Deep Conditional Measure Quantization
This work addresses a specific problem in probability theory and machine learning for researchers in those fields, but it appears incremental as it builds on existing quantization methods.
The paper tackles the problem of quantizing conditional probability measures, which is less explored compared to unconditional quantization, by proposing DCMQ, a method combining a Huber-energy kernel with deep neural networks, and reports promising results on several examples.
Quantization of a probability measure means representing it with a finite set of Dirac masses that approximates the input distribution well enough (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.