Computer Assisted Research Mathematics and its Applications. The mathematics community will benefit from infusion of new computer-assisted techniques and modalities for research and training post-graduate students, both from my pure research project and through development of an associated research centre. Ultimately, this should also help more school students learn mathematics well and so play a part in addressing Australia's skill shortage. Also, the work on optimization algorithms promises to ....Computer Assisted Research Mathematics and its Applications. The mathematics community will benefit from infusion of new computer-assisted techniques and modalities for research and training post-graduate students, both from my pure research project and through development of an associated research centre. Ultimately, this should also help more school students learn mathematics well and so play a part in addressing Australia's skill shortage. Also, the work on optimization algorithms promises to improve the performance and quality of many practical signal reconstruction methods. These are used by varied Australian industries from telecommunication to mining and by researchers in the digital arts and fields such as astronomy, physics, chemistry, bioscience, geoscience, engineering and medicine.Read moreRead less
Asymptotic Geometric Analysis and Machine Learning. Phenomena in large dimensions appear in a number of domains of Mathematics and adjacent domains of science (e.g. Computer Science), dealing with functions of infinitely growing number of parameters. Here, we focus on several questions naturally linked to Asymptotic Geometric Analysis which have natural applications to Statistical Learning Theory. We intend to use geometric, probabilistic and combinatorial methods to investigate these problems, ....Asymptotic Geometric Analysis and Machine Learning. Phenomena in large dimensions appear in a number of domains of Mathematics and adjacent domains of science (e.g. Computer Science), dealing with functions of infinitely growing number of parameters. Here, we focus on several questions naturally linked to Asymptotic Geometric Analysis which have natural applications to Statistical Learning Theory. We intend to use geometric, probabilistic and combinatorial methods to investigate these problems, with an emphasis on modern tools in Empirical Processes Theory and the theory of Random Matrices.Read moreRead less
Geometric parameters in Learning Theory. We aim to investigate the behaviour of geometric parameters which appear naturally in Statistical Learning Theory. Those parameters are used to control the sample complexity, which is the size of a random sample needed to produce an accurate prediction. They are also of independent interest in the local theory of Banach spaces. We shall use geometric methods originating in the local theory of Banach spaces to investigate the parameters and the way they in ....Geometric parameters in Learning Theory. We aim to investigate the behaviour of geometric parameters which appear naturally in Statistical Learning Theory. Those parameters are used to control the sample complexity, which is the size of a random sample needed to produce an accurate prediction. They are also of independent interest in the local theory of Banach spaces. We shall use geometric methods originating in the local theory of Banach spaces to investigate the parameters and the way they influence sample complexity. All the problems we focus on are not only important from the Machine Learning point of view, but are intriguing in their theoretical implications.Read moreRead less