Conditional Decomposition Discrepancy: Separating Conditional Bias from Sampling Bias in Small-Sample Cross-Domain Cost Forecasting

Sample discrepancy measurement is an essential step in transfer learning models such as cross-domain cost forecasting. However, tools that can effectively separate conditional bias from sampling bias are still lacking, so discrepancy information cannot fully support sample screening and model-update decisions. This paper analyzes the information boundary of the maximum mean discrepancy (MMD) in bias attribution, states and proves the relevant propositions, and proposes shifting the object of testing from the joint distribution to the conditional distribution. On this basis, the conditional decomposition discrepancy (CDD) measure is designed: a conditional mean and a residual bandwidth are estimated from an independent calibration sample, the data are projected onto a common residual axis and subjected to a kernel two-sample test, and the test result is converted into a continuous risk score with reference to the permutation null distribution. Numerical experiments are then designed on a UK property transaction price dataset. The results show that, provided the conditional difference is transmitted to the residual marginal, the proposed measure effectively detects conditional bias and reduces the proportion of contaminated source-domain samples under controlled injection, thus offering a new discrepancy measurement tool for data screening in transfer learning.