CARD: Classification and Regression Diffusion Models
This improves uncertainty estimation in supervised learning for statistics and machine learning applications, though it is incremental as it builds on existing diffusion models.
The paper tackles the problem of accurately predicting the distribution of a response variable given covariates, addressing limitations in uncertainty estimation of deep neural networks, and shows that CARD outperforms state-of-the-art methods, especially for multi-modal distributions.
Learning the distribution of a continuous or categorical response variable $\boldsymbol y$ given its covariates $\boldsymbol x$ is a fundamental problem in statistics and machine learning. Deep neural network-based supervised learning algorithms have made great progress in predicting the mean of $\boldsymbol y$ given $\boldsymbol x$, but they are often criticized for their ability to accurately capture the uncertainty of their predictions. In this paper, we introduce classification and regression diffusion (CARD) models, which combine a denoising diffusion-based conditional generative model and a pre-trained conditional mean estimator, to accurately predict the distribution of $\boldsymbol y$ given $\boldsymbol x$. We demonstrate the outstanding ability of CARD in conditional distribution prediction with both toy examples and real-world datasets, the experimental results on which show that CARD in general outperforms state-of-the-art methods, including Bayesian neural network-based ones that are designed for uncertainty estimation, especially when the conditional distribution of $\boldsymbol y$ given $\boldsymbol x$ is multi-modal. In addition, we utilize the stochastic nature of the generative model outputs to obtain a finer granularity in model confidence assessment at the instance level for classification tasks.