Jesus Arroyo

Zhirui Li, Jesus Arroyo, Konstantinos Pantazis et al.

Given a collection of vertex-aligned networks and an additional label-shuffled network, we propose procedures for leveraging the signal in the vertex-aligned collection to recover the labels of the shuffled network. We consider matching the shuffled network to averages of the networks in the vertex-aligned collection at different levels of granularity. We demonstrate both in theory and practice that if the graphs come from different network classes, then clustering the networks into classes followed by matching the new graph to cluster-averages can yield higher fidelity matching performance than matching to the global average graph. Moreover, by minimizing the graph matching objective function with respect to each cluster average, this approach simultaneously classifies and recovers the vertex labels for the shuffled graph. These theoretical developments are further reinforced via an illuminating real data experiment matching human connectomes.

Adam Li, Ronan Perry, Chester Huynh et al.

Decision forests (Forests), in particular random forests and gradient boosting trees, have demonstrated state-of-the-art accuracy compared to other methods in many supervised learning scenarios. In particular, Forests dominate other 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, and speech) deep networks (Networks), specifically convolutional deep networks (ConvNets), tend to outperform Forests. We conjecture that at least part of the reason for this is that the input to Networks is not simply the feature magnitudes, but also their indices. In contrast, naive Forest implementations fail to explicitly consider feature indices. A recently proposed Forest approach demonstrates that Forests, for each node, implicitly sample a random matrix from some specific distribution. These Forests, like some classes of Networks, learn by partitioning the feature space into convex polytopes corresponding to linear functions. We build on that approach and show that one can choose distributions in a manifold-aware fashion to incorporate feature locality. We demonstrate the empirical performance on data whose features live on three different manifolds: a torus, images, and time-series. Moreover, we demonstrate its strength in multivariate simulated settings and also show superiority in predicting surgical outcome in epilepsy patients and predicting movement 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 and challenges the performance of ConvNets. Moreover, MORF runs fast and maintains interpretability and theoretical justification.