Calibration is a well-studied property of predictors which guarantees meaningful uncertainty estimates.

We also provide public access to the official algorithm implementations. "KRR" is short for Kernel Ridge Regression and "CTC" is short for computation tree compression. "GNN" is short for Graph, "GNTK" is short for graph

The learnware paradigm aims to enable users to leverage numerous existing well-trained models instead of building machine learning models from scratch.

Context-dependent systems have been widely studied; see Mooij et al.

In the context of modern machine learning, models deployed in real-world scenarios often encounter diverse data shifts like covariate and semantic shifts, leading to challenges in both out-of-distribution (OOD) generalization and detection.

Synthetic data can improve generalization when real data is scarce, but excessive reliance may introduce distributional mismatches that degrade performance. In this paper, we present a learning-theoretic framework to quantify the trade-off between synthetic and real data. Our approach leverages algorithmic stability to derive generalization error bounds, characterizing the optimal synthetic-to-real data ratio that minimizes expected test error as a function of the Wasserstein distance between the real and synthetic distributions. We motivate our framework in the setting of kernel ridge regression with mixed data, offering a detailed analysis that may be of independent interest. Our theory predicts the existence of an optimal ratio, leading to a U-shaped behavior of test error with respect to the proportion of synthetic data. Empirically, we validate this prediction on CIFAR-10 and a clinical brain MRI dataset. Our theory extends to the important scenario of domain adaptation, showing that carefully blending synthetic target data with limited source data can mitigate domain shift and enhance generalization. We conclude with practical guidance for applying our results to both in-domain and out-of-domain scenarios.