Experimenting with randomized trace estimators.
- How do hutch++ (fast low rank approximation and trace estimation) and classic hustchinson estimators perform in applications to statistical genetics problems?
- For what kind of matrices can hutch++ outperform hutchinson? Matrices with a few dominant eigenvalues?
Briefly what I learned: estimating the trace of the square of a GRM in statistical genetics is a perfect application of these estimators for two key reasons. (1) The number of people and number of snps at biobank scale are both very large so reducing the computation to a series of matrix vector multiplication accelerates computation significantly. (2) The square of a GRM has eigenvalues squared, which means the spread of eigenvalues likely increases - great opportunity for a method like hutch++ which exploits the dominant low rank subspace to reduce variance in the estimator. However, after first few PCs are regressed out from genetic data the dominant eigenvalues of a GRM basically disappear and the low rank subspace is not as dominant anymore. So in practive it is not that helpful. Interesting stuff though.