Abstract: Inference in practice is often based on multi-dimensional quantized data, often due to computation, communication or privacy constraints. While errors introduced by quantization are often treated as a general nuisance and incorporated into the data uncertainty, we consider the scenario where quantization can also be adapted to inference requirements. In particular, we focus on risk-constrained inference, where the quality of inference is measured in terms of a distortion risk measure, rather than the Bayes risk. We show that the risk contribution of quantization can be isolated, providing a means of tailoring compression to specific inference tasks and risk requirements. We establish upper and lower bounds on the resolution of the quantizer in terms of risk constraints, which hold for data in general spaces. We also discuss scenarios with i.i.d. high-dimensional data and establish a link between the required resolution and the rate-distortion function.   



Bio: Malcolm Egan received the Ph.D. in Electrical Engineering in 2014 from the University of Sydney, Australia. He is currently a Chargé de Recherche (Tenured Research Scientist) in Inria and a member of CITI, a joint laboratory between Inria, INSA Lyon and Université de Lyon, France. Previously he was an assistant professor in INSA-Lyon, and a postdoctoral researcher with the Laboratoire de Mathématiques, Université Blaise Pascal, France and the Department of Computer Science, Czech Technical University in Prague, Czech Republic. He has also held visiting positions at Princeton University and the University of Bristol. His research interests are in the areas of information theory, statistical signal processing and machine learning with applications in communications and bio-chemical modelling.