  More often than not in benchmark supervised ML, tabular data is flat, i.e.
consists of a single $m \times d$ (rows, columns) file, but cases abound in the
real world where observations are described by a set of tables with structural
relationships. Neural nets-based deep models are a classical fit to incorporate
general topological dependence among description features (pixels, words,
etc.), but their suboptimality to tree-based models on tabular data is still
well documented. In this paper, we introduce an attention mechanism for
structured data that blends well with tree-based models in the training context
of (gradient) boosting. Each aggregated model is a tree whose training involves
two steps: first, simple tabular models are learned descending tables in a
top-down fashion with boosting's class residuals on tables' features. Second,
what has been learned progresses back bottom-up via attention and aggregation
mechanisms, progressively crafting new features that complete at the end the
set of observation features over which a single tree is learned, boosting's
iteration clock is incremented and new class residuals are computed.
Experiments on simulated and real-world domains display the competitiveness of
our method against a state of the art containing both tree-based and neural
nets-based models.
