The Living Thing / Notebooks :

Randomised regression

Tackling your regression, by using random projections of the predictors.

Usually this means using those projections to reduce the dimensionality of a high dimensional regression. In this case it is not far from compressed sensing, except in how we handle noise. In this linear model case, this is of course random linear algebra, and may be a randomised matrix factorisation.

Occasionally we might use non-linear projections to increase the dimensionality of our data in the hope of making a non-linear regression approximately linear, which dates back to Cover (Cove65).

I am especially interested in seeing how this might be useful for dependent data, especially time series.

Brian McWilliams, Gabriel Krummenacher and Mario Lučić, Randomized Linear Regression: A brief overview and recent results. Gabriel implemented some of the algorithms mentioned, e.g.

Martin Wainright, Statistics meets Optimization: Randomization and approximation for high-dimensional problems.

In the modern era of high-dimensional data, the interface between mathematical statistics and optimization has become an increasingly vibrant area of research. In this course, we provide some vignettes into this interface, including the following topics: