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Bayesian Nonparametric Spectral Estimation
Felipe Tobar

Tue Dec 04 01:55 PM -- 02:00 PM (PST) @ Room 220 CD

Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time series) is distributed across different frequencies. This can become particularly challenging when only partial and noisy observations of the signal are available, where current methods fail to handle uncertainty appropriately. In this context, we propose a joint probabilistic model for signals, observations and spectra, where SE is addressed as an inference problem. Assuming a Gaussian process prior over the signal, we apply Bayes' rule to find the analytic posterior distribution of the spectrum given a set of observations. Besides its expressiveness and natural account of spectral uncertainty, the proposed model also provides a functional-form representation of the power spectral density, which can be optimised efficiently. Comparison with previous approaches is addressed theoretically, showing that the proposed method is an infinite-dimensional variant of the Lomb-Scargle approach, and also empirically through three experiments.

Author Information

Felipe Tobar (Universidad de Chile)

Felipe Tobar is an Assistant Professor at the Data & AI Initiative at Universidad de Chile. He holds Researcher positions at the Center for Mathematical Modeling and the Advanced Center for Electrical Engineering. Felipe received the BSc/MSc degrees in Electrical Engineering (U. de Chile, 2010) and a PhD in Signal Processing (Imperial College London, 2014), and he was an Associate Researcher in Machine Learning at the University of Cambridge (2014-2015). Felipe teaches Statistics and Machine Learning courses at undergraduate, graduate and professional levels. His research interests lie in the interface between Machine Learning and Statistical Signal Processing, including Gaussian processes, spectral estimation, approximate inference, Bayesian nonparametrics, and optimal transport.

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