论文标题
卡：分类和回归扩散模型
CARD: Classification and Regression Diffusion Models
论文作者
论文摘要
考虑到其协变量$ \ boldsymbol x $的连续或分类响应变量$ \ boldsymbol y $的分布是统计和机器学习中的基本问题。深度神经网络的监督学习算法在预测给定$ \ boldsymbol y $的平均值方面取得了长足的进步，但是他们经常因其准确捕捉预测的不确定性的能力而受到批评。在本文中，我们介绍了分类和回归扩散（卡）模型，该模型结合了基于扩散的条件生成模型和预训练的条件均值估计器，以准确预测给定$ \ boldsymbol y $给定$ \ boldsymbol x $的分布。我们证明了与玩具示例和现实数据集的有条件分配预测的出色能力，实验结果表明，该卡通常优于最先进的方法，包括基于贝叶斯的神经网络的方法，这些方法是为不确定性估算而设计的，尤其是当$ \ boldsymbol y $ \ boldsymbol y $ \ boldsymbol x $ multem x $ sulters ys Multimod is Mults y is Mults y is Mults y is Mults ys $ \\\\\\\\\\\\\\\\\\\\之际。此外，我们利用生成模型输出的随机性质在实例级别的分类任务中获得模型置信度评估中的较细性。
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.
