residual Component Analysis: Generalizing PCA for more flexible inference in linear-Gaussian models

Discussion

RCA is an algorithm for describ- ing a low-dimensional representation of the residuals of a data set, given partial explanation by a covariance matrix [math]\displaystyle{ \Sigma }[/math].The low-rank component of the model can be determined through a generalized eigenvalue problem. The paper illustrated how a treatment and a control time series could have their differences highlighted through appropriate selection of [math]\displaystyle{ \Sigma }[/math](in this case we used an RBF kernel). The paper also introduced an algorithm for fitting a variant of CCA where the private spaces are explained through low dimensional latent variables.

Full covariance matrix model is often run into problem as their parameterization scales with [math]\displaystyle{ D^2 }[/math]. This technique combined sparse-inverse covariance (as in GLASSO) with low rank (as in probabilistic PCA) approaches, and have good effect in the experiment.