It is not only the increasingly used universal deep learning models that lack explainability. Even smaller and more specialized models may be difficult to explain if they are not prone to mathematical analysis. For these models, one has to resort to computer simulations, which suffer from the same explainability problems as the modern deep learning architectures. In this talk, I will outline the key ideas in topology and geometry, and discuss how they are used in topological data analysis, and geometric machine learning. Although these data modeling strategies are computationally rather expensive, they are also very robust, and allow extracting low-dimensional information manifolds from high-dimensional noisy data representations.

Nearly 30 years of experience in mathematical modeling, signal processing and data mining related to various engineering as well as biological systems. As Principal Investigator and Co-Investigator, involved in numerous academic and industrial collaborative projects. Over 10 years of direct experience in cross-disciplinary collaborations at intersection of engineering, mathematics, biology, and economics in the areas spanning rural Internet, IoT, wireless sensor networks, computational molecular biology, renewable energy and air transport management. Expert level knowledge of designing and implementing statistical and digital signal processing algorithms and methods. Solid background in applied probability and statistics. Avid Linux user and programmer since 1996. The current research focus on adopting the methods and strategies from telecommunication engineering and computer science to improve the efficiency of system modeling and analysis. The research topics of particular interest include designing computer experiments, probabilistic modeling, automated hypothesis discovery, signals processing with incomplete and/or constrained knowledge, signal representations for efficient statistical learning, and distributed signal processing.