IPAB Workshop - 12/04/2018

Title:  Analysis of Sampling-Based Integrators: Theory and applications Abstract: Numerical integration is a common problem encountered across computational science. In practice, the integrands involved are often ill-behaved (e.g. discontinuous) functions that span high-dimensional domains. In such cases, the use of  sampling-based integrators is inevitable and convenient but can also be potentially inefficient. For example, a naive estimate of an integral can be constructed by averaging the integrand evaluated at a random set of locations in the domain. Not surprisingly, the estimation error depends heavily on the sampling strategy used to determine the set of locations. For many applications, the evaluation of the integrand, at each sample point, is costly and so there is considerable interest in mitigating error for a (given) fixed budget of sample evaluations. In the first part of his talk, Kartic will present a few recent results in rendering (computer graphics), image processing and robotics to motivate the importance of sampling strategies. Kartic will then present recent developments in Fourier analysis of stochastic, sampling-based integrators.  Finally, Kartic will summarise ongoing work, and hopes to learn of potential connections to your own work.