Primary supervisor
Daniel SchmidtThe spectral density of a time series (a series of time ordered data points -- for example, daily rainfall in the Amazon or the monthly stocks of fish in the Pacific) gives substantial information about the periodic patterns hidden in the data. Learning a good model of the spectral density is usually done through parametric methods like autoregressive moving average processes [1] because non-parametric methods struggle to deal with the interesting “non-smooth” nature of spectral densities. This project aims to apply a powerful and new non-parametric smoothing technique to this problem.
Student cohort
Aim/outline
The aim of this project is to apply the technique of trend filtering [2], a new, state of the art methodology for adaptive one dimensional signal smoothing to learning spectral densities. You would be required to implement or adapt existing software tools/algorithms for sparse L1 minimisation techniques to this setting, and compare the results against standard spectral smoothing techniques.
URLs/references
[1] Broersen, Petrus M.T., “Automatic Autocorrelation and Spectral Analysis”, Springer, 2006
[2] Ryan J Tibshirani, “Adaptive piecewise polynomial estimation via trend filtering”, The Annals of Statistics, pp. 285-323
Required knowledge
Machine learning, Some Linear Algebra, Python/R/MATLAB.