Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
The k-tied Normal Distribution: A Compact Parameterization of Gaussian Mean Field Posteriors in Bayesian Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use rank 1 instead of the full mean-field standard-deviation matrix (ablation) | Mean-field posterior · MNIST, MLP | Accuracy: 97.6 ± 0.15 -> 93.6 ± 0.25 | Hurt |
| Use rank 1 instead of the full mean-field standard-deviation matrix (ablation) | Mean-field posterior · CIFAR-10, ResNet-18 | NLL: 0.495 ± 0.0080 -> 0.658 ± 0.0069 | Hurt |
| Use rank 2 instead of the full mean-field standard-deviation matrix (ablation) | Mean-field posterior · MNIST, MLP | Accuracy: 97.6 ± 0.15 -> 97.6 ± 0.15 | No clear effect |
| Use rank 2 instead of the full mean-field standard-deviation matrix (ablation) | Mean-field posterior · CIFAR-100, CNN | Accuracy: 42.1 ± 0.49 -> 42.2 ± 0.49 | No clear effect |
| Use rank 2 instead of the full mean-field standard-deviation matrix (ablation) | Mean-field posterior · IMDB, LSTM | Accuracy: 80.1 ± 0.25 -> 80.1 ± 0.25 | No clear effect |
| Use rank 2 instead of the full mean-field standard-deviation matrix (ablation) | Mean-field posterior · CIFAR-10, ResNet-18 | Accuracy: 83.5 ± 0.37 -> 83.2 ± 0.37 | No clear effect |
| Tie posterior standard-deviation parameters using a rank-2 factorization | GMFVI · MNIST, MLP | convergence speed | Helped |
| Tie posterior standard-deviation parameters in only the two dense layers | LeNet CNN · CIFAR-100 | convergence speed | Mixed |
| Use rank-2 tying rather than standard GMFVI standard-deviation parameters | GMFVI · Simple model, two dense layers | Train step time [ms]: 7.17 ± 0.014 -> 6.14 ± 0.018 | Helped |
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