimization. Comment: ICML 2023
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.03968 Zobrazit plný text záznamu View this record from Arxiv