3,338 research outputs found
Recovering Latent Signals from a Mixture of Measurements using a Gaussian Process Prior
In sensing applications, sensors cannot always measure the latent quantity of
interest at the required resolution, sometimes they can only acquire a blurred
version of it due the sensor's transfer function. To recover latent signals
when only noisy mixed measurements of the signal are available, we propose the
Gaussian process mixture of measurements (GPMM), which models the latent signal
as a Gaussian process (GP) and allows us to perform Bayesian inference on such
signal conditional to a set of noisy mixture of measurements. We describe how
to train GPMM, that is, to find the hyperparameters of the GP and the mixing
weights, and how to perform inference on the latent signal under GPMM;
additionally, we identify the solution to the underdetermined linear system
resulting from a sensing application as a particular case of GPMM. The proposed
model is validated in the recovery of three signals: a smooth synthetic signal,
a real-world heart-rate time series and a step function, where GPMM
outperformed the standard GP in terms of estimation error, uncertainty
representation and recovery of the spectral content of the latent signal.Comment: Published on IEEE Signal Processing Letters on Dec. 201
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
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