Non-parametric distributional regression has achieved significant milestones in recent years. Among these, the Tabular Prior-Data Fitted Network (TabPFN) has demonstrated state-of-the-art performance on various benchmarks. However, a challenge remains in extending these grid-based approaches to a truly multivariate setting. In a naive non-parametric discretization with $N$ bins per dimension, the complexity of an explicit joint grid scales exponentially and the paramer count of the neural networks rise sharply. This scaling is particularly detrimental in low-data regimes, as the final projection layer would require many parameters, leading to severe overfitting and intractability.

翻译：近年来，非参数分布回归取得了重要进展。其中，表格先验数据拟合网络（TabPFN）在各种基准测试中展现了最先进的性能。然而，将这些基于网格的方法扩展到真正的多元场景仍面临挑战。在每维度使用$N$个区间的朴素非参数离散化方案中，显式联合网格的复杂度呈指数级增长，神经网络参数量急剧上升。这种扩展特性在低数据量场景下尤为不利，因为最终投影层需要大量参数，导致严重的过拟合与计算不可行性。