Towards Bayesian Data Compression

In order to handle large data sets omnipresent in modern science, efficient compression algorithms are necessary. Here, a Bayesian data compression (BDC) algorithm that adapts to the specific measurement situation is derived in the context of signal reconstruction. BDC compresses a data set under conservation of its posterior structure with minimal information loss given the prior knowledge on the signal, the quantity of interest. Its basic form is valid for Gaussian priors and likelihoods. For constant noise standard deviation, basic BDC becomes equivalent to a Bayesian analog of principal component analysis. Using Metric Gaussian Variational Inference, BDC generalizes to non-linear settings. In its current form, BDC requires the storage of effective instrument response functions for the compressed data and corresponding noise encoding the posterior covariance structure. Their memory demand counteract the compression gain. In order to improve this, sparsity of the compressed responses can be obtained by separating the data into patches and compressing them separately. The applicability of BDC is demonstrated by applying it to synthetic data and radio astronomical data. Still the algorithm needs further improvement as the computation time of the compression and subsequent inference exceeds the time of the inference with the original data.