Adjusting Model Size in Continual Gaussian Processes: How Big is Big Enough?

Many machine learning models require setting a parameter that controls their size before training, e.g.~number of neurons in DNNs, or inducing points in GPs. Increasing capacity typically improves performance until all the information from the dataset is captured. After this point, computational cost keeps increasing without improved performance. This leads to the question ``How big is big enough?'' We investigate this problem for Gaussian processes (single-layer neural networks) in continual learning. Here, data becomes available incrementally, and the final dataset size will therefore not be known before training, preventing the use of heuristics for setting a fixed model size. We develop a method to automatically adjust model size while maintaining near-optimal performance. Our experimental procedure follows the constraint that any hyperparameters must be set without seeing dataset properties. For our method, a single hyperparameter setting works well across diverse datasets, showing that it requires less tuning compared to others.