1,498 research outputs found
Compositional Uncertainty in Deep Gaussian Processes
Gaussian processes (GPs) are nonparametric priors over functions. Fitting a
GP implies computing a posterior distribution of functions consistent with the
observed data. Similarly, deep Gaussian processes (DGPs) should allow us to
compute a posterior distribution of compositions of multiple functions giving
rise to the observations. However, exact Bayesian inference is intractable for
DGPs, motivating the use of various approximations. We show that the
application of simplifying mean-field assumptions across the hierarchy leads to
the layers of a DGP collapsing to near-deterministic transformations. We argue
that such an inference scheme is suboptimal, not taking advantage of the
potential of the model to discover the compositional structure in the data. To
address this issue, we examine alternative variational inference schemes
allowing for dependencies across different layers and discuss their advantages
and limitations.Comment: 17 page
Aligned Multi-Task Gaussian Process
Multi-task learning requires accurate identification of the correlations
between tasks. In real-world time-series, tasks are rarely perfectly temporally
aligned; traditional multi-task models do not account for this and subsequent
errors in correlation estimation will result in poor predictive performance and
uncertainty quantification. We introduce a method that automatically accounts
for temporal misalignment in a unified generative model that improves
predictive performance. Our method uses Gaussian processes (GPs) to model the
correlations both within and between the tasks. Building on the previous work
by Kazlauskaiteet al. [2019], we include a separate monotonic warp of the input
data to model temporal misalignment. In contrast to previous work, we formulate
a lower bound that accounts for uncertainty in both the estimates of the
warping process and the underlying functions. Also, our new take on a monotonic
stochastic process, with efficient path-wise sampling for the warp functions,
allows us to perform full Bayesian inference in the model rather than MAP
estimates. Missing data experiments, on synthetic and real time-series,
demonstrate the advantages of accounting for misalignments (vs standard
unaligned method) as well as modelling the uncertainty in the warping
process(vs baseline MAP alignment approach)
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