Conditional Distribution Quantization in Machine Learning
This addresses the need for more accurate uncertainty quantification and multimodal data generation in machine learning, particularly in tasks like computer vision inpainting, though it is an incremental adaptation of existing methods.
The paper tackled the problem of approximating complex multimodal conditional distributions, which single-valued conditional expectations fail to capture, by proposing n-point conditional quantizations that provide multiple representative points, enabling better uncertainty quantification and multimodal data generation.
Conditional expectation \mathbb{E}(Y \mid X) often fails to capture the complexity of multimodal conditional distributions \mathcal{L}(Y \mid X). To address this, we propose using n-point conditional quantizations--functional mappings of X that are learnable via gradient descent--to approximate \mathcal{L}(Y \mid X). This approach adapts Competitive Learning Vector Quantization (CLVQ), tailored for conditional distributions. It goes beyond single-valued predictions by providing multiple representative points that better reflect multimodal structures. It enables the approximation of the true conditional law in the Wasserstein distance. The resulting framework is theoretically grounded and useful for uncertainty quantification and multimodal data generation tasks. For example, in computer vision inpainting tasks, multiple plausible reconstructions may exist for the same partially observed input image X. We demonstrate the effectiveness of our approach through experiments on synthetic and real-world datasets.