Conformal Risk Minimization for Semi-Supervised Domain Adaptation via Optimal Transport

Manos Giannopoulos; Yi Shen; Michael M. Zavlanos

cs.LGAug 24, 2026

Conformal Risk Minimization for Semi-Supervised Domain Adaptation via Optimal Transport

Authors: Manos Giannopoulos, Yi Shen, Michael M. Zavlanos

Organizations: Duke University

Abstract

In high-stakes healthcare applications, machine learning models are frequently trained on data from one patient population and deployed on another, creating a distribution shift that degrades both accuracy and reliability. Semi-Supervised Domain Adaptation (SSDA) addresses this by leveraging labeled data from some source domain to improve model performance on a target domain where labels are scarce. However, existing SSDA methods optimize primarily for point-prediction accuracy and offer no principled uncertainty quantification --- a prerequisite for clinical trust. Conformal Prediction (CP) can address this limitation by providing prediction sets with rigorous, distribution-free coverage guarantees. However, applying CP post-hoc to a pre-trained model can yield prohibitively large prediction sets, as SSDA pre-training methods do not account for the nonconformity score geometry that determines conformal set size. Conformal Risk Minimization (CRM) has been used to resolve this issue in the fully supervised setting by integrating the CP objective directly into model training, but it requires a large labeled dataset to compute nonconformity thresholds during training, precisely the data that is scarce in the SSDA regime. We propose an end-to-end framework that integrates CRM into the SSDA training objective, enabling effective CRM in the limited-labeled-target-data regime. The key idea is to utilize Optimal Transport (OT) to generate pseudolabels for unlabeled target instances, providing the additional training signal needed by CRM to operate using only a small labeled target set. This results in a model jointly optimized for domain invariance and conformal efficiency, producing prediction sets that are compact, coverage-valid, and support domain-specific constraints such as excluding mutually contradictory diagnoses in skin lesion classification.

Figures & tables

Figure 1: Our proposed framework (CP-JDOT) that integrates conformal optimization in-the-loop for Semi-Supervised Domain Adaptation tasks. Our algorithm uses the labeled target dataset to compute a differentiable quantile of the nonconformity score distribution. Then, it optimizes a loss function that contains a Domain Alignment component and a Conformal Alignment component derived from the sizes of the conformal sets constructed on the unlabeled target data, using pseudolabels generated from optimally transported source data.

Method	A $\rightarrow$ C	A $\rightarrow$ P	A $\rightarrow$ R	C $\rightarrow$ A	C $\rightarrow$ P	C $\rightarrow$ R	P $\rightarrow$ A	P $\rightarrow$ C	P $\rightarrow$ R	R $\rightarrow$ A	R $\rightarrow$ C	R $\rightarrow$ P	Avg
S&T	$48.32\pm 2.10$	$24.18\pm 1.20$	$9.84\pm 1.10$	$19.45\pm 2.30$	$22.67\pm 2.80$	$10.21\pm 1.05$	$23.14\pm 2.15$	$46.23\pm 2.05$	$8.93\pm 1.20$	$15.67\pm 1.85$	$44.21\pm 2.10$	$22.34\pm 1.40$	$24.60$
MME	$45.12\pm 1.95$	$22.43\pm 1.25$	$8.87\pm 1.05$	$17.98\pm 2.20$	$21.34\pm 2.60$	$9.43\pm 1.02$	$21.87\pm 2.10$	$43.67\pm 2.00$	$8.12\pm 1.15$	$14.87\pm 1.80$	$42.56\pm 2.00$	$20.98\pm 1.35$	$23.10$
CDAC	$44.23\pm 1.88$	$21.87\pm 1.18$	$8.43\pm 1.00$	$17.12\pm 2.15$	$20.87\pm 2.50$	$8.98\pm 0.98$	$21.23\pm 2.05$	$42.98\pm 1.92$	$7.87\pm 1.10$	$14.23\pm 1.75$	$41.87\pm 1.92$	$20.23\pm 1.28$	$22.49$
DECOTA	$44.87\pm 1.82$	$22.34\pm 1.10$	$9.65\pm 0.92$	$17.87\pm 2.05$	$21.23\pm 2.40$	$9.87\pm 0.92$	$21.43\pm 1.98$	$43.23\pm 1.85$	$9.12\pm 1.02$	$15.12\pm 1.68$	$42.34\pm 1.85$	$20.87\pm 1.22$	$23.16$
IDMNE	$41.34\pm 1.78$	$21.12\pm 1.08$	$7.23\pm 0.90$	$14.98\pm 2.00$	$20.45\pm 2.35$	$7.54\pm 0.88$	$18.87\pm 1.92$	$39.87\pm 1.80$	$6.87\pm 0.98$	$12.54\pm 1.62$	$38.92\pm 1.80$	$19.43\pm 1.18$	$20.93$
ProML	$43.12\pm 1.80$	$19.87\pm 1.05$	$6.98\pm 0.88$	$15.43\pm 1.98$	$18.87\pm 2.28$	$8.23\pm 0.90$	$19.87\pm 1.95$	$40.54\pm 1.82$	$7.34\pm 1.00$	$13.87\pm 1.65$	$39.87\pm 1.82$	$18.12\pm 1.20$	$21.01$

Table 1: Avg. Set Size on Office-Home (ResNet-34 / 1-Shot / APS)

Method	A $\rightarrow$ C	A $\rightarrow$ P	A $\rightarrow$ R	C $\rightarrow$ A	C $\rightarrow$ P	C $\rightarrow$ R	P $\rightarrow$ A	P $\rightarrow$ C	P $\rightarrow$ R	R $\rightarrow$ A	R $\rightarrow$ C	R $\rightarrow$ P	Avg
S&T	$45.87\pm 2.05$	$22.43\pm 1.18$	$8.92\pm 1.05$	$17.87\pm 2.25$	$20.98\pm 2.72$	$9.43\pm 1.02$	$21.56\pm 2.10$	$44.12\pm 2.00$	$8.12\pm 1.15$	$14.23\pm 1.80$	$42.34\pm 2.05$	$20.87\pm 1.35$	$23.06$
MME	$43.23\pm 1.92$	$21.12\pm 1.22$	$8.43\pm 1.00$	$16.87\pm 2.18$	$20.12\pm 2.55$	$8.87\pm 0.98$	$20.43\pm 2.05$	$41.87\pm 1.95$	$7.65\pm 1.10$	$13.98\pm 1.75$	$40.87\pm 1.95$	$19.87\pm 1.30$	$21.94$
CDAC	$42.12\pm 1.85$	$20.54\pm 1.15$	$7.98\pm 0.95$	$16.12\pm 2.12$	$19.54\pm 2.48$	$8.43\pm 0.95$	$19.87\pm 2.00$	$41.12\pm 1.88$	$7.34\pm 1.05$	$13.34\pm 1.70$	$39.98\pm 1.88$	$19.12\pm 1.25$	$21.29$
DECOTA	$40.54\pm 1.78$	$19.12\pm 1.08$	$7.23\pm 0.88$	$14.87\pm 2.00$	$18.12\pm 2.35$	$7.43\pm 0.88$	$18.23\pm 1.92$	$39.12\pm 1.80$	$6.65\pm 0.98$	$12.23\pm 1.62$	$38.23\pm 1.80$	$17.76\pm 1.18$	$20.13$
IDMNE	$39.12\pm 1.75$	$19.87\pm 1.05$	$6.87\pm 0.85$	$13.98\pm 1.95$	$19.23\pm 2.30$	$7.12\pm 0.85$	$17.65\pm 1.88$	$37.65\pm 1.75$	$6.43\pm 0.95$	$11.65\pm 1.58$	$36.87\pm 1.75$	$18.23\pm 1.15$	$19.73$
ProML	$40.98\pm 1.76$	$18.65\pm 1.02$	$6.54\pm 0.85$	$14.43\pm 1.92$	$17.65\pm 2.22$	$7.76\pm 0.88$	$18.65\pm 1.90$	$38.43\pm 1.78$	$6.87\pm 0.95$	$12.87\pm 1.60$	$37.65\pm 1.78$	$17.01\pm 1.17$	$19.79$

Table 2: Avg. Set Size on Office-Home (ResNet-34 / 3-Shot / APS)

Method	HAM $\rightarrow$ PH2	HAM $\rightarrow$ MSK	HAM $\rightarrow$ Derm7pt	HAM $\rightarrow$ SONIC	HAM $\rightarrow$ UDA	Avg
S&T	$2.87\pm 0.43$	$3.98\pm 0.61$	$4.54\pm 0.55$	$2.23\pm 0.22$	$4.37\pm 0.68$	$3.60$
MME	$2.43\pm 0.38$	$3.54\pm 0.54$	$4.12\pm 0.48$	$1.17\pm 0.15$	$3.93\pm 0.61$	$3.04$
CDAC	$2.34\pm 0.35$	$3.43\pm 0.51$	$3.98\pm 0.45$	$1.26\pm 0.13$	$3.82\pm 0.58$	$2.97$
DECOTA	$1.98\pm 0.31$	$3.23\pm 0.48$	$3.76\pm 0.42$	$1.14\pm 0.20$	$3.37\pm 0.54$	$2.70$
IDMNE	$2.12\pm 0.33$	$2.98\pm 0.45$	$3.54\pm 0.40$	$1.12\pm 0.07$	$3.62\pm 0.56$	$2.68$
ProML	$1.87\pm 0.29$	$3.12\pm 0.47$	$3.87\pm 0.43$	$1.12\pm 0.15$	$3.15\pm 0.51$	$2.63$

Table 3: Avg. Set Size on Skin Lesion Classification (ResNet-18 / 10-Shot / APS)

Figure 2: Ablation study comparing CP-JDOT trained with $\mathcal{L}_{\text{cls}}$ versus $\mathcal{L}_{\text{control}}$ on the skin lesion classification setting. Training with $\mathcal{L}_{\text{control}}$ consistently reduces the proportion of conflicting sets across all target domains, at the cost of a modest increase in average set size.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Method	A $\rightarrow$ C	A $\rightarrow$ P	A $\rightarrow$ R	C $\rightarrow$ A	C $\rightarrow$ P	C $\rightarrow$ R	P $\rightarrow$ A	P $\rightarrow$ C	P $\rightarrow$ R	R $\rightarrow$ A	R $\rightarrow$ C	R $\rightarrow$ P	Avg
S&T	$50.9$	$69.8$	$73.8$	$56.3$	$68.1$	$70.0$	$57.2$	$48.3$	$74.4$	$66.2$	$52.1$	$78.6$	$63.8$
MME	$59.6$	$75.5$	$77.8$	$65.7$	$74.5$	$74.8$	$64.7$	$57.4$	$79.2$	$71.2$	$61.9$	$82.8$	$70.4$
CDAC	$61.2$	$75.9$	$78.5$	$64.5$	$75.1$	$75.3$	$64.6$	$59.3$	$80.0$	$72.7$	$61.9$	$83.1$	$71.0$
DECOTA	$42.1$	$68.5$	$72.6$	$60.3$	$70.4$	$70.7$	$60.0$	$48.8$	$76.9$	$71.3$	$56.0$	$79.4$	$64.8$
IDMNE	$62.4$	$77.9$	$76.7$	$65.5$	$77.9$	$77.0$	$66.4$	$61.4$	$80.7$	$73.6$	$66.7$	$85.6$	$72.6$
ProML	$64.5$	$79.7$	$81.7$	$69.1$	$80.5$	$79.0$	$69.3$	$61.4$	$81.9$	$73.7$	$67.5$	$86.1$	$74.5$

Appendix

Table 4: Top-1 Accuracy on Office-Home (ResNet-34 / 1-Shot)

Method	A $\rightarrow$ C	A $\rightarrow$ P	A $\rightarrow$ R	C $\rightarrow$ A	C $\rightarrow$ P	C $\rightarrow$ R	P $\rightarrow$ A	P $\rightarrow$ C	P $\rightarrow$ R	R $\rightarrow$ A	R $\rightarrow$ C	R $\rightarrow$ P	Avg
S&T	$54.0$	$73.1$	$74.2$	$57.6$	$72.3$	$68.3$	$63.5$	$53.8$	$73.1$	$67.8$	$55.7$	$80.8$	$66.2$
MME	$63.6$	$79.0$	$79.7$	$67.2$	$79.3$	$76.6$	$65.5$	$64.6$	$80.1$	$71.3$	$64.6$	$85.5$	$73.1$
CDAC	$65.9$	$80.3$	$80.6$	$67.4$	$81.4$	$80.2$	$67.5$	$67.0$	$81.9$	$72.2$	$67.8$	$85.6$	$74.8$
DECOTA	$64.0$	$81.8$	$80.5$	$68.0$	$83.2$	$79.0$	$69.9$	$68.0$	$82.1$	$74.0$	$70.4$	$87.7$	$75.7$
IDMNE	$66.3$	$82.4$	$79.3$	$69.1$	$83.0$	$79.4$	$68.9$	$67.5$	$82.6$	$75.1$	$71.7$	$88.0$	$76.1$
ProML	$67.8$	$83.9$	$82.2$	$72.1$	$84.1$	$82.3$	$72.5$	$68.9$	$83.8$	$75.8$	$71.0$	$88.6$	$77.8$

Appendix

Table 5: Top-1 Accuracy on Office-Home (ResNet-34 / 3-Shot)

Method	HAM $\rightarrow$ PH2	HAM $\rightarrow$ MSK	HAM $\rightarrow$ Derm7pt	HAM $\rightarrow$ SONIC	HAM $\rightarrow$ UDA	Avg
S&T	$80.2$	$68.4$	$60.1$	$88.0$	$65.8$	$72.10$
MME	$84.8$	$73.1$	$64.9$	$93.5$	$72.6$	$77.78$
CDAC	$85.2$	$73.6$	$65.4$	$93.8$	$73.1$	$78.22$
DECOTA	$85.6$	$74.2$	$65.8$	$94.1$	$73.6$	$78.66$
IDMNE	$85.9$	$74.6$	$66.1$	$94.4$	$74.0$	$79.00$
ProML	$86.4$	$75.0$	$66.7$	$94.8$	$74.5$	$79.48$

Appendix

Table 6: Top-1 Accuracy on Skin Lesion Classification (ResNet-18 / 10-Shot)

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When few labeled target data suffice: a theory of semi-supervised domain adaptation via fine-tuning from multiple adaptive starts

Wooseok Ha, Yuansi Chen

Department of Mathematical Sciences, KAIST · Department of Mathematics, ETH Zürich

Fine-Tuning Domain Adaptation

Open paper AskPDF arXiv

Semi-supervised domain adaptation (SSDA) seeks to achieve accurate predictions in a target domain with limited labeled target data by exploiting abundant source and unlabeled target data. We study this problem under structural causal models (SCMs), which provide a statistical framework to describe distribution shifts between source and target domains as interventions in the data-generating process rather than ad hoc changes in model parameters. The central phenomenon is that, under low-dimensional interventions, source and unlabeled target data can help identify the high-dimensional shared structure, leaving only a low-dimensional target-specific correction to be learned from limited labeled target data. We formalize this principle for three canonical intervention models and propose the corresponding SSDA methods FT-DIP, FT-OLS-Src and FT-CIP. Under each intervention model, we demonstrate how extending an unsupervised domain adaptation (UDA) method to SSDA can achieve minimax-optimal target performance with limited target labels, with the labeled-target sample complexity scaling with the intervention dimension rather than the ambient dimension. When the distribution shift is underspecified, we propose the Multi-Adaptive-Start Fine-Tuning (MASFT) algorithm, which fine-tunes from multiple adaptive starts and selects among them using a small target validation set, incurring only logarithmic overhead in the number of starts. We validate the effectiveness of our proposed methods through simulated and real data experiments.

Abstract

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