The matching pursuit algorithm revisited: A variant for big data and new stopping rules

On the selection of predictors by using greedy algorithms and information theoretic criteria

“…Unfortunately, this is not possible in the case of big data (n p n ). It has been proven in Li et al . (2019) that df m can be computed without accessing the entries of X and only by using the matrix D ∈ R p n ×p n .…”

“…A solution consists of generating and evaluating a subset of all possible models by applying greedy algorithms. Either cross-validation (CV) or information theoretic (IT) criteria were applied for selecting the 'best' model from the family of models produced by a greedy algorithm (Bühlmann & Hothorn 2007;Sancetta 2016;Li et al . 2019).…”

“…The evaluation of IT criteria involves the calculation of the degrees of freedom (df) and, in some cases, this might be computationally intensive. Interestingly enough, the calculation of df is hard not only in the high-dimensional context, but also in the big data case when n p n (Li et al . 2019).…”

“…The use of CV is discussed in Bühlmann & van de Geer (2011), but it has been argued in (Li et al . 2017(Li et al . , 2019 that the IT criteria represent a better alternative because they are less computationally intensive.…”

“…The reader can find in Section 3 the original expressions of the criteria employed in this study as well as the modifications operated such that to make them compatible with MPA. The mathematical background for these alterations can be found in Li et al . (2019).…”