Test-Time Adaptation (TTA) methods aim to bridge the domain gap between the source and target domains. However, traditional TTA methods become ineffective when the label distribution shift occurs, a challenge commonly referred to as an open-world scenario. In this paper, we introduce a new method named Reliable Neural Collapse approximation (ReNC) for Open-World Test-Time Adaptation (OWTTA). Specifically, we leverage neural collapse as a structural prior for reliable target-domain adaptation. Guided by this prior, we justify that the pre-trained classifier weights can serve as the prototypes of the source domain. By measuring the similarity between samples and prototypes, we filter out the Out-Of-Distribution~(OOD) samples for reliable updates. Furthermore, we propose a neural collapse approximation mechanism to refine these prototypes, ensuring they can gradually adapt to the target domain while maintaining the neural collapse structure. Extensive experiments on several open-world benchmarks demonstrate the superiority of the proposed method. Our empirical analysis suggests that ReNC better preserves NC-related properties in the target domain, providing useful evidence for explaining reliable OWTTA and offering new insights for model design. Code is available at https://github.com/JiaqiLin-AI/ReNC.
Juan Pablo Villa Serna, Rohan Asthana, Vasileios Belagianniscs.LG
Time series forecasting with pretrained foundation models has demonstrated strong zero-shot capabilities. However, achieving optimal performance on time series with short or negligible historical data in domain-specific applications typically requires adaptation via either fine-tuning or RAG. While fine-tuning is effective, it incurs substantial computational costs. This work explores RAG within univariate time series (Retrieval Augmented Generation) as a more efficient alternative, in particular RAF (Retrieval Augmented Forecasting), and introduces RAEF (Retrieval-Augmented Extended Forecasting), a model-agnostic method built upon RAF. RAEF incorporates key refinements to the retrieval and aggregation mechanisms: (1) direct retrieval in input-space rather than embedding-space, reducing inference overhead, and (2) concatenation-based aggregation that preserves temporal structure instead of averaging. Empirical evaluation across multiple benchmark datasets demonstrates that RAEF outperforms RAF in both accuracy and inference overhead. Furthermore, comprehensive comparisons with zero-shot and fine-tuned foundation models show that RAEF achieves competitive or superior performance to fine-tuning while avoiding its computational burden, establishing it as a practical and scalable approach for domain adaptation in time series forecasting.
In high-stakes applications, reliable confidence estimates are as important as the predictions themselves. Confidence calibration ensures that predicted probabilities reflect the likelihood of correctness, making it essential for safe deployment of deep learning models. However, existing methods typically assume access to clean validation data, which is often unrealistic due to label noise and domain shifts. This thesis develops methods for improving calibration under these conditions. First, we address calibration under label noise. Standard methods can produce misleading confidence estimates when labels are unreliable. We propose a framework that uses an estimated noise model to reconstruct noise-free confidence estimates by modeling the relationship between noisy and clean label distributions. We extend this approach to Conformal Prediction (CP), which provides set-valued predictions with guaranteed coverage. Our noise-aware CP method estimates clean conformity scores despite label noise, enabling reliable uncertainty quantification. Next, we study calibration in unsupervised domain adaptation, where a model trained on a labeled source domain is adapted to an unlabeled target domain. Since labeled target data are unavailable, we estimate target-domain accuracy from source performance and domain discrepancies, enabling calibration without target labels. We also consider privacy-preserving settings in which user labels and model outputs must remain protected. We propose a locally differentially private conformal prediction framework that provides valid uncertainty quantification while maintaining privacy guarantees and balancing privacy, computational feasibility, and prediction reliability. Our results bridge calibration theory and practical deployment in safety-critical applications, contributing to reliable, privacy-preserving, and noise-resilient neural network predictions.
Unsupervised time-series domain adaptation (DA) addresses the challenge of transferring a classifier from a labeled source domain to an unlabeled target domain under distribution shifts induced by different users, sensors, devices, acquisition conditions, or temporal dynamics. Existing methods typically mitigate this shift by aligning marginal feature distributions through adversarial training, optimal transport, or moment-based discrepancies. In this paper, we propose Class-Conditional Path Distribution Alignment (CPDA), a non-adversarial discrepancy-based framework that aligns source and target class-conditional latent path distributions rather than only global feature marginals. CPDA introduces a composite signature-spectral kernel that jointly captures pooled semantic features, temporal path structure, frequency-domain information, and low-rank path-signature dynamics, while using source labels and target soft pseudo-labels to perform class-preserving alignment. We further provide a theoretical analysis showing that CPDA defines a valid kernel discrepancy, admits existing moment-matching methods as restricted cases, and yields a class-conditional target-risk bound. Extensive experiments with CNN, ResNet18, and TCN backbones on 13 different time-series DA benchmarks demonstrate the effectiveness of CPDA against 30 discrepancy, adversarial, and pseudo-labeling baselines.
