arXiv subjects

Jesus Arroyo

Publications and source records attributed to Jesus Arroyo.

3 recordsLinked to original sources

arXiv2023

Clustered Graph Matching for Label Recovery and Graph Classification

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.

stat.ML↗

arXiv2022

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

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.

cs.LG↗

arXiv2021

Valid Two-Sample Graph Testing via Optimal Transport Procrustes and Multiscale Graph Correlation with Applications in Connectomics

Testing whether two graphs come from the same distribution is of interest in many real world scenarios, including brain network analysis. Under the random dot product graph model, the nonparametric hypothesis testing frame-work consists of embedding the graphs using the adjacency spectral embedding (ASE), followed by aligning the embeddings using the median flip heuristic, and finally applying the nonparametric maximum mean discrepancy(MMD) test to obtain a p-value. Using synthetic data generated from Drosophila brain networks, we show that the median flip heuristic results in an invalid test, and demonstrate that optimal transport Procrustes (OTP) for alignment resolves the invalidity. We further demonstrate that substituting the MMD test with multiscale graph correlation(MGC) test leads to a more powerful test both in synthetic and in simulated data. Lastly, we apply this powerful test to the right and left hemispheres of the larval Drosophila mushroom body brain networks, and conclude that there is not sufficient evidence to reject the null hypothesis that the two hemispheres are equally distributed.

stat.ME↗