Main Effects and Interactions in Mixed and Incomplete Data Frames.

Summary A mixed data frame (MDF) is a table collecting categorical, numerical and count observations. The use of MDF is widespread in statistics and the applications are numerous from abundance data in ecology to recommender systems. In many cases, an MDF exhibits simultaneously main effects, such as row, column or group effects and interactions, for which a low-rank model has often been suggested. Although the literature on low-rank approximations is very substantial, with few exceptions, existing methods do not allow to incorporate main effects and interactions while providing statistical guarantees. The present work fills this gap. * This work has been funded by the DataScience Inititiative (Ecole Polytechnique) and the Russian Academic Excellence Project '5-100.