A.1 RelationofInverseCovarianceMatrixandPartialCorrelation ForacovariancematrixofjointdistributionforvariablesX,Y,thecovariancematrixis

LetP Rn n be a fixed projection onto a space of dimensiond. Next we consider the estimation error that characterizes the number of samples needed to learn a predictionfunctionf(x1)= ˆWψ (x1)thatgeneralizes. This section explains what we claim in Remark C.1. Assumption D.1 (Approximate Conditional Independent Given Latent Variables). To understand what Cφxφy is, we note it is of the same shape asφx(x) φy(y) for each individual x X,y Y.