Explore score estimation techniques using infinite-dimensional exponential families in this 54-minute lecture by Dougal Sutherland from UCL, presented at the Alan Turing Institute. Delve into the mathematical foundations of approximating high-dimensional functions from limited data, addressing the curse of dimensionality and modern approaches to overcome it. Learn about reproducing kernel Hilbert spaces, maximum likelihood, score matching, and Nyström approximation. Examine theoretical aspects, competitor approaches, and experimental results. Gain insights into minimizing scores, loss functions, and practical applications in science and engineering for reconstructing complex processes with numerous parameters.