In recent years, the size of datasets have grown exponentially as a result of advances in technology, signal acquisition, and the sophistication of modern day mobile phones and devices. This has enabled researchers, statisticians and machine learning practitioners to build increasingly accurate models as a consequence of larger sample sizes and feature dimensions. Nevertheless, this poses a fundamental challenge to large scale learning as (i) traditional algorithms have computational complexity that scales with the order of the dataset dimensions (ii) the whole dataset has to be stored or transferred on to local RAM as optimisation methods need to return to the data (or a random subset of the data) at subsequent iterations, and (iii) one is vulnerable to malicious attacks of potentially sensitive and personal information as the data needs to be stored or transferred locally. Compressive learning (CL) [1, 2] partially addresses these fundamental challenges by severely compressing the whole dataset into a random representation of fixed size, named a so-called sketch, in a single (or limited) pass of the data prior to learning. Once the sketch is formed, the parameters of the model are inferred solely from the sketch, hence a CL algorithm, for a given task or model, needs never to return to the original dataset, and it can be deleted from memory as a result. At the core of the CL framework [1, 3], is that in general, the size of the sketch does not scale with the dimensions of the dataset, or indeed the data's underlying dimensionality, but instead is driven by the complexity or dimensionality of the task or model of interest.