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Deep kernel learning (DKL) leverages the connection between Gaussian process (GP) and neural networks (NN) to build an end-to-end, hybrid model. It combines the capability of NN to learn rich representations under massive data and the non-parametric property of GP to achieve automatic regularization that incorporates a trade-off between model fit and model complexity. However, the deterministic encoder may weaken the model regularization of the following GP part, especially on small datasets, due to the free latent representation. We therefore present a complete deep latent-variable kernel learning (DLVKL) model wherein the latent variables perform stochastic encoding for regularized representation. We further enhance the DLVKL from two aspects: (i) the expressive variational posterior through neural stochastic differential equation (NSDE) to improve the approximation quality, and (ii) the hybrid prior taking knowledge from both the SDE prior and the posterior to arrive at a flexible trade-off. Intensive experiments imply that the DLVKL-NSDE performs similarly to the well calibrated GP on small datasets, and outperforms existing deep GPs on large datasets.
In many scientific problems such as video surveillance, modern genomic analysis, and clinical studies, data are often collected from diverse domains across time that exhibit time-dependent heterogeneous properties. It is important to not only integra
We present a model that can automatically learn alignments between high-dimensional data in an unsupervised manner. Our proposed method casts alignment learning in a framework where both alignment and data are modelled simultaneously. Further, we aut
Deep latent variable models (DLVMs) combine the approximation abilities of deep neural networks and the statistical foundations of generative models. Variational methods are commonly used for inference; however, the exact likelihood of these models h
Recent studies show a close connection between neural networks (NN) and kernel methods. However, most of these analyses (e.g., NTK) focus on the influence of (infinite) width instead of the depth of NN models. There remains a gap between theory and p
Although with progress in introducing auxiliary amortized inference models, learning discrete latent variable models is still challenging. In this paper, we show that the annoying difficulty of obtaining reliable stochastic gradients for the inferenc