53 research outputs found
Gaussian process deconvolution
Let us consider the deconvolution problem, that is, to recover a latent
source from the observations of a
convolution process , where is an additive noise,
the observations in might have missing parts with respect to ,
and the filter could be unknown. We propose a novel strategy to address
this task when is a continuous-time signal: we adopt a Gaussian process
(GP) prior on the source , which allows for closed-form Bayesian
nonparametric deconvolution. We first analyse the direct model to establish the
conditions under which the model is well defined. Then, we turn to the inverse
problem, where we study i) some necessary conditions under which Bayesian
deconvolution is feasible, and ii) to which extent the filter can be learnt
from data or approximated for the blind deconvolution case. The proposed
approach, termed Gaussian process deconvolution (GPDC) is compared to other
deconvolution methods conceptually, via illustrative examples, and using
real-world datasets.Comment: Accepted at Proceedings of the Royal Society
On Negative Transfer and Structure of Latent Functions in Multi-output Gaussian Processes
The multi-output Gaussian process () is based on the
assumption that outputs share commonalities, however, if this assumption does
not hold negative transfer will lead to decreased performance relative to
learning outputs independently or in subsets. In this article, we first define
negative transfer in the context of an and then derive
necessary conditions for an model to avoid negative transfer.
Specifically, under the convolution construction, we show that avoiding
negative transfer is mainly dependent on having a sufficient number of latent
functions regardless of the flexibility of the kernel or inference
procedure used. However, a slight increase in leads to a large increase in
the number of parameters to be estimated. To this end, we propose two latent
structures that scale to arbitrarily large datasets, can avoid negative
transfer and allow any kernel or sparse approximations to be used within. These
structures also allow regularization which can provide consistent and automatic
selection of related outputs
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
Convolved Gaussian process priors for multivariate regression with applications to dynamical systems
In this thesis we address the problem of modeling correlated outputs using Gaussian process priors. Applications of modeling correlated outputs include the joint prediction of pollutant metals in geostatistics and multitask learning in machine learning. Defining a Gaussian process prior for correlated outputs translates into specifying a suitable covariance function that captures dependencies between the different output variables. Classical models for obtaining such a covariance function include the linear model of coregionalization and process convolutions. We propose a general framework for developing multiple output covariance functions by performing convolutions between smoothing kernels particular to each output and covariance functions that are common to all outputs. Both the linear model of coregionalization and the process convolutions turn out to be special cases of this framework. Practical aspects of the proposed methodology are studied in this thesis. They involve the use of domain-specific knowledge for defining relevant smoothing kernels, efficient approximations for reducing computational complexity and a novel method for establishing a general class of nonstationary covariances with applications in robotics and motion capture data.Reprints of the publications that appear at the end of this document, report case studies and experimental results in sensor networks, geostatistics and motion capture data that illustrate the performance of the different methods proposed.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
- …