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Decision forests (Forests), in particular random forests and gradientboosting trees, have demonstrated state-of-the-art accuracy compared to othermethods in many supervised learning scenarios. In particular, Forests dominateother methods in tabular data, that is, when the feature space is unstructured,so that the signal is invariant to a permutation of the feature indices.However, in structured data lying on a manifold (such as images, text, andspeech) deep networks (Networks), specifically convolutional deep networks(ConvNets), tend to outperform Forests. We conjecture that at least part of thereason for this is that the input to Networks is not simply the featuremagnitudes, but also their indices. In contrast, naive Forest implementationsfail to explicitly consider feature indices. A recently proposed Forestapproach demonstrates that Forests, for each node, implicitly sample a randommatrix from some specific distribution. These Forests, like some classes ofNetworks, learn by partitioning the feature space into convex polytopescorresponding to linear functions. We build on that approach and show that onecan choose distributions in a manifold-aware fashion to incorporate featurelocality. We demonstrate the empirical performance on data whose features liveon three different manifolds: a torus, images, and time-series. Moreover, wedemonstrate its strength in multivariate simulated settings and also showsuperiority in predicting surgical outcome in epilepsy patients and predictingmovement direction from raw stereotactic EEG data from non-motor brain regions.In all simulations and real data, Manifold Oblique Random Forest (MORF)algorithm outperforms approaches that ignore feature space structure andchallenges the performance of ConvNets. Moreover, MORF runs fast and maintainsinterpretability and theoretical justification.

Manifold Oblique Random Forests: Towards Closing the Gap on Convolutional Deep Networks