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Bayesian inference for neural networks, or Bayesian deep learning, has thepotential to provide well-calibrated predictions with quantified uncertaintyand robustness. However, the main hurdle for Bayesian deep learning is itscomputational complexity due to the high dimensionality of the parameter space.In this work, we propose a novel scheme that addresses this limitation byconstructing a low-dimensional subspace of the neural networkparameters-referred to as an active subspace-by identifying the parameterdirections that have the most significant influence on the output of the neuralnetwork. We demonstrate that the significantly reduced active subspace enableseffective and scalable Bayesian inference via either Monte Carlo (MC) samplingmethods, otherwise computationally intractable, or variational inference.Empirically, our approach provides reliable predictions with robust uncertaintyestimates for various regression tasks.

Learning Active Subspaces for Effective and Scalable Uncertainty Quantification in Deep Neural Networks