Greedy Block Coordinate Descent for Large Scale Gaussian Process Regression
This work addresses scalability issues in Gaussian process regression for researchers and practitioners dealing with large datasets, representing an incremental improvement over existing methods.
The paper tackles the challenge of making dense Gaussian process regression practical for large-scale problems by proposing a greedy block coordinate descent algorithm, which is shown to be an order of magnitude faster than competing dense methods and capable of handling datasets with over 100,000 samples while maintaining accuracy.
We propose a variable decomposition algorithm -greedy block coordinate descent (GBCD)- in order to make dense Gaussian process regression practical for large scale problems. GBCD breaks a large scale optimization into a series of small sub-problems. The challenge in variable decomposition algorithms is the identification of a subproblem (the active set of variables) that yields the largest improvement. We analyze the limitations of existing methods and cast the active set selection into a zero-norm constrained optimization problem that we solve using greedy methods. By directly estimating the decrease in the objective function, we obtain not only efficient approximate solutions for GBCD, but we are also able to demonstrate that the method is globally convergent. Empirical comparisons against competing dense methods like Conjugate Gradient or SMO show that GBCD is an order of magnitude faster. Comparisons against sparse GP methods show that GBCD is both accurate and capable of handling datasets of 100,000 samples or more.