199 research outputs found
A Mutually-Dependent Hadamard Kernel for Modelling Latent Variable Couplings
We introduce a novel kernel that models input-dependent couplings across
multiple latent processes. The pairwise joint kernel measures covariance along
inputs and across different latent signals in a mutually-dependent fashion. A
latent correlation Gaussian process (LCGP) model combines these non-stationary
latent components into multiple outputs by an input-dependent mixing matrix.
Probit classification and support for multiple observation sets are derived by
Variational Bayesian inference. Results on several datasets indicate that the
LCGP model can recover the correlations between latent signals while
simultaneously achieving state-of-the-art performance. We highlight the latent
covariances with an EEG classification dataset where latent brain processes and
their couplings simultaneously emerge from the model.Comment: 17 pages, 6 figures; accepted to ACML 201
Learning Space-Time Continuous Neural PDEs from Partially Observed States
We introduce a novel grid-independent model for learning partial differential
equations (PDEs) from noisy and partial observations on irregular
spatiotemporal grids. We propose a space-time continuous latent neural PDE
model with an efficient probabilistic framework and a novel encoder design for
improved data efficiency and grid independence. The latent state dynamics are
governed by a PDE model that combines the collocation method and the method of
lines. We employ amortized variational inference for approximate posterior
estimation and utilize a multiple shooting technique for enhanced training
speed and stability. Our model demonstrates state-of-the-art performance on
complex synthetic and real-world datasets, overcoming limitations of previous
approaches and effectively handling partially-observed data. The proposed model
outperforms recent methods, showing its potential to advance data-driven PDE
modeling and enabling robust, grid-independent modeling of complex
partially-observed dynamic processes
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