Support Collapse of Deep Gaussian Processes with Polynomial Kernels for a Wide Regime of Hyperparameters
This work addresses the instability in deep Gaussian processes for practitioners, but it is incremental as it mirrors known results from convolution-based methods.
The paper analyzes the prior of Deep Gaussian Processes with polynomial kernels, finding that without careful hyperparameter tuning, the prior either collapses to zero or places negligible mass on low-norm functions as depth increases, aligning with experimental results.
We analyze the prior that a Deep Gaussian Process with polynomial kernels induces. We observe that, even for relatively small depths, averaging effects occur within such a Deep Gaussian Process and that the prior can be analyzed and approximated effectively by means of the Berry-Esseen Theorem. One of the key findings of this analysis is that, in the absence of careful hyper-parameter tuning, the prior of a Deep Gaussian Process either collapses rapidly towards zero as the depth increases or places negligible mass on low norm functions. This aligns well with experimental findings and mirrors known results for convolution based Deep Gaussian Processes.