Bayesian sparse reconstruction: a brute-force approach to astronomical imaging and machine learning
This provides a principled Bayesian approach to sparse reconstruction and neural network architecture selection, though it appears incremental on existing Bayesian/sparse methods.
The authors developed a Bayesian framework for signal reconstruction that automatically determines the number and type of basis functions from data, applying it to noisy 1D/2D signals including astronomical images. They demonstrated order-of-magnitude computational efficiency gains and showed the method can determine neural network architecture by treating nodes and layers as parameters.
We present a principled Bayesian framework for signal reconstruction, in which the signal is modelled by basis functions whose number (and form, if required) is determined by the data themselves. This approach is based on a Bayesian interpretation of conventional sparse reconstruction and regularisation techniques, in which sparsity is imposed through priors via Bayesian model selection. We demonstrate our method for noisy 1- and 2-dimensional signals, including astronomical images. Furthermore, by using a product-space approach, the number and type of basis functions can be treated as integer parameters and their posterior distributions sampled directly. We show that order-of-magnitude increases in computational efficiency are possible from this technique compared to calculating the Bayesian evidences separately, and that further computational gains are possible using it in combination with dynamic nested sampling. Our approach can also be readily applied to neural networks, where it allows the network architecture to be determined by the data in a principled Bayesian manner by treating the number of nodes and hidden layers as parameters.