Digital pens are commonly used to write on digital devices, providing the handwriting trace and enhancing human-computer interation. This study focuses on a digital pen equipped with kinematic sensors, allowing users to write on any surface while simultaneously preserving a digital trajectory of handwriting. This technology holds significant potential as a valuable educational tool, particularly in classrooms where it can facilitate the process of learning to write. A major issue is based on the difference in captured signals between adults and children. For similar handwriting trace, we have large differences in sensor signals due to differences in speed and confidence in the handwriting gesture of children. To address this, we investigate a domain adaptation approach to build a unified intermediate feature representation aimed at facilitating the trajectory reconstruction. We demonstrate the interest of domain adaptation methods in leveraging existing knowledge for application in different contexts. Specifically, we compare our domain adaptation approach with two other methods: training the model from scratch and fine-tuning the model.
This paper studies the problem of stochastic variance reduction (SVR) for the maximum mean discrepancy (MMD) and correlation alignment (CORAL) loss functions. Although various offline SVR algorithms for these losses have been proposed, these are incompatible with online, distributed, or incremental learning settings. This paper presents Adaptive vaRiance Reduction via Online reWeighting (ARROW), the first online SVR algorithm for the MMD and CORAL for streamed data. The method maintains moving average references of the alignment statistics, and adaptively reweights incoming minibatches so that the minibatch and reference statistics are aligned. Further, we propose a relaxed reweighting scheme so that the ensuing weight-optimisation problem is tractable. In experiments and simulations, we show that ARROW performs competitively with offline algorithms in terms of runtime, degree of variance reduction achieved, and target domain accuracy.
Correlation alignment and the maximum mean discrepancy are two widely used distribution-matching frameworks for unsupervised domain adaptation (UDA). However, high variance in these losses has been shown to undermine their effectiveness in minibatch optimisation settings. Furthermore, the losses lack finite-sum structure, which renders them incompatible with classical stochastic variance reduction (SVR) methods. This paper proposes Paired Sampling for Domain Adaptation (PSDA), a novel SVR technique tailored to such objectives. PSDA pairs observations both within and across domains, to form quadruplets that are always sampled together during training. The pairings are designed to minimise expected gradient variance, and reduce to solving a set of linear assignment problems. Our simulations demonstrate reduced variance compared to related methods, and experiments on three domain shift datasets show improved target domain accuracy.
Predicting thermal volatility in high-performance EV powertrains is difficult as internal temperatures are rarely observable outside the lab, and models calibrated on lab drive cycles fail when deployed against real-world loads. We study this lab-to-track transfer problem using conformal prediction, offering distribution-free uncertainty bounds. We implement Ensemble Batch Prediction Intervals (EnbPI; Xu & Xie, 2021), a leave-one-out bootstrap-ensemble conformal method for autocorrelated time series, and calibrate it on real CALCE lithium-ion cycler data (A123 SP20 cells, FUDS profile). We evaluate it under a genuine, measured covariate shift: a second real CALCE test condition (US06 Highway Driving Schedule at 45°C). The unweighted EnbPI bound, achieving its nominal 95% coverage in-distribution (measured: 95.00%), degrades to 70.13% empirical coverage under this real shift. We introduce a weighted EnbPI procedure combining EnbPI's ensemble residuals with density-ratio weighting (Tibshirani et al., 2019), estimating the density ratio via a probabilistic domain classifier. This recovers coverage to 72.42%, a modest, honestly-reported improvement, not a complete fix. We additionally apply the calibrated model to real 2023 Formula 1 telemetry (Monza and Silverstone, driver VER) as an unsupervised out-of-distribution diagnostic. Because no internal thermal channel exists in public trackside telemetry, we report only unsupervised flag rates (65.6% at Monza, 58.0% at Silverstone, well above the 5% in-distribution base rate) and note inconsistent associations between flags and braking/DRS zones. We conclude that conformal domain adaptation is a promising but only partially solved tool for this problem, detailing exactly where it falls short.
Covariance matrices serve as compact descriptors of feature distributions in many machine-learning pipelines, including domain adaptation and Gaussian embeddings. Under a centered Gaussian approximation, the unregularized Wasserstein-2 optimal-transport (OT) discrepancy admits a closed form on covariances given by the Bures-Wasserstein (BW) objective on the symmetric positive definite (SPD) cone. We propose ITSPACE (Iterative Transport for Stable Proximal Alignment of Covariance Embeddings), a proximal majorization-minimization method that directly optimizes this exact BW objective through closed-form updates in a square-root factorization. In exact arithmetic, each iteration satisfies a sufficient-decrease inequality for the BW objective; under inexact polar computations, we provide an explicit certificate-gap bound controlling deviations from exact descent. The resulting iterations preserve PSD structure by construction and naturally support rank-restricted factors, making ITSPACE well-suited as a lightweight inner-loop primitive in settings where adaptation must be performed from unlabeled target batches under strict step and compute budgets. Across real-world covariance-alignment benchmarks, ITSPACE reaches low-BW-gap solutions substantially faster than BW-gradient descent, methods based on other covariance geometries, and entropically regularized sample-OT baselines.
