Deep Conditional Measure Quantization

The quantization of a (probability) measure is replacing it by a sum of Dirac masses that is close enough to it (in some metric space of probability measures). Various methods exists to do so, but the situation of quantizing a conditional law has been less explored. We propose a method, called DCMQ, involving a Huber-energy kernel-based approach coupled with a deep neural network architecture. The method is tested on several examples and obtains promising results.