Conditional Distribution Quantization in Machine Learning

Conditional expectation E(Y | X) often fails This limitation has important implications for downstream to capture the complexity of multimodal conditional tasks, particularly in uncertainty quantification for image distributions L(Y | X). To address this, restoration models used in safety-critical domains such as we propose using n-point conditional quantizations--functional autonomous driving and biological imaging. Many existing mappings of X that are learnable approaches rely on per-pixel estimates such as variance via gradient descent--to approximate L(Y | heatmaps (Kendall and Gal, 2017) or confidence intervals X). This approach adapts Competitive Learning (Angelopoulos et al., 2022) to visualize uncertainty. Vector Quantization (CLVQ), tailored for conditional While these methods provide valuable insights, they can distributions. It goes beyond single-valued struggle to represent structured uncertainty, overlooking predictions by providing multiple representative spatial correlations between neighboring pixels.