KernelNet: A Data-Dependent Kernel Parameterization for Deep Generative Modeling
This work addresses the hyperparameter tuning burden in kernel methods for machine learning practitioners, offering an incremental improvement by integrating deep learning into kernel construction.
The paper tackles the problem of predefined kernels requiring careful hyperparameter selection in kernel methods by proposing KernelNet, a framework for constructing and learning data-dependent kernels using deep neural networks, which consistently achieves better performance in deep generative modeling scenarios like MMD-GAN and implicit VAE.
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a framework to construct and learn a data-dependent kernel based on random features and implicit spectral distributions that are parameterized by deep neural networks. The constructed network (called KernelNet) can be applied to deep generative modeling in various scenarios, including two popular learning paradigms in deep generative models, MMD-GAN and implicit Variational Autoencoder (VAE). We show that our proposed kernel indeed exists in applications and is guaranteed to be positive definite. Furthermore, the induced Maximum Mean Discrepancy (MMD) can endow the continuity property in weak topology by simple regularization. Extensive experiments indicate that our proposed KernelNet consistently achieves better performance compared to related methods.