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Wasserstein Transfer Learning

NeurIPS 2025 · Label-efficient and robust learning › Domain adaptation and generalization · approach: Statistical transfer learning · 0 citations (OpenAlex)

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Proposes Wasserstein Transfer Learning (WaTL) and an adaptive variant (AWaTL) for Fréchet regression with distributional (1D Wasserstein-space) outputs, with convergence-rate theory and simulation/NHANES/mortality experiments.

Problem

Transfer learning for regression models whose outputs are univariate probability distributions in the Wasserstein space, where the lack of linear structure makes standard transfer methods inapplicable and negative transfer from dissimilar sources is a risk.

Approach

Extends Fréchet regression to transfer learning by aggregating sample-size-weighted source estimates of the quantile-function mean, correcting bias with a regularized target-only step in L2 of quantile functions, and projecting back onto the Wasserstein space; an adaptive variant selects informative sources by discrepancy ranking.

Key results

• In simulations, WaTL achieves lower RMSPR than Only Target and Only Source across target sizes 200-800, with the advantage growing as source sample size increases.
• In the K=1 ablation, WaTL outperforms Only Target when the similarity parameter psi_1 < 0.9 and Only Target is preferable for psi_1 >= 0.9.
• On the mortality data, WaTL attains RMSPR 0.022 versus 0.027 for Fréchet regression and 0.025 for Wasserstein Regression with 24 target samples, and 0.033 for naive pooling.

Measured effects reported in the paper

Surprising findings

• Naive pooling of target and source data performs worse than target-only baselines on the mortality data, highlighting domain shift.

Limitations

• Focuses on univariate distributions; multivariate extension left to future work.
• Theory assumes fixed K and that sources satisfy sample-size conditions; sources with small n_k may need exclusion.
• Requires choosing number of informative sources L (by cross-validation) and regularization lambda.

Experimental setup

Datasets: NHANES 2005-2006 UN World Population Prospects 2022 age-at-death data simulated distributional data

Benchmarks: simulated distributional regression NHANES 2005-2006 physical activity human mortality age-at-death

Metrics: RMSPR (root mean squared prediction risk in Wasserstein dist selection rate

Baselines: Only Target Only Source Target + Source pooling Wasserstein Regression

Builds on: Fréchet regression local Fréchet regression Wasserstein regression with empirical measures

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