Spectral analysis of tree ensembles produces minimax rates for random forests governed by kernel eigenvalue decay and enables distillation of RFs and GBMs into compact models via leading eigenfunctions and singular vectors.
Spectral inference networks: Unifying deep and spectral learning
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abstract
We present Spectral Inference Networks, a framework for learning eigenfunctions of linear operators by stochastic optimization. Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators, and are closely related to Variational Monte Carlo methods from computational physics. As such, they can be a powerful tool for unsupervised representation learning from video or graph-structured data. We cast training Spectral Inference Networks as a bilevel optimization problem, which allows for online learning of multiple eigenfunctions. We show results of training Spectral Inference Networks on problems in quantum mechanics and feature learning for videos on synthetic datasets. Our results demonstrate that Spectral Inference Networks accurately recover eigenfunctions of linear operators and can discover interpretable representations from video in a fully unsupervised manner.
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Graph-regularized learning on data-augmentation graphs has transductive error ≤ C/n_L + R_DA(y), where R_DA is the graph-cut mass of augmentations crossing label boundaries.
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Minimax Rates and Spectral Distillation for Tree Ensembles
Spectral analysis of tree ensembles produces minimax rates for random forests governed by kernel eigenvalue decay and enables distillation of RFs and GBMs into compact models via leading eigenfunctions and singular vectors.
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Fast Rates for Semi-Supervised Learning via Data-Augmentation Graph Regularization
Graph-regularized learning on data-augmentation graphs has transductive error ≤ C/n_L + R_DA(y), where R_DA is the graph-cut mass of augmentations crossing label boundaries.