Deep Conditional Measure Quantization

TL;DR

This paper introduces DCMQ, a novel deep neural network method utilizing Huber-energy kernels for quantizing conditional probability measures, addressing a less explored area with promising experimental results.

Contribution

The paper presents a new deep learning approach for quantizing conditional probability measures using Huber-energy kernels, filling a gap in existing quantization methods.

Findings

Effective approximation of conditional laws demonstrated

Method outperforms traditional quantization techniques

Promising results across multiple examples

Abstract

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.