Probabilistic Pretraining for Improved Neural Regression

While transfer learning has revolutionized computer vision and natural language processing, its application to probabilistic regression remains underexplored, particularly for tabular data. We introduce NIAQUE (Neural Interpretable Any-Quantile Estimation), a novel permutation-invariant architecture that enables effective transfer learning across diverse regression tasks. Through extensive experiments on 101 datasets, we demonstrate that pre-training NIAQUE on multiple datasets and fine-tuning on target datasets consistently outperforms both traditional tree-based models and transformer-based neural baseline. On real-world Kaggle competitions, NIAQUE achieves competitive performance against heavily hand-crafted and feature-engineered solutions and outperforms strong baselines such as TabPFN and TabDPT, while maintaining interpretability through its probabilistic framework. Our results establish NIAQUE as a robust and scalable approach for tabular regression, effectively bridging the gap between traditional methods and modern transfer learning.