Primary supervisor
Daniel SchmidtAdaptively smoothing one-dimensional signals remains an important problem, with applications in time series analysis, additive modelling and forecasting. The trend filter provides an novel class of adaptive smoothers; however, it is usually implemented in a frequentist framework using tools like the lasso and cross-validation. Bayesian implementations tend to rely on posterior sampling and as such do not provide simple, sparse point-estimates of the underlying curve.
Student cohort
Aim/outline
In this project we will apply recent work on using the expectation-maximization algorithm to find exact, sparse posterior estimates for a powerful method called the "horseshoe" prior, which has no immediate non-Bayesian counterpart. This will provide a smoothing algorithm that will automatically determine the degree of regularisation needed to smooth the noise out of the signal, and will yield sparse piece-wise linear trend estimates that can be used for denoising and forecasting.
Required knowledge
Python and/or R; some linear algebra; some basics in Bayesian statistics