Machine Learning for Physics and Astronomy 2020/2021 Lecture slides 1 - Overview 2 - Probability Exercises Solutions Murphy 2.1, 2.2

Overall logic DataStore Components model tag list of DataSets sample method, which takes mask, returns z or (x, z) pair Class DataSet Components

I propose to use autoregressive convolutional layers to model local correlations in the source parameters. Good discussions about the topic can be found here: https://arxiv.org/abs/1901.11137 Given some image $x$, the basic goal is to perform a convolution $$ x' = C x $$ with convolution layer $C$ such that the log determinant of this operation is simple to calculate. This is in fact the case when kernels of the form are used (being strictly zero in the white regions). Convolution with this kernel leads to a strictly triangular convolution matrix, of the form The determinant is in this case just given by a product of diagonal elements. It is given by $$