My main research focus is on probabilistic models for time series, this includes modelling, imputation, denoising, filtering and spectral estimation.

My Google Scholar profile can be seen here.

Selected research projects

bse Bayesian spectral estimation. Spectral estimation aims to identify how the energy of a time series is distributed across frequencies; this can be challenging when only partial and noisy observations are available. In this context, we are interested in developing probabilistic models for signals, observations and spectra, all to address SE as a Bayesian inference problem. This would enable us to compute posterior distributions of power spectral densities (PSDs) as shown in the figure: only using a 10% of a heart-rate time series, we were able to compute a posterior distribution over PSDs (red) and successfully contained the ground truth (blue).
See [C19] below and click here for code and demo.

Preprints

Cazelles, Robert, Tobar, "The Wasserstein-Fourier Distance for Stationary Time Series". Available on the arXiv

Journal articles

[J12]
G. Rios and F. Tobar, ‘Compositionally-warped Gaussian process’, Neural Networks, vol. 118, pp. 235–246, 2019. Available: Elsevier, arXiv.
[J11]
J. Dunstan, M. Aguirre, M. Bastías, C. Nau, T. A. Glass, and F. Tobar, ‘Predicting nationwide obesity from food sales using machine learning’, Health Informatics Journal, p. 1460458219845959, 2019. Available: SAGE.
[J10]
B. Poblete, J. Guzman, J. Maldonado, and F. Tobar, ‘Robust detection of extreme events using Twitter: Worldwide earthquake monitoring’, IEEE Transactions on Multimedia, vol. 20, no. 10, pp. 2551–2561, 2018. Available: IEEEXplore
[J9]
F. Tobar, I. Castro, J. Silva, and M. Orchard, ‘Improving battery voltage prediction in an electric bicycle using altitude measurements and kernel adaptive filters’, Pattern Recognition Letters, vol. 105, pp. 200–206, 2018. Available: Elsevier
[J8]
D. Cabrera, F. Sancho, M. Cerrada, R.-V. Sánchez, and F. Tobar, ‘Echo state network and variational autoencoder for efficient one-class learning on dynamical systems’, Journal of Intelligent & Fuzzy Systems., vol. 34, no. 6, pp. 3799–3809, 2018. Available: IOS Press
[J7]
F. Tobar, G. Rios, T. Valdivia, and P. Guerrero, ‘Recovering latent signals from a mixture of measurements using a Gaussian process prior’, IEEE Signal Processing Letters, vol. 24, no. 2, pp. 231–235, 2017. Available: IEEEXplore, ArXiV
[J6]
F. Tobar and D. Mandic, ‘Design of positive-definite quaternion kernels’, IEEE Signal Processing Letters, vol. 22, no. 11, pp. 2117–2121, 2015. Available: IEEEXplore
[J5]
F. Tobar, P. Djurić, and D. Mandic, ‘Unsupervised state-space modeling using reproducing kernels’, IEEE Trans. on Signal Processing, vol. 63, no. 19, pp. 5210–5221, 2015. Available: IEEEXplore
[J4]
F. A. Tobar, S. Kung, and D. P. Mandic, ‘Multikernel Least Mean Square Algorithm’, IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 2, pp. 265–277, 2014. Available: IEEEXplore
[J3]
F. Tobar and D. Mandic, ‘Quaternion reproducing kernel Hilbert spaces: Existence and uniqueness conditionss’, IEEE Trans. on Inf. Theory, vol. 60, no. 9, pp. 5736–5749, 2014. Available: IEEEXplore
[J2]
F. Tobar and M. Orchard, ‘Study of financial systems volatility using suboptimal estimation algorithms’, Studies in Informatics and Control, vol. 21, no. 1, pp. 59–66, 2012. Available: here
[J1]
M. Orchard, F. Tobar, and G. Vachtsevanos, ‘Outer feedback correction loops in particle filtering-based prognostic algorithms: Statistical performance comparison’, Studies in Informatics and Control, vol. 18, no. 4, pp. 295–304, 2009. Available: here

Conferences articles (peer-reviewed only)

[C21]
F. Tobar, ‘Band-limited Gaussian processes: The Sinc kernel’, in Advances in Neural Information Processing Systems 32, 2019, pp. 12728-12738. Available: Paper, Poster, Presentation.
[C20]
C. Valenzuela and F. Tobar, ‘Low-pass filtering as Bayesian inference ’, Proc. of IEEE ICASSP, 2019, pp. 3367–3371. Available: arXiv and IEEEXplore
[C19]
F. Tobar, ‘Bayesian Nonparametric Spectral Estimation’, in Advances in Neural Information Processing Systems 31, 2018, pp. 10148–10158. Available: Paper, Poster, Spotlight Presentation.
[C18]
G. Rios and F. Tobar, ‘The Box-Cox Gaussian Process’, in Proc. of the IEEE International Joint Conference on Neural Networks, 2018, pp. 1–8. Available: IEEEXplore
[C17]
G. Parra and F. Tobar, ‘Spectral Mixture Kernels for Multioutput Gaussian Processes’, in Advances in Neural Information Processing Systems 30, 2017, pp. 6681--6690. Available: Paper, Poster
[C16]
F. Tobar, ‘Improving sparsity in kernel adaptive filters using a unit-norm dictionary’, in Proc. of the 22nd International Conference on Digital Signal Processing (DSP), 2017, pp. 1–5. Available: IEEEXplore
[C15]
A. Cuevas, A. Veragua, S. Español, G. Chiang, and F. Tobar, ‘Unsupervised Blue Whale Call Detection Using Multiple Time-Frequency Features’, in Proc. of IEEE Chilecon, 2017, pp. 1–6. Available: IEEEXplore
[C14]
I. Castro, C. Silva, and F. Tobar, ‘Initialising kernel adaptive filters via probabilistic inference’, in Proc. of the 22nd International Conference on Digital Signal Processing (DSP), 2017, pp. 1–5. Available: IEEEXplore
[C13]
D. Cabrera, F. Sancho, and F. Tobar, ‘Combining reservoir computing and variational inference for efficient one-class learning on dynamical systems’, in Proc. of the IEEE International Conference on Sensing, Diagnostics, Prognostics, and Control (SDPC), 2017, pp. 57–62. Available: IEEEXplore
[C12]
L. Araya-Hernández, J. Silva, A. Osses, and F. Tobar, ‘A Bayesian mixture-of-Gaussians model for astronomical observations in interferometry’, in Proc. of IEEE Chilecon, 2017. Available: IEEEXplore
[C11]
F. Tobar and R. Turner, ‘Modelling time series via automatic learning of basis functions’, in Proc. of the IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM), 2016, pp. 1–5. Available: IEEEXplore
[C10]
T. Thanthawaritthisai, F. Tobar, A. Constantinides, and D. Mandic, ‘The widely linear quaternion recursive total least squares’, in Proc. of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2015, pp. 3357–3361. Available: IEEEXplore
[C9]
F. Tobar and R. Turner, ‘Modelling of complex signals using Gaussian processes’, in Proc. of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2015, pp. 2209–2213. Available: IEEEXplore
[C8]
F. Tobar, T. Bui, and R. Turner, ‘Learning stationary time series using Gaussian processes with nonparametric kernels’, in Advances in Neural Information Processing Systems 28, 2015, pp. 3501--3509. Available: NeurIPS
[C7]
F. Tobar, M. Orchard, D. Mandic, and A. Constantinides, ‘Estimation of financial indices volatility using a model with time-varying parameters’, in Proc. of IEEE Conference on Computational Intelligence for Financial Engineering Economics (CIFEr), 2014, pp. 318–324. Available: IEEEXplore
[C6]
F. Tobar and D. Mandic, ‘A particle filtering based kernel HMM predictor’, in Proc. of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2014, pp. 7969–7973. Available: IEEEXplore
[C5]
F. Tobar and D. Mandic, ‘The quaternion kernel least squares’, in Proc. of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2013, pp. 6128–6132. Available: IEEEXplore
[C4]
F. Tobar and D. Mandic, ‘Multikernel least squares estimation’, in Proc. of the Sensor Signal Processing for Defence Conference(SSPD), 2012, pp. 1–5. Available: IEEEXplore
[C3]
F. Tobar, A. Kuh, and D. Mandic, ‘A novel augmented complex valued kernel LMS’, in Proc. of the 7th IEEE Sensor Array and Multichannel Signal Processing Workshop, 2012, pp. 473–476. Available: IEEEXplore
[C2]
A. Ahrabian, D. Looney, F. Tobar, J. Hallatt, and D. Mandic, ‘Noise assisted multivariate empirical mode decomposition applied to Doppler radar data’, in Proc. of the Sensor Signal Processing for Defence Conference(SSPD), 2012, pp. 1–4. Available: IEEEXplore
[C1]
F. Tobar, L. Yacher, R. Paredes, and M. Orchard, ‘Anomaly detection in power generation plants using similarity-based modeling and multivariate analysis’, in Proc. of the American Control Conference (ACC), 2011, pp. 1940–1945. Available: IEEEXplore
Last updated: 15 December 2019
(by myself)