High-dimensional regression with potential prior information on variable importance

Abstract There are a variety of settings where vague prior information may be available on the importance predictors in high-dimensional regression settings. Examples include ordering variables offered by their empirical variances (which is typically discarded through standardisation), lag when fitting autoregressive models time series settings, or level missingness variables. Whilst such orderings not match true variables, we argue that there little to lost, and potentially much gained, using them. We propose simple scheme involving sequence indicated ordering. show computational cost for all ridge used no more than single fit regression, describe strategy Lasso makes use previous fits greatly speed up entire models. select final estimator cross-validation provide general result quality best performing test set selected from among number M competing estimators linear setting. Our requires sparsity assumptions shows only $$\log M$$ log M price incurred compared unknown estimator. demonstrate effectiveness our approach applied missing corrupted data, An R package github.