Estimating Model Uncertainty of Neural Networks in Sparse Information Form
This addresses the challenge of uncertainty quantification in deep learning for practitioners, though it appears incremental as it builds on existing information form methods.
The paper tackles the problem of estimating model uncertainty in deep neural networks by proposing a sparse representation using the information form of a multivariate normal distribution, showing that it can be scalably applied with competitive results on benchmarks.
We present a sparse representation of model uncertainty for Deep Neural Networks (DNNs) where the parameter posterior is approximated with an inverse formulation of the Multivariate Normal Distribution (MND), also known as the information form. The key insight of our work is that the information matrix, i.e. the inverse of the covariance matrix tends to be sparse in its spectrum. Therefore, dimensionality reduction techniques such as low rank approximations (LRA) can be effectively exploited. To achieve this, we develop a novel sparsification algorithm and derive a cost-effective analytical sampler. As a result, we show that the information form can be scalably applied to represent model uncertainty in DNNs. Our exhaustive theoretical analysis and empirical evaluations on various benchmarks show the competitiveness of our approach over the current methods.