Search Results for « Bayesian Transfer Learning »

Multi-source transfer learning asks which auxiliary studies should be borrowed from. The Bayesian answer is to place a prior on the informative set and average over it. We study the resulting posterior on source-inclusion configurations and show it is more delicate than the pairwise Bayes factor asymptotics suggest. The informative set admits a predictive definition through partial exchangeability, with a Sanov rate function equal to a design-weighted contrast norm plus a covariate-shift term that the contrast parameterization cannot represent. The Bayes factor for including a source compares two ways of explaining that source's data rather than the source against its absence, so the nuisance specification for excluded sources governs consistency: pooling excluded sources into one coefficient vector gives inclusion probabilities for noninformative sources that do not decay with sample size, while assigning each excluded source its own vector restores consistency once n k exceeds p. Compatibility is moreover unidentified when the informative pool has one member, since a p-dimensional contrast absorbs any single source's deviation. We establish all three by exact enumeration of the 2 K posterior in a conjugate Gaussian model, which separates the statistical question from Markov chain mixing, and show that integrating out the block variances aggravates rather than repairs the pooled specification, in one case inverting the ordering so that noninformative sources are preferred. Whether any of this reaches the target depends sharply on the target sample size. At the n 0 used in published benchmarks the contrast absorbs the contamination and the choice of nuisance specification moves target error by 0.03%; at an n 0 one third as large, naive pooling produces genuine negative transfer and the same choice is the difference between attaining the oracle and tripling its error. Selection is load-bearing precisely where transfer learning is used rather than benchmarked. We close with a collapsed marginal likelihood for logistic transfer learning under Pólya-Gamma augmentation, a Thorin-class characterization of admissible mixing measures, and a generative computation that never instantiates the configuration vector.