Incomplete covariate vectors are known to be problematic for estimation and inferences on model parameters, but their impact on prediction performance is less understood. We develop an imputation-free method that builds on a random partition model admitting variable-dimension covariates. Cluster-specific response models further incorporate covariates via linear predictors, facilitating estimation of smooth prediction surfaces with relatively few clusters. We exploit marginalization techniques of Gaussian kernels to analytically project response distributions according to any pattern of missing covariates, yielding a local regression with internally consistent uncertainty propagation that utilizes only one set of coefficients per cluster. Aggressive shrinkage of these coefficients regulates uncertainty due to missing covariates. The method allows in- and out-of-sample prediction for any missingness pattern, even if the pattern in a new subject's incomplete covariate vector was not seen in the training data. We develop an MCMC algorithm for posterior sampling that improves a computationally expensive update for latent cluster allocation. Finally, we demonstrate the model's effectiveness for nonlinear point and density prediction under various circumstances by comparing with other recent methods for regression of variable dimensions on synthetic and real data.

翻译：不完整的协变量向量已知会给模型参数的估计和推断带来问题，但其对预测性能的影响尚不明确。我们开发了一种无需插补的方法，该方法基于一种允许变维协变量的随机划分模型。聚类特定的响应模型进一步通过线性预测因子整合协变量，从而以相对较少的聚类实现平滑预测曲面的估计。我们利用高斯核的边缘化技术，根据任何缺失协变量的模式以解析方式投影响应分布，从而得到一种仅利用每聚类一组系数、并具有内部一致不确定性传播的局部回归。这些系数的主动收缩正则化了因缺失协变量引起的不确定性。该方法允许对任何缺失模式进行样本内和样本外预测，即使新对象不完整协变量向量中的模式在训练数据中未曾出现。我们开发了一种用于后验采样的MCMC算法，该算法改进了潜在聚类分配中计算开销较大的更新步骤。最后，通过将本模型与近期其他针对变维回归的方法在合成数据和真实数据上进行对比，我们展示了该模型在各种情况下对非线性点预测和密度预测的有效性。