We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However, in some instances additional constraints may be available that can reduce the uncertainty in the resulting predictive models. In particular, we consider the case of monotonically ordered latent input, which occurs in many application domains that deal with temporal data. We present a novel inference and learning approach based on non-parametric Gaussian variational approximation to learn the GP model while taking into account the new constraints. The resulting strategy allows one to gain access to posterior estimates of both the input and the output and results in improved predictive performance. We compare our proposed models to state-of-the-art Noisy Input Gaussian Process (NIGP) and other competing approaches on synthetic and real sea-level rise data. Experimental results suggest that the proposed approach consistently outperforms selected methods while, at the same time, reducing the computational costs of learning and inference.
[1]
Agathe Girard,et al.
Learning a Gaussian Process Model with Uncertain Inputs
,
2003
.
[2]
Brahim Chaib-draa,et al.
Learning Gaussian Process Models from Uncertain Data
,
2009,
ICONIP.
[3]
Robert E. Kopp,et al.
Late Holocene sea- and land-level change on the U.S. southeastern Atlantic coast
,
2014
.
[4]
Carl E. Rasmussen,et al.
Gaussian Process Training with Input Noise
,
2011,
NIPS.
[5]
P. Dellaportas,et al.
BAYESIAN ANALYSIS OF ERRORS-IN-VARIABLES REGRESSION MODELS
,
1995
.
[6]
Christopher K. I. Williams,et al.
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
,
2005
.
[7]
Neil D. Lawrence,et al.
Bayesian Gaussian Process Latent Variable Model
,
2010,
AISTATS.
[8]
David M. Blei,et al.
Nonparametric variational inference
,
2012,
ICML.
[9]
C. Rasmussen,et al.
Gaussian Process Priors with Uncertain Inputs - Application to Multiple-Step Ahead Time Series Forecasting
,
2002,
NIPS.