Global Convolutional Neural Processes
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by
Xuesong Wang, Lina Yao, Xianzhi Wang, Hye-young Paik, Sen Wang
2021
Abstract
The ability to deal with uncertainty in machine learning models has become
equally, if not more, crucial to their predictive ability itself. For instance,
during the pandemic, governmental policies and personal decisions are
constantly made around uncertainties. Targeting this, Neural Process Families
(NPFs) have recently shone a light on prediction with uncertainties by bridging
Gaussian processes and neural networks. Latent neural process, a member of NPF,
is believed to be capable of modelling the uncertainty on certain points (local
uncertainty) as well as the general function priors (global uncertainties).
Nonetheless, some critical questions remain unresolved, such as a formal
definition of global uncertainties, the causality behind global uncertainties,
and the manipulation of global uncertainties for generative models. Regarding
this, we build a member GloBal Convolutional Neural Process(GBCoNP) that
achieves the SOTA log-likelihood in latent NPFs. It designs a global
uncertainty representation p(z), which is an aggregation on a discretized input
space. The causal effect between the degree of global uncertainty and the
intra-task diversity is discussed. The learnt prior is analyzed on a variety of
scenarios, including 1D, 2D, and a newly proposed spatial-temporal COVID
dataset. Our manipulation of the global uncertainty not only achieves
generating the desired samples to tackle few-shot learning, but also enables
the probability evaluation on the functional priors.
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