We propose several variants of latent Gaussian models for large spatio-temporal datasets robustly and efficiently. We have developed Gaussian process models that capture both short length-scale and long length-scale variability of global sea-surface temperature (Luttinen et al. 2012a, Luttinen et al. 2009). In order to capture complex temporal structure, (Luttinen et al. 2014) proposes a linear state-space model with time-varying dynamics. Because real-world datasets are often of bad quality, (Luttinen et al. 2012) discusses different robust noise distributions to handle outliers. Inference for all these models can be very slow, thus (Luttinen et al. 2010, Luttinen 2013) develop methods to speed up the learning process significantly.

References

J. Luttinen, A. Ilin.
Efficient Gaussian Process Inference for Short-Scale Spatio-Temporal Modeling.
In Proceedings of AISTATS 2012, pp. 741-750, 2012a.

J. Luttinen, A. Ilin.
Variational Gaussian-Process Factor Analysis for Modeling Spatio-Temporal Data.
In Advances in Neural Information Processing Systems 22, pp. 1177-1185, 2009.

J. Luttinen, T. Raiko, A. Ilin.
Linear State-Space Model with Time-Varying Dynamics.
In Machine Learning and Knowledge Discovery in Databases, ECML/PKDD'2014, volume 8725 of Lecture Notes in Computer Science, pages 338-353, 2014.

J. Luttinen, A. Ilin, J. Karhunen.
Bayesian Robust PCA of Incomplete Data.
In Neural Processing Letters, volume 36, pp. 189-202, 2012b.

J. Luttinen, A. Ilin.
Transformations for Variational Factor Analysis to Speed up Learning.
In Neurocomputing, volume 73, pp. 1093-1102, 2010.

J. Luttinen.
Fast Variational Bayesian Linear State-Space Model.
In Machine Learning and Knowledge Discovery in Databases, ECML/PKDD'2013, volume 8188 of Lecture Notes in Computer Science, pages 305-320, 2013.