Compressive learning: new models and applications

Today’s world is fuelled by data. From self-driving cars through to agriculture, massive amounts of data are used to fit learning models to provide valuable insights and predictions. Such insights come at a significant price as many traditional learning procedures have both memory and computational costs that scale with the size of the data. This quickly becomes prohibitive, even when substantial resources are available. A new way of learning is therefore needed to allow for efficient model fitting in the 21st century. The birth of compressive learning in recent years has provided a novel solution to the bottleneck of learning from big data. Situated at the core of the compressive learning framework is the construction of a so-called sketch. The sketch is a compact representation of the data that provides sufficient information for specific learning tasks. In this thesis we develop the compressive learning framework to a host of new models and applications. In the first part of the thesis, we consider the group of semi-parametric models and demonstrate the unique advantages and challenges associated with creating a compressive learning paradigm for these particular models. Concentrating on the independent component analysis model, we develop a framework of algorithms and theory enabling magnitudes of compression with respect to memory complexity compared to existing methods. In the second part of the thesis, we develop a compressive learning framework to the emerging technology of single-photon counting lidar. We demonstrate that forming a sketch of the time-of-flight data circumvents the inherent data-transfer bottleneck of existing lidar techniques. Finally, we extend the compressive lidar technology by developing both an efficient sketch-based detection algorithm that can detect the presence of a surface solely from the sketch and a sketched plug and play framework that can integrate existing powerful denoisers that are robust to noisy lidar scenes with low photon counts