We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic $k$-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based on similarities to each observed data point, yielding predictive distributions represented by Gaussian mixtures. Posterior inference is performed on the parameters of the mixture components as well as the distance metric using a mean-field variational Bayes algorithm accompanied with a stochastic gradient-based optimization procedure. The proposed method is especially advantageous in settings where inputs are of relatively high dimension in comparison to the data size, where input--output relationships are complex, and where predictive distributions may be skewed or multimodal. Computational studies on two synthetic datasets and one dataset comprising dose statistics of radiation therapy treatment plans show that our mixture-of-experts method performs similarly or better than a conditional Dirichlet process mixture model both in terms of validation metrics and visual inspection.

翻译：我们提出了一个新的非参数专家混合模型,用于多变量回归问题,这种模型的灵感来自概率性美元最近邻的近邻算法。使用一个有条件指定的模型,对非抽样投入的预测基于与每个观察数据点的相似性,产生高斯混合物代表的预测分布。根据混合成分的参数以及使用平均场变异波段算法的距离计量法,并辅之以一个随机梯度优化程序,对使用投入与数据大小相对高、投入-产出关系复杂、预测分布可能是偏斜或多式的模型特别有利。关于两个合成数据集和一个由辐射治疗计划剂量统计组成的数据集的计算研究表明,我们的混合专家方法在验证指标和直观检查方面,其效果与有条件的脱脂过程混合模型相似或更好。