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Andrew Smith

Andrew Smith. Denoising UK house prices 16th September 2010. Regression on a graph. Denoising UK house prices Discrete spatial processes Longitudinal data analysis Scatterplot smoothing Image analysis. Outline. UK house price data The need for regression

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Andrew Smith

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  1. Andrew Smith Denoising UK house prices 16th September 2010

  2. Regression on a graph • Denoising UK house prices • Discrete spatial processes • Longitudinal data analysis • Scatterplot smoothing • Image analysis

  3. Outline • UK house price dataThe need for regression • Graph structureRegression on a graph • Penalised regressionResults and uses of algorithm

  4. Video available at http://www.maths.bris.ac.uk/~as1637/research/warwick1.wmv

  5. Regression • Seek a (simpler) pattern that explains observed data • Model:

  6. Challenges for existing methods • No covariate values • Euclidean distance inappropriate • Missing values

  7. Regression on a graph • Consider observations Priceyear,townto be taken at the vertices of a graph • Edges of the graph give an idea of closeness

  8. Regression on a graph • Consider observationsPriceyear,townto be taken at the vertices of a graph • Edges of the graph (neighbouring towns)give an idea of closeness

  9. Penalised regression on a graph • Need to penalise distance from data • Penalty term:Sum (over all vertices)of squares of residuals

  10. Penalised regression on a graph • Need to penalise roughness • Penalty term:Sum (over all edges)of absolute differences

  11. Penalised regression on a graph • Minimise:Distance from data + λ Roughness • Computationally intensive,so use new algorithm

  12. Video available at http://www.maths.bris.ac.uk/~as1637/research/warwick2.wmv

  13. Regional analysis • The estimate identifies regions of constant value • These regions change in a similar way through time

  14. Regional analysis • The estimate identifies regions of constant value • These regions change in a similar way through time • They are not the same as government office regions

  15. Summary • Detecting a smooth national trend in noisy UK house price data • Use regression on a graph • Penalise distance from data (vertices) and roughness (edges) • arxiv.org/abs/0911.1928 (Kovac & Smith 2009) • All house price data courtesy of Halifax

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