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

T0 review · 2 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Under anticausal linear causal models, low-dimensional distribution shifts let a few labeled target samples achieve the rate that would otherwise require d labeled samples.

desk verdict Solid SCM-based minimax theory for SSDA with a real gap: the upper bounds rely on oracle tuning constants, so the central r/n^0 claim is not yet certified for an implementable procedure. read the letter →

arxiv 2507.14661 v2 pith:QHBRV4UU submitted 2025-07-19 stat.ML cs.LGmath.STstat.TH

Wooseok Ha , Yuansi Chen This is my paper
classification stat.MLcs.LGmath.STstat.TH MSC 62J0562J0768T05
keywords semi-superviseddomainadaptationstructuralcausalmodelsanticausallearningfine-tuninglow-dimensionaldistributionshiftminimaxexcessriskconditionalinvariance
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Under anticausal linear structural causal models (label causes covariates), this paper claims that if the source-to-target shift is confined to a low-dimensional intervention—confounded additive noise, sparse connectivity, or shifts in the anticausal weights—then semi-supervised domain adaptation can learn the target predictor from $n^{(0)}$ labeled target samples, with the required number scaling as the intervention dimension $r$ rather than the ambient dimension $d$. The paper proposes three fine-tuning estimators, FT-DIP, FT-OLS-Src, and FT-CIP, each initialized from a corresponding unsupervised domain adaptation estimate that uses source and unlabeled target data, then using the few target labels only to adjust along the low-dimensional directions in which the target differs from source. Matching minimax lower bounds show the resulting $r/n^{(0)}$ excess-risk rate is optimal, so the paper's central contribution is a precise account of when and why a handful of target labels can substitute for $d$ labels. When the shift type is unknown, the MASFT procedure fine-tunes from multiple adaptive starts and selects among them with a small validation set at only logarithmic cost.

What carries the argument

The load-bearing object is the UDA-start plus low-dimensional correction decomposition: for each canonical intervention, the target-specific deviation $\beta^{\star} - \beta_{\mathrm{UDA}}$ is confined to a subspace (or a sparse support set) that is identifiable without target labels. FT-DIP estimates this subspace from the rank-$r_{\mathrm{ca}}$ covariance difference $\Sigma_X^{(0)} - \Sigma_X^{(1)}$ and fine-tunes subject to the constraint that the correction has no component in its orthogonal complement; FT-OLS-Src imposes an $\ell^1$ constraint around the source OLS estimator because $\beta^{\star} - \beta_{\mathrm{LS}}^{(1)}$ is supported on the $r_{\mathrm{sc}}$ intervened columns; FT-CIP builds the conditionally invariant subspace $V_{\mathrm{aw}}$ from heterogeneous source domains and uses the identity $Q_{\mathrm{aug}}^\top \Sigma_X^{(1)}(\beta^{\star} - \beta_{\mathrm{CIP}}) = 0$, removing the need for unlabeled target covariates. Gaussian-width and eigen-gap conditions control how many unlabeled samples are needed to learn these subspaces, and once the subspace is fixed the $r/n^{(0)}$ rate is the ordinary cost of $r$-dimensional constrained least squares.

What would settle it

Simulate an anticausal linear SCM with $d=100$ and true intervention rank $r=5$, but generate the target with a rank-$6$ perturbation; running FT-DIP with $r=5$ across increasing $n^{(0)}$ should show excess risk scaling as $6/n^{(0)}$ rather than the advertised $5/n^{(0)}$, which would falsify the rank condition's role. A cheaper check on real data is to estimate the rank of $\Sigma_X^{(0)} - \Sigma_X^{(1)}$ or of the conditional-mean differences from unlabeled data and compare it with the subspace dimension used by the fine-tuned method.

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Extended reading notes

Core claim

Within the anticausal linear SCMs of Assumption 1, and for the three canonical intervention classes of Assumptions 3–5, the paper demonstrates that the oracle target coefficient $\beta^{\star}$ differs from the associated UDA estimator along a subspace of dimension $r$ that can be identified from source and unlabeled target data alone. Under confounded additive shifts, $\beta^{\star} - \beta^{(1)}_{\mathrm{DIP}}$ lies in $\operatorname{col}((\Sigma_X^{(0)})^{-1}V)$; under sparse connectivity shifts, $\beta^{\star} - \beta^{(1)}_{\mathrm{LS}}$ is $r_{\mathrm{sc}}$-sparse; and under anticausal weight shifts, the correction obeys $Q_{\mathrm{aug}}^\top \Sigma_X^{(1)}(\beta^{\star} - \beta_{\mathrm{CIP}}) = 0$, so no unlabeled target covariates are needed. Constrained least squares on the labeled target data within that subspace estimates only $r$ parameters, giving target excess risk of order $r/n^{(0)}$ up to logarithmic factors, while target-only estimators suffer $d/n^{(0)}$. Matching minimax lower bounds establish that this rate is optimal, and MASFT makes the choice among the three shift-specific strategies adaptive with only a $\log M$ validation penalty.

Load-bearing premise

The load-bearing premise is that the true source-to-target shift is exactly one of the three low-dimensional linear intervention classes, satisfying the exact rank, span, and support conditions of Assumptions 3, 4, and 5; if the shift is higher-dimensional, nonlinear, or fails the span condition, the identified fine-tuning subspace is misspecified and the $r/n^{(0)}$ guarantee collapses.

Editorial extensions

If this is right

  • Under CA, SC, or AW shifts, a practitioner needs only $n^{(0)} \asymp r \log(1/\delta)$ labeled target samples, plus enough source and unlabeled data, to reach the target-only rate that would require $n^{(0)} \asymp d$.
  • Unlabeled target data are not essential in every regime: FT-OLS-Src under SC shifts and FT-CIP under AW shifts achieve the minimax rate using only source data and a few target labels.
  • When the shift type is unknown, MASFT makes model selection safe: a validation set of size about $\log M$ recovers the performance of the best candidate fine-tuning strategy.
  • The covariance-matching DIP start identifies the CA shift subspace, so mean-matching-only alignments fail in centered confounded additive shifts; second-moment matching is the right alignment.
  • In the covariate-only CA subcase ($w_Y = 0$), the paper notes the rate is not tight and the plug-in estimator can reach the oracle without any target labels.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the true shift is only approximately low-dimensional, as in the NIR and Light Tunnel systems, the theory predicts the excess risk should degrade with the approximation error; a direct test is to measure how performance changes as the estimated rank of the covariance difference grows toward $d$.
  • The same template suggests a cheap pre-screening diagnostic: estimate the rank of $\Sigma_X^{(0)} - \Sigma_X^{(1)}$ or the conditional-mean difference from unlabeled data before investing in labels; if the spectrum is flat, the $r/n^{(0)}$ guarantee should not be expected.
  • The linear-SCM identities that carry the argument are specific to squared loss and linear predictors; extending the template to logistic or cross-entropy losses would require re-deriving the subspace decomposition, so the practical lesson for nonlinear models is architectural rather than rate-based.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper develops a theory of semi-supervised domain adaptation (SSDA) under anticausal linear structural causal models, focusing on three low-dimensional intervention classes: confounded additive (CA) shifts, sparse connectivity (SC) shifts, and anticausal weight (AW) shifts. For each class it proposes a fine-tuning estimator (FT-DIP, FT-OLS-Src, FT-CIP) that starts from a corresponding UDA solution and uses the limited labeled target data only in the low-dimensional fine-tuning subspace. The main theoretical results are upper bounds of order r/n^(0) (up to logarithmic factors) on the target excess risk using n^(0) labeled target samples, complemented by minimax lower bounds of the same order. When the intervention type is unknown, the paper introduces MASFT, which selects among candidate fine-tuned estimators using a small target validation set. The theoretical findings are supported by synthetic experiments and by real-data experiments on light-tunnel and near-infrared spectroscopy datasets.

Significance. If the results hold, the paper provides a principled explanation of when few labeled target samples suffice: under low-dimensional interventions, source and unlabeled target data identify the high-dimensional shared structure, reducing the labeled-target sample complexity from the ambient dimension d to the intervention dimension r. A particular strength is the construction of the minimax lower bounds, where the source and unlabeled target data are kept identical across hypotheses, so the lower bounds correctly isolate the information carried by the labeled target samples. The paper also gives detailed finite-sample proofs, explicit conditions for each intervention class, and reproducible experiments with synthetic and physical-system data. The central caveat is that the upper-bound theorems are stated for oracle-tuned parameters, which is a load-bearing gap discussed below.

major comments (2)
  1. [§4.2, Eq. (20); §4.1, Eq. (16); Theorems 4.1 and 4.3] The tuning parameters in the proposed estimators depend on unknown population quantities. In Theorem 4.3, the constraint radius is set to gamma = ||beta* - hat_beta_LS^(1)||_1 and rho >= ||beta*||_2, where beta* is the unknown oracle target coefficient defined in Eq. (7). In Theorem 4.1, the bound requires choosing varrho >= c lambda_max(||beta*||_2 + ...), again involving the unknown beta*. The proofs therefore establish excess-risk bounds only for oracle-tuned members of the estimator family, and not for a procedure that selects these parameters from data. Since no data-driven tuning analysis is provided, the stated upper bounds do not certify an implementable algorithm that achieves the claimed r/n^(0) rate. The lower bounds remain valid, but the matching upper-bound claim is not yet supported for the practical versions of the methods.
  2. [§5, Corollary 1] The MASFT selection result inherits the oracle-tuning gap. Corollary 1 states that, under the conditions of Theorems 4.1, 4.3, and 4.5, validation-based selection among the candidates achieves the best candidate's rate up to a logarithmic overhead. However, each candidate's guarantee in those theorems assumes that its own tuning parameters (gamma, rho, varrho) are chosen using the unknown beta*. Thus the validation set selects among oracle-tuned members of the candidate families, not among implementable data-driven procedures. A complete result would require either a data-driven tuning procedure with a valid excess-risk bound or an explicit statement that the theory covers only oracle-tuned versions.
minor comments (4)
  1. [§3.2, Example (Additive mean shift)] The numerical values in the additive mean-shift example appear to be incorrect. For the stated noise means (source means all 1, target means -1, 0, 1), solving the constrained least-squares problem in (5) with the mean-matching penalty gives beta_DIP^(1) = (-1/11, 2/11, 5/11) and v_DIP = Sigma_X^(0)^{-1}(E[X^(1)] - E[X^(0)]) = (5/4, 1/4, -3/4), not the values (47,59,71)/272 and (7,3,-1)/12 reported in the text. The qualitative conclusion that beta* - beta_DIP is parallel to v_DIP still holds with the corrected values, but the displayed numbers should be fixed to avoid misleading readers.
  2. [§4.3.1] The variant FT-CIP-Tar, which uses unlabeled target covariates, is introduced and evaluated empirically but is not covered by a finite-sample theorem. The paper explicitly states that it focuses on the setting without unlabeled target covariates, so this is a clear scope limitation, but it would be helpful to add a sentence in Section 6 reminding readers that the theoretical guarantees for FT-CIP do not apply to FT-CIP-Tar.
  3. [Appendix G.1] The proof of Proposition 3.1 assumes d >= 32 and dismisses the small-dimensional case with a brief remark that a lower bound can be obtained by a one-parameter Fano construction. Since the small-d case is needed for a fully general statement, a few lines of detail would improve completeness, though this is not a barrier to the main claims.
  4. [§5, Corollary 1] The displayed bound in Corollary 1 writes "c'' eta_s sqrt(log(M/delta)/n_val^(0)) + epsilon_type" without explicitly showing that epsilon_type may also carry a log(1/delta) factor from applying the individual theorems at failure probability delta/M. The statement is acceptable if this is understood, but a short clarifying sentence would prevent misreading.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the r/n^(0) rates are derived from structural identities (Eqs. 15, 19, 25) and matched by independent minimax lower bounds; oracle-scale tuning constants are a flagged implementability gap, not a circular reduction.

full rationale

The central claim — that labeled-target sample complexity scales with the intervention dimension r rather than the ambient dimension d — is not reached by fitting or by definitional fiat. For each intervention model the low-dimensional correction is derived, not assumed: for CA shifts, Eq. (15) and Appendix C.1 prove β* − β_DIP lies in the r_ca-dimensional subspace col(Σ_X^(0)^{-1}V) via projection identities and covariance/cross-moment matching on the common subspace, instead of being imposed; for SC shifts, Eq. (19) and Appendix C.2 derive the r_sc-sparsity of β* − β_LS^(1) from the column-sparse difference B^(0) − B^(1) via the Sherman–Morrison formula; for AW shifts, Eqs. (25)–(27) and Appendix C.3 derive the (r_aw+1)-dimensional constraint from the span condition (22). The matching minimax lower bounds (Theorems 4.2, 4.4, 4.6; Appendices G.2–G.4) are genuine Fano constructions over the assumed classes in which source and unlabeled data are uninformative while the oracle varies in an r-dimensional family, proving that no method can beat r/n^(0) — so the class is shown to be genuinely r-hard rather than the conclusion being a tautology. The stated upper bounds do rely on oracle-scale tuning constants (Theorem 4.1: ϱ ≥ c_2 λ_max(||β*||_2 + κ^{3/2}||β_LS^(1)||_2 + κ^{3/2}σ_Y/σ_X); Theorem 4.3: ρ ≥ ||β*||_2 and γ = ||β* − \hat{β}_LS^(1)||_1; Theorem 4.5: ϱ ≥ c_3 λ_max(||β*||_2 + κ^{3/2}||β_Pool||_2 + κ^{3/2}σ_Y/σ_X)), so the theorems certify an infeasible parameter choice rather than a fully data-driven procedure; this implementability gap (inherited by Corollary 1's candidates) is a correctness risk, not a circular reduction, because the r-scaling in each bound follows from the structural dimension of the feasible set and not from the fitted constants. No load-bearing self-citation chain was found: the cited identifiability results [13, 76] contextualize but do not prove the new bounds, which are proved internally in Appendices C–F, and the overlap of FT-OLS-Src's ℓ1 constraint with [41] is explicitly acknowledged with a genuinely added source-estimation-uncertainty analysis. The empirical sections tune hyperparameters on separate validation sets and report held-out test MSE, so no fitted quantity is renamed as a prediction.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The theoretical machinery rests on the linear anticausal SCM, sub-Gaussian noise, exactly low-dimensional interventions, and standard concentration and Fano lemmas. No new physical or ontological entity is introduced. The practical methods additionally tune subspace dimension and regularization on the target validation set, which the theory does not cover.

free parameters (2)
  • fine-tuning subspace dimension = tuned on target validation set in experiments
    FT-DIP, FT-CIP and MASFT need an estimate of the intervention dimension r_ca, r_sc, or r_aw; the theory assumes r known, while the experiments tune this dimension on a validation set.
  • regularization or penalty parameters = tuned on target validation set in experiments
    The theoretical upper bounds use oracle choices such as gamma = ||beta_star - beta_LS^(1)||_1; the implemented versions tune penalties instead, so the data-driven algorithm is not covered by the theorem as stated.
assumptions (6)
  • domain assumption Assumption 1: data follow anticausal linear SCMs with I-B invertible in every domain.
    This linear structural model is the foundation for all derivations in Sections 3 and 4.
  • domain assumption Assumption 2: noise terms are zero-mean sub-Gaussian and covariances are invertible.
    Sub-Gaussianity is used for concentration bounds in Lemmas B.4, B.7, and B.8.
  • domain assumption Assumption 3: CA shift interventions with rank(W+bw_Y^T)=r_ca.
    Exact rank condition guarantees the perturbation subspace is r_ca-dimensional and identifiable from covariance differences.
  • domain assumption Assumption 4: SC shift interventions modify exactly r_sc columns of B.
    This implies beta_star - beta_LS is r_sc-sparse, which is the basis for the l1 fine-tuning method.
  • domain assumption Assumption 5: AW shift with b(0)-b(1) in the span of the source perturbation directions.
    This condition guarantees existence of conditionally invariant components; if it fails, FT-CIP is misspecified.
  • standard math Standard concentration and Fano-type inequalities used in the proofs.
    Lemmas B.4, B.6, G.1, and related results are adapted from known literature and are not new to this paper.

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Pith. "Pith review of When few labeled target data suffice: a theory of semi-supervised domain adaptation via fine-tuning from multiple adaptive starts." pith.science (2026). https://pith.science/paper/QHBRV4UU

@misc{pith2026250714661,
  author       = {Pith},
  title        = {Pith review of: When few labeled target data suffice: a theory of semi-supervised domain adaptation via fine-tuning from multiple adaptive starts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QHBRV4UU}},
  note         = {Machine review of arXiv:2507.14661}
}
read the original abstract

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.

Figures

Figures reproduced from arXiv: 2507.14661 by the authors.

Figure 1
Figure 1. The causal diagrams and structural equations illustrating the example of additive mean [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. A ground-truth causal graph provided by the Causal Chambers benchmark Light-tunnel experiments Method lt CA lt SC lt AW OLS-Src 0.056 ± 0.003 0.115 ± 0.009 0.281 ± 0.011 OLS-Pool 0.066 ± 0.003 43.860 ± 2.015 0.130 ± 0.005 DIP 0.065 ± 0.005 0.076 ± 0.007 0.181 ± 0.011 CIP 0.065 ± 0.003 29.217 ± 2.223 0.079 ± 0.004 groupDRO 0.059 ± 0.004 1.650 ± 0.078 0.107 ± 0.004 IRM 0.056 ± 0.003 0.146 ± 0.012 0.113 ± 0.004 V-REx 0… view at source ↗
Figure 3
Figure 3. Comparison of empirical target excess risks for Simulation 1 under CA shift interventions. [PITH_FULL_IMAGE:figures/full_fig_p030_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Comparison of empirical target excess risks for Simulation 2 under SC shift interventions. [PITH_FULL_IMAGE:figures/full_fig_p031_4.png]
Figure 5
Figure 5. Figure 5: Comparison of empirical target excess risks for Simulation 3 under AW shift interventions. [PITH_FULL_IMAGE:figures/full_fig_p032_5.png]
Figure 6
Figure 6. Figure 6: Empirical diagnostics for the light-tunnel experiments. In our notation, [PITH_FULL_IMAGE:figures/full_fig_p032_6.png]

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Reference graph

Works this paper leans on

86 extracted references · 62 canonical work pages

  1. [1]

    Achieving robustness across season, location and cultivar for a nirs model for intact mango fruit dry matter content.Postharvest Biology and Technology, 168:111202, 2020

    NT Anderson, KB Walsh, PP Subedi, and CH Hayes. Achieving robustness across season, location and cultivar for a nirs model for intact mango fruit dry matter content.Postharvest Biology and Technology, 168:111202, 2020

    2020

  2. [2]

    Invariant risk mini- mization.arXiv preprint arXiv:1907.02893, 2019

    Martin Arjovsky, L´ eon Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk mini- mization.arXiv preprint arXiv:1907.02893, 2019

    arXiv 1907

  3. [3]

    MIT press, 2024

    Francis Bach.Learning theory from first principles. MIT press, 2024

    2024

  4. [4]

    Un- supervised domain adaptation by domain invariant projection

    Mahsa Baktashmotlagh, Mehrtash T Harandi, Brian C Lovell, and Mathieu Salzmann. Un- supervised domain adaptation by domain invariant projection. InProceedings of the IEEE International Conference on Computer Vision, pages 769–776, 2013

    2013

  5. [5]

    Predicting with proxies: Transfer learning in high dimension.Management Science, 67(5):2964–2984, 2021

    Hamsa Bastani. Predicting with proxies: Transfer learning in high dimension.Management Science, 67(5):2964–2984, 2021

    2021

  6. [6]

    A theory of learning from different domains.Machine learning, 79 (1-2):151–175, 2010

    Shai Ben-David, John Blitzer, Koby Crammer, Alex Kulesza, Fernando Pereira, and Jen- nifer Wortman Vaughan. A theory of learning from different domains.Machine learning, 79 (1-2):151–175, 2010

    2010

  7. [7]

    Springer Science & Business Media, 2013

    Rajendra Bhatia.Matrix analysis, volume 169. Springer Science & Business Media, 2013

    2013

  8. [8]

    Simultaneous analysis of lasso and dantzig selector.The Annals of Statistics, 37(4):1705, 2009

    Peter J Bickel, Ya’acov Ritov, and Alexandre B Tsybakov. Simultaneous analysis of lasso and dantzig selector.The Annals of Statistics, 37(4):1705, 2009

    work page 2009

Show all 86 references
  1. [9]

    Combining labeled and unlabeled data with co-training

    Avrim Blum and Tom Mitchell. Combining labeled and unlabeled data with co-training. In Proceedings of the eleventh annual conference on Computational learning theory, pages 92–100, 1998

    1998

  2. [10]

    Invariance, causality and robustness.Statistical Science, 35(3):404–426, 2020

    Peter B¨ uhlmann. Invariance, causality and robustness.Statistical Science, 35(3):404–426, 2020

    2020

  3. [11]

    Causality matters in medical imaging.Nature Communications, 11(1):3673, 2020

    Daniel C Castro, Ian Walker, and Ben Glocker. Causality matters in medical imaging.Nature Communications, 11(1):3673, 2020

    2020

  4. [12]

    An empirical study of training self-supervised vision transformers

    Xinlei Chen, Saining Xie, and Kaiming He. An empirical study of training self-supervised vision transformers. InProceedings of the IEEE/CVF international conference on computer vision, pages 9640–9649, 2021

    2021

  5. [13]

    Domain adaptation under structural causal models.Journal of Machine Learning Research, 22(261):1–80, 2021

    Yuansi Chen and Peter B¨ uhlmann. Domain adaptation under structural causal models.Journal of Machine Learning Research, 22(261):1–80, 2021

    2021

  6. [14]

    Spectral methods for data science: A statistical perspective.Foundations and Trends®in Machine Learning, 14(5):566–806, 2021

    Yuxin Chen, Yuejie Chi, Jianqing Fan, Cong Ma, et al. Spectral methods for data science: A statistical perspective.Foundations and Trends®in Machine Learning, 14(5):566–806, 2021

    2021

  7. [15]

    Optimal transport for domain adaptation.IEEE transactions on pattern analysis and machine intelligence, 39(9): 1853–1865, 2016

    Nicolas Courty, R´ emi Flamary, Devis Tuia, and Alain Rakotomamonjy. Optimal transport for domain adaptation.IEEE transactions on pattern analysis and machine intelligence, 39(9): 1853–1865, 2016

    2016

  8. [16]

    The bayesian approach to inverse problems.arXiv preprint arXiv:1302.6989, 2013

    Masoumeh Dashti and Andrew M Stuart. The bayesian approach to inverse problems.arXiv preprint arXiv:1302.6989, 2013. 88

    2013 arXiv

  9. [17]

    Semi-supervised domain adaptation with instance constraints

    Jeff Donahue, Judy Hoffman, Erik Rodner, Kate Saenko, and Trevor Darrell. Semi-supervised domain adaptation with instance constraints. InProceedings of the IEEE conference on com- puter vision and pattern recognition, pages 668–675, 2013

    2013

  10. [18]

    Statistics of robust optimization: A generalized empirical likelihood approach.Mathematics of Operations Research, 46(3):946–969, 2021

    John C Duchi, Peter W Glynn, and Hongseok Namkoong. Statistics of robust optimization: A generalized empirical likelihood approach.Mathematics of Operations Research, 46(3):946–969, 2021

    2021

  11. [19]

    Causal chambers as a real-world physical testbed for ai methodology.Nature Machine Intelligence, 7(1):107–118, 2025

    Juan L Gamella, Jonas Peters, and Peter B¨ uhlmann. Causal chambers as a real-world physical testbed for ai methodology.Nature Machine Intelligence, 7(1):107–118, 2025

    2025

  12. [20]

    Domain-adversarial training of neural networks.The Journal of Machine Learning Research, 17(1):2096–2030, 2016

    Yaroslav Ganin, Evgeniya Ustinova, Hana Ajakan, Pascal Germain, Hugo Larochelle, Fran¸ cois Laviolette, Mario Marchand, and Victor Lempitsky. Domain-adversarial training of neural networks.The Journal of Machine Learning Research, 17(1):2096–2030, 2016

    2016

  13. [21]

    Shortcut learning in deep neural networks.Nature Machine Intelligence, 2(11):665–673, 2020

    Robert Geirhos, J¨ orn-Henrik Jacobsen, Claudio Michaelis, Richard Zemel, Wieland Brendel, Matthias Bethge, and Felix A Wichmann. Shortcut learning in deep neural networks.Nature Machine Intelligence, 2(11):665–673, 2020

    2020

  14. [22]

    Domain adaptation with conditional transferable components

    Mingming Gong, Kun Zhang, Tongliang Liu, Dacheng Tao, Clark Glymour, and Bernhard Sch¨ olkopf. Domain adaptation with conditional transferable components. InInternational conference on machine learning, pages 2839–2848. PMLR, 2016

    2016

  15. [23]

    Improving neural network training in low dimensional random bases.Advances in Neural Information Processing Systems, 33: 12140–12150, 2020

    Frithjof Gressmann, Zach Eaton-Rosen, and Carlo Luschi. Improving neural network training in low dimensional random bases.Advances in Neural Information Processing Systems, 33: 12140–12150, 2020

    2020

  16. [24]

    A kernel two-sample test.The Journal of Machine Learning Research, 13(1):723–773, 2012

    Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Sch¨ olkopf, and Alexander Smola. A kernel two-sample test.The Journal of Machine Learning Research, 13(1):723–773, 2012

    2012

  17. [25]

    Domain adaptation for medical image analysis: A survey.IEEE Transactions on Biomedical Engineering, 2022

    Hao Guan and Mingxia Liu. Domain adaptation for medical image analysis: A survey.IEEE Transactions on Biomedical Engineering, 2022

    2022

  18. [26]

    In search of lost domain generalization

    Ishaan Gulrajani and David Lopez-Paz. In search of lost domain generalization. InInterna- tional Conference on Learning Representations (ICLR), 2020

    2020

  19. [27]

    Adap- tive wavelet distillation from neural networks through interpretations.Advances in Neural Information Processing Systems, 34:20669–20682, 2021

    Wooseok Ha, Chandan Singh, Francois Lanusse, Srigokul Upadhyayula, and Bin Yu. Adap- tive wavelet distillation from neural networks through interpretations.Advances in Neural Information Processing Systems, 34:20669–20682, 2021

    2021

  20. [28]

    Delving deep into rectifiers: Surpassing human-level performance on imagenet classification

    Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. InProceedings of the IEEE international conference on computer vision, pages 1026–1034, 2015

    2015

  21. [29]

    Conditional variance penalties and domain shift robustness.Machine Learning, 110(2):303–348, 2021

    Christina Heinze-Deml and Nicolai Meinshausen. Conditional variance penalties and domain shift robustness.Machine Learning, 110(2):303–348, 2021

    2021

  22. [30]

    Benchmarking neural network robustness to common corruptions and perturbations

    Dan Hendrycks and Thomas Dietterich. Benchmarking neural network robustness to common corruptions and perturbations. InInternational Conference on Learning Representations, 2019

    2019

  23. [31]

    Random design analysis of ridge regression

    Daniel Hsu, Sham M Kakade, and Tong Zhang. Random design analysis of ridge regression. InConference on learning theory, pages 9–1. JMLR Workshop and Conference Proceedings, 2012. 89

    2012

  24. [32]

    Lora: Low-rank adaptation of large language models.ICLR, 1 (2):3, 2022

    Edward J Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, Weizhu Chen, et al. Lora: Low-rank adaptation of large language models.ICLR, 1 (2):3, 2022

    2022

  25. [33]

    Bidirectional adversarial training for semi-supervised domain adaptation

    Pin Jiang, Aming Wu, Yahong Han, Yunfeng Shao, Meiyu Qi, and Bingshuai Li. Bidirectional adversarial training for semi-supervised domain adaptation. InIJCAI, pages 934–940, 2020

    2020

  26. [34]

    Support and invertibility in domain-invariant representations

    Fredrik D Johansson, David Sontag, and Rajesh Ranganath. Support and invertibility in domain-invariant representations. InThe 22nd International Conference on Artificial Intelli- gence and Statistics, pages 527–536. PMLR, 2019

    2019

  27. [35]

    Do better imagenet models transfer better? InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 2661–2671, 2019

    Simon Kornblith, Jonathon Shlens, and Quoc V Le. Do better imagenet models transfer better? InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 2661–2671, 2019

    2019

  28. [36]

    Imagenet classification with deep convolutional neural networks.Advances in neural information processing systems, 25, 2012

    Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks.Advances in neural information processing systems, 25, 2012

    2012

  29. [37]

    Out-of-distribution generalization via risk extrapolation (rex)

    David Krueger, Ethan Caballero, Joern-Henrik Jacobsen, Amy Zhang, Jonathan Binas, Dinghuai Zhang, Remi Le Priol, and Aaron Courville. Out-of-distribution generalization via risk extrapolation (rex). InInternational Conference on Machine Learning, pages 5815–5826. PMLR, 2021

    2021

  30. [38]

    How to fine-tune vision models with sgd

    Ananya Kumar, Ruoqi Shen, Sebastien Bubeck, and Suriya Gunasekar. How to fine-tune vision models with sgd. InThe Twelfth International Conference on Learning Representations, 2022

    2022

  31. [39]

    Distributional robustness and transfer learning through empirical bayes.arXiv preprint arXiv:2312.08485, 2023

    Michael Law, Peter B¨ uhlmann, and Ya’acov Ritov. Distributional robustness and transfer learning through empirical bayes.arXiv preprint arXiv:2312.08485, 2023

    2023 arXiv

  32. [40]

    Measuring the intrinsic dimension of objective landscapes

    Chunyuan Li, Heerad Farkhoor, Rosanne Liu, and Jason Yosinski. Measuring the intrinsic dimension of objective landscapes. InInternational Conference on Learning Representations, 2018

    2018

  33. [41]

    Sai Li, T Tony Cai, and Hongzhe Li. Transfer learning for high-dimensional linear regression: Prediction, estimation and minimax optimality.Journal of the Royal Statistical Society Series B: Statistical Methodology, 84(1):149–173, 2022

    2022

  34. [42]

    Deep domain generalization via conditional invariant adversarial networks

    Ya Li, Xinmei Tian, Mingming Gong, Yajing Liu, Tongliang Liu, Kun Zhang, and Dacheng Tao. Deep domain generalization via conditional invariant adversarial networks. InProceedings of the European Conference on Computer Vision (ECCV), pages 624–639, 2018

    2018

  35. [43]

    A simple tool for bounding the deviation of random matrices on geometric sets

    Christopher Liaw, Abbas Mehrabian, Yaniv Plan, and Roman Vershynin. A simple tool for bounding the deviation of random matrices on geometric sets. InGeometric Aspects of Func- tional Analysis: Israel Seminar (GAF A) 2014–2016, pages 277–299. Springer, 2017

    2014

  36. [44]

    Semi-supervised domain adaptation for automatic quality control of flair mris in a clinical data warehouse

    Sophie Loizillon, Olivier Colliot, Lydia Chougar, Sebastian Stroer, Yannick Jacob, Aur´ elien Maire, Didier Dormont, and Ninon Burgos. Semi-supervised domain adaptation for automatic quality control of flair mris in a clinical data warehouse. InMICCAI Workshop on Domain Adapta...

    2023

  37. [45]

    Concentration inequalities under sub-gaussian and sub-exponential conditions.Advances in Neural Information Processing Systems, 34:7588– 7597, 2021

    Andreas Maurer and Massimiliano Pontil. Concentration inequalities under sub-gaussian and sub-exponential conditions.Advances in Neural Information Processing Systems, 34:7588– 7597, 2021. 90

    2021

  38. [46]

    Marginal likelihood for distance matrices.Statistica Sinica, pages 631–649, 2009

    Peter McCullagh. Marginal likelihood for distance matrices.Statistica Sinica, pages 631–649, 2009

    2009

  39. [47]

    A brief note on application of domain-invariant pls for adapting near-infrared spectroscopy calibrations between different physical forms of samples.Talanta, 232:122461, 2021

    Puneet Mishra and Ramin Nikzad-Langerodi. A brief note on application of domain-invariant pls for adapting near-infrared spectroscopy calibrations between different physical forms of samples.Talanta, 232:122461, 2021

    2021

  40. [48]

    Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices.The Annals of Statistics, 50(4):2157–2178, 2022

    Jaouad Mourtada. Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices.The Annals of Statistics, 50(4):2157–2178, 2022

    2022

  41. [49]

    Domain-invariant partial-least-squares regression.Analytical chemistry, 90(11):6693–6701, 2018

    Ramin Nikzad-Langerodi, Werner Zellinger, Edwin Lughofer, and Susanne Saminger-Platz. Domain-invariant partial-least-squares regression.Analytical chemistry, 90(11):6693–6701, 2018

    2018

  42. [50]

    Random perturbation of low rank matrices: Improving classical bounds.Linear Algebra and its Applications, 540:26–59, 2018

    Sean O’Rourke, Van Vu, and Ke Wang. Random perturbation of low rank matrices: Improving classical bounds.Linear Algebra and its Applications, 540:26–59, 2018

    2018

  43. [51]

    A quantitative formulation of sylvester’s law of inertia.Proceedings of the National Academy of Sciences, 45(5):740–744, 1959

    Alexander M Ostrowski. A quantitative formulation of sylvester’s law of inertia.Proceedings of the National Academy of Sciences, 45(5):740–744, 1959

    1959

  44. [52]

    Cambridge university press, 2009

    Judea Pearl.Causality. Cambridge university press, 2009

    2009

  45. [53]

    Moment matching for multi-source domain adaptation

    Xingchao Peng, Qinxun Bai, Xide Xia, Zijun Huang, Kate Saenko, and Bo Wang. Moment matching for multi-source domain adaptation. InProceedings of the IEEE/CVF international conference on computer vision, pages 1406–1415, 2019

    2019

  46. [54]

    Jonas Peters, Peter B¨ uhlmann, and Nicolai Meinshausen. Causal inference by using invariant prediction: identification and confidence intervals.Journal of the Royal Statistical Society: Series B (Statistical Methodology), 78(5):947–1012, 2016

    2016

  47. [55]

    A survey on domain adaptation theory: learning bounds and theoretical guarantees.arXiv preprint arXiv:2004.11829, 2020

    Ievgen Redko, Emilie Morvant, Amaury Habrard, Marc Sebban, and Youn` es Bennani. A survey on domain adaptation theory: learning bounds and theoretical guarantees.arXiv preprint arXiv:2004.11829, 2020

    2004 arXiv

  48. [56]

    An improved cosmological parameter inference scheme motivated by deep learning.Nature Astronomy, 3(1):93–98, 2019

    Dezs˝ o Ribli, B´ alint´Armin Pataki, and Istv´ an Csabai. An improved cosmological parameter inference scheme motivated by deep learning.Nature Astronomy, 3(1):93–98, 2019

    2019

  49. [57]

    An empirical bayes approach to statistics

    Herbert E Robbins. An empirical bayes approach to statistics. InBreakthroughs in Statistics: Foundations and basic theory, pages 388–394. Springer, 1992

    1992

  50. [58]

    Cloning instru- ments, model maintenance and calibration transfer.TrAC Trends in Analytical Chemistry, 191:118319, 2025

    Jean-Michel Roger, Valeria Fonseca Diaz, and Ramin Nikzad-Langerodi. Cloning instru- ments, model maintenance and calibration transfer.TrAC Trends in Analytical Chemistry, 191:118319, 2025

    2025

  51. [59]

    The risks of invariant risk mini- mization.arXiv preprint arXiv:2010.05761, 2020

    Elan Rosenfeld, Pradeep Ravikumar, and Andrej Risteski. The risks of invariant risk mini- mization.arXiv preprint arXiv:2010.05761, 2020

    2010 arXiv

  52. [60]

    Causal dantzig.The Annals of Statistics, 47(3):1688–1722, 2019

    Dominik Rothenh¨ ausler, Peter B¨ uhlmann, and Nicolai Meinshausen. Causal dantzig.The Annals of Statistics, 47(3):1688–1722, 2019

    2019

  53. [61]

    Anchor regression: Heterogeneous data meet causality.Journal of the Royal Statistical Society Series B: Statistical Methodology, 83(2):215–246, 2021

    Dominik Rothenh¨ ausler, Nicolai Meinshausen, Peter B¨ uhlmann, and Jonas Peters. Anchor regression: Heterogeneous data meet causality.Journal of the Royal Statistical Society Series B: Statistical Methodology, 83(2):215–246, 2021. 91

    2021

  54. [62]

    Hanson-wright inequality and sub-gaussian concentra- tion.Electronic Communications in Probability, 18:1–9, 2013

    Mark Rudelson and Roman Vershynin. Hanson-wright inequality and sub-gaussian concentra- tion.Electronic Communications in Probability, 18:1–9, 2013

    2013

  55. [63]

    Distributionally robust neural networks for group shifts: On the importance of regularization for worst-case generalization

    Shiori Sagawa, Pang Wei Koh, Tatsunori B Hashimoto, and Percy Liang. Distributionally robust neural networks for group shifts: On the importance of regularization for worst-case generalization. InInternational Conference on Learning Representations (ICLR), 2020

    2020

  56. [64]

    Semi- supervised domain adaptation via minimax entropy

    Kuniaki Saito, Donghyun Kim, Stan Sclaroff, Trevor Darrell, and Kate Saenko. Semi- supervised domain adaptation via minimax entropy. InProceedings of the IEEE/CVF in- ternational conference on computer vision, pages 8050–8058, 2019

    2019

  57. [65]

    On causal and anticausal learning

    Bernhard Sch¨ olkopf, Dominik Janzing, Jonas Peters, Eleni Sgouritsa, Kun Zhang, and Joris Mooij. On causal and anticausal learning. In29th International Conference on Machine Learning (ICML 2012). International Conference on Machine Learning, 2012

    2012

  58. [66]

    Causality-oriented robustness: Exploiting general noise interventions.Journal of the American Statistical Association, 121(553):704–715, 2026

    Xinwei Shen, Peter B¨ uhlmann, and Armeen Taeb. Causality-oriented robustness: Exploiting general noise interventions.Journal of the American Statistical Association, 121(553):704–715, 2026

    2026

  59. [67]

    Deep coral: Correlation alignment for deep domain adaptation

    Baochen Sun and Kate Saenko. Deep coral: Correlation alignment for deep domain adaptation. InEuropean conference on computer vision, pages 443–450. Springer, 2016

    2016

  60. [68]

    Xudong Sun, Phul Subedi, Rachel Walker, and Kerry B Walsh. Nirs prediction of dry mat- ter content of single olive fruit with consideration of variable sorting for normalisation pre- treatment.Postharvest Biology and Technology, 163:111140, 2020

    2020

  61. [69]

    Achieving robustness to temperature change of a nirs-plsr model for intact mango fruit dry matter content.Postharvest Biology and Tech- nology, 162:111117, 2020

    Xudong Sun, Phul Subedi, and Kerry B Walsh. Achieving robustness to temperature change of a nirs-plsr model for intact mango fruit dry matter content.Postharvest Biology and Tech- nology, 162:111117, 2020

    2020

  62. [70]

    Springer Series in Statistics, 2009

    Alexandre B Tsybakov.Introduction to nonparametric estimation. Springer Series in Statistics, 2009

    2009

  63. [71]

    Weak convergence and empirical processes with ap- plications to statistics.Journal of the Royal Statistical Society-Series A Statistics in Society, 160(3):596–608, 1997

    A W van der Vaart and Jon A Wellner. Weak convergence and empirical processes with ap- plications to statistics.Journal of the Royal Statistical Society-Series A Statistics in Society, 160(3):596–608, 1997

    1997

  64. [72]

    A survey on semi-supervised learning.Machine learning, 109(2):373–440, 2020

    Jesper E Van Engelen and Holger H Hoos. A survey on semi-supervised learning.Machine learning, 109(2):373–440, 2020

    2020

  65. [73]

    Cambridge university press, 2018

    Roman Vershynin.High-dimensional probability: An introduction with applications in data science, volume 47. Cambridge university press, 2018

    2018

  66. [74]

    Cambridge University Press, 2019

    Martin J Wainwright.High-dimensional statistics: A non-asymptotic viewpoint, volume 48. Cambridge University Press, 2019

    2019

  67. [75]

    A survey of unsupervised deep domain adaptation.ACM Transactions on Intelligent Systems and Technology (TIST), 11(5):1–46, 2020

    Garrett Wilson and Diane J Cook. A survey of unsupervised deep domain adaptation.ACM Transactions on Intelligent Systems and Technology (TIST), 11(5):1–46, 2020

    2020

  68. [76]

    Prominent roles of conditionally invariant components in domain adaptation: Theory and algorithms.Journal of Machine Learning Research, 26(110):1–92, 2025

    Keru Wu, Yuansi Chen, Wooseok Ha, and Bin Yu. Prominent roles of conditionally invariant components in domain adaptation: Theory and algorithms.Journal of Machine Learning Research, 26(110):1–92, 2025. 92

    2025

  69. [77]

    Distributionally robust transfer learning.arXiv preprint arXiv:2309.06534, 2023

    Xin Xiong, Zijian Guo, and Tianxi Cai. Distributionally robust transfer learning.arXiv preprint arXiv:2309.06534, 2023

    2023 arXiv

  70. [78]

    Multi-level consistency learning for semi-supervised domain adaptation.arXiv preprint arXiv:2205.04066, 2022

    Zizheng Yan, Yushuang Wu, Guanbin Li, Yipeng Qin, Xiaoguang Han, and Shuguang Cui. Multi-level consistency learning for semi-supervised domain adaptation.arXiv preprint arXiv:2205.04066, 2022

    2022 arXiv

  71. [79]

    Deep co-training with task decomposition for semi-supervised domain adaptation

    Luyu Yang, Yan Wang, Mingfei Gao, Abhinav Shrivastava, Kilian Q Weinberger, Wei-Lun Chao, and Ser-Nam Lim. Deep co-training with task decomposition for semi-supervised domain adaptation. InProceedings of the IEEE/CVF international conference on computer vision, pages 8906–8916, 2021

    2021

  72. [80]

    Im- proving domain generalization with domain relations

    Huaxiu Yao, Xinyu Yang, Xinyi Pan, Shengchao Liu, Pang Wei Koh, and Chelsea Finn. Im- proving domain generalization with domain relations. InThe Twelfth International Conference on Learning Representations, 2024. URLhttps://openreview.net/forum?id=Dc4rXq3HIA

    2024

  73. [81]

    A useful variant of the davis–kahan theorem for statisticians.Biometrika, 102(2):315–323, 2015

    Yi Yu, Tengyao Wang, and Richard J Samworth. A useful variant of the davis–kahan theorem for statisticians.Biometrika, 102(2):315–323, 2015

    2015

  74. [82]

    Semi-supervised domain adaptation with source label adapta- tion

    Yu-Chu Yu and Hsuan-Tien Lin. Semi-supervised domain adaptation with source label adapta- tion. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 24100–24109, 2023

    2023

  75. [83]

    On learning invariant representations for domain adaptation

    Han Zhao, Remi Tachet Des Combes, Kun Zhang, and Geoffrey Gordon. On learning invariant representations for domain adaptation. InInternational conference on machine learning, pages 7523–7532. PMLR, 2019

    2019

  76. [84]

    Pls subspace- based calibration transfer for near-infrared spectroscopy quantitative analysis.Molecules, 24 (7):1289, 2019

    Yuhui Zhao, Jinlong Yu, Peng Shan, Ziheng Zhao, Xueying Jiang, and Shuli Gao. Pls subspace- based calibration transfer for near-infrared spectroscopy quantitative analysis.Molecules, 24 (7):1289, 2019

    2019

  77. [85]

    Calibration transfer based on affine invariance for nir without transfer standards.Molecules, 24(9):1802, 2019

    Yuhui Zhao, Ziheng Zhao, Peng Shan, Silong Peng, Jinlong Yu, and Shuli Gao. Calibration transfer based on affine invariance for nir without transfer standards.Molecules, 24(9):1802, 2019

    2019

  78. [86]

    Domain generalization: A survey.IEEE transactions on pattern analysis and machine intelligence, 45(4):4396–4415, 2022

    Kaiyang Zhou, Ziwei Liu, Yu Qiao, Tao Xiang, and Chen Change Loy. Domain generalization: A survey.IEEE transactions on pattern analysis and machine intelligence, 45(4):4396–4415, 2022. 93

    2022

Pith tools

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