  Capturing the microscopic interactions that determine molecular reactivity
poses a challenge across the physical sciences. Even a basic understanding of
the underlying reaction mechanisms can substantially accelerate materials and
compound design, including the development of new catalysts or drugs. Given the
difficulties routinely faced by both experimental and theoretical
investigations that aim to improve our mechanistic understanding of a reaction,
recent advances have focused on data-driven routes to derive structure-property
relationships directly from high-throughput screens. However, even these
high-quality, high-volume data are noisy, sparse and biased -- placing them in
a regime where machine-learning is extremely challenging. Here we show that a
statistical approach based on deep filtering of nonlinear feature networks
results in physicochemical models that are more robust, transparent and
generalize better than standard machine-learning architectures. Using diligent
descriptor design and data post-processing, we exemplify the approach using
both literature and fresh data on asymmetric catalytic hydrogenation,
Palladium-catalyzed cross-coupling reactions, and drug-drug synergy. We
illustrate how the sparse models uncovered by the filtering help us formulate
physicochemical reaction ``pharmacophores'', investigate experimental bias and
derive strategies for mechanism detection and classification.