The goal of source-free domain adaptation (SFDA) for time-series data is to transfer knowledge from a pre-trained source model to an unlabeled target domain without requiring access to source data, while addressing feature shift and temporal drift inherent in the signals. Although existing approaches have explored temporal dynamics in unsupervised source-free adaptation, they largely overlook spectral shifts in time-series data. Towards this end, we propose a novel approach termed temporal-Spectral Alignment with Frequency Adaptation (SAFA) for source-free time-series domain adaptation. Specifically, we first model the source domain at multiple scales by jointly capturing temporal dependencies and spectral characteristics. To adapt time-series data in the target domain, we introduce a trainable frequency adaptation module that modulates the phase and amplitude of target signals in the frequency domain to align them with the source distribution. Extensive experiments on multiple benchmark datasets demonstrate the efficacy and robustness of SAFA.
Hanna Myleiko, Sergei Solodky, Vasyl Semenovstat.ML cs.LG math.NA
This paper investigates convergence properties of regularized Nyström subsampling applied to the unsupervised domain adaptation problem under covariate shift. We focus on the low-smoothness (misspecified) case where the target function lies outside the reproducing kernel Hilbert space. By combining Tikhonov regularization with Nyström projection onto a subsampled subspace, we obtain upper bounds on the excess risk that hold with high probability and are expressed in terms of the source condition, the effective dimension, and the sample sizes. We further extend the analysis to the setting where the Radon-Nikodym derivative between the target and source marginal distributions is unknown and must be approximated, and we identify the minimal additional sample sizes required to maintain the same convergence rate as in the oracle case.
Synthesizing realistic time series with generative models has wide-ranging applications in real-world scenarios. Despite recent progress, most existing methods are trained under the assumption of abundant training data, which substantially limits their effectiveness in data-scarce settings. In this paper, we propose TimeMoDE, a novel framework that integrates Diffusion Transformers with Mixture-of-Experts to exploit both domain adaptability and diffusion-stage awareness for time series generation under data scarcity. It is pre-trained on a large-scale collection of multi-domain datasets to extract domain-agnostic temporal representations and domain-specific information benefiting generalization during fine-tuning. We propose Domain Prompts to condition expert assignment for indistinguishable noised tokens, mitigating the limitations of capturing inter-dataset relationships. Moreover, we incorporate diffusion timestep signals to equip the experts with awareness of time series degradation variations, facilitating adaptive calibrate to stage-dependent denoising requirements. Extensive experiments demonstrate that TimeMoDE outperforms existing methods under diverse low-data settings. It establishes an innovative paradigm for advanced time series few-shot generation.
Optimal Transport has become recently a powerful method for domain adaptation by aligning source and target distributions. We study a supervised domain adaptation problem where source and target domains are related by a rotation or a translation or a homothety in $\mathbb{R}^2$. We prove that the optimal transport map recovers the underlying map when using a $p-$norm cost with $p \geq 2$. Based on this insight, we develop a method combining $K-$means and optimal transport to estimate the underlying map, enabling adaptation of linear regression models when target data is scarce. Simulations demonstrate improved performance over baseline methods. Rather than relying on highly expressive deep learning architectures, we focus on classical machine learning models to emphasize interpretability and theoretical insight. This perspective allows us to explicitly characterize the role of optimal transport in recovering geometric transformations such as rotations, translations, and homotheties. Our contributions include a theoretical result linking optimal transport and rotations, translations and homothecies in $\mathbb{R}^2$, and a practical method for adaptation in linear regression offering both conceptual clarity and applied value in domain adaptation tasks in this space.
Julia Kostin, Kasra Jalaldoust, Elias Bareinboim +2cs.LG stat.ML
Machine learning models often degrade when they are deployed on a target distribution that differs from the source distributions they were trained on. Recent work in causality-based domain generalization has shown how shared causal structure between domains can induce invariant predictors, e.g., models on a subset of features which have stable risk across structured domain shifts. However, the extent to which such population-level causal invariances can lead to gains in finite-sample settings remains underexplored. In particular, in practice we often have access to a few labeled target samples, a setting called supervised domain adaptation (sDA). In this paper, we explore when (full or partial) causal knowledge can provably improve supervised domain adaptation. As a first step, we study linear regression, where full or partial causal knowledge specifies a collection of invariant or possibly invariant feature subsets, each yielding a source-trained candidate predictor. We derive matching upper and lower bounds showing that finite-sample gains are governed by the target-risk margins separating the candidates, together with the finite-source estimation error. When these margins are sufficiently large relative to $n_Q$, an adaptive aggregation procedure can match the best candidate predictor while avoiding negative transfer relative to target-only learning. On the other hand, when the margins are too small, no algorithm can reliably exploit the candidate collection to obtain faster finite-sample rates. We further connect these margins to structural shift magnitude in linear SCMs and validate the theory on real-world causal benchmarks.
Modern data-driven applications increasingly involve learning from multiple heterogeneous sources, where a target dataset is limited but related information is available across domains. Naively combining these sources can degrade performance when relevance varies or spurious signals are present, posing a fundamental challenge for trustworthy cross-domain learning. We propose Projection Transfer Learning (ProjectionTL), a unified framework that integrates hierarchical Bayesian modeling with adaptