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Model Selection in Bayesian Neural Networks via Horseshoe Priors

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Figure 1: Predictive distributions from a single layer BNN with N(0, 1) priors overweights, ReLU activations, containing ten, hundred, and thousand units, trainedon noisy samples (in black) from a smooth one dimensional function shown inblack, y = N(sin(x)
Figure 2: Horseshoe and regularized horseshoe densities. Both densities exhibit aspike at zero
Figure 3: Graphical models capturing the conditional dependencies assumed by BayesianNeural Networks with horseshoe priors
Table 1 summarizes the variational approximations introduced in this section. All our
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