March 22, 2008

Ever Alone Hunk - Discretization and Orthogonality

Far far far away from the last post on compressive sensing, two other talks closer to every day problems with standard data (orthogonal matrices and quantization), which i have been watching during breakfast (quite a long one).

Ofer Zeitouni: A Correlation Inequality for Nonlinear Reconstruction, on the question whether the Karhunen-Loève transform remains optimal in the non-linear approximation for gaussian vectors. Karhunen-Loève transform (or Proper orthogonal decomposition, or Principal component analysis) is a central tool in statistics (often named after Hotelling) and signal processing, yielding "optimal" orthogonal transforms for uncorrelated data. The duet formed by Kari Karhunen and Michel Loève (even a triplet which Harold Hotelling) reassembles to an Ever Alone Hunk.

Zhidong Bai: Statistical Analysis for Rounding Data. Most of the discrete versions of the continuous setting deal with the discretization of time or space, i.e. sampling. Now what happens to the discrete amplitudes, i.e. discretization in the "value" domain? Especially that standard estimation of mean and variance are not consistant. Some counter-intuitive experiments with respect to the central limit theorem. Here, the larger, the worse.