Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Convergence Rates of Variational Inference in Sparse Deep Learning
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use sparse spike-and-slab variational inference with the architecture specified for Hölder smoothness | Tempered Bayesian ReLU DNNs · Hölder regression, 0<β<d | expected L2 generalization error rate: n^{\frac{-2\beta}{2\beta+d}} up to a squared logarithmic factor | Helped |
| Select network architecture by maximizing the penalized ELBO | Sparse variational DNNs · Nonparametric regression with unknown function properties | expected L2 generalization error rate: The bound includes the architecture penalty \frac{\log(1/\pi_{S,L,D})}{n} | Helped |
| Reduce the optimization error by making the ELBO gap sufficiently small | Sparse variational DNN optimization · Sparse DNN regression, structure (S,L,D) | expected L2 generalization error rate: \frac{2\sigma^2}{\alpha(1-\alpha)} \cdot \frac{\mathbb{E}[\mathcal{L}^*_n-\mathcal{L}_n^k]}{n} | Helped |
| Use a spike-and-slab prior and sparse network structure to control estimation error despite a large parameter count | Bayesian deep ReLU networks · Hölder regression, 0<β<d | expected L2 generalization error rate: n^{\frac{-2\beta}{2\beta+d}} up to a squared logarithmic factor | Helped |
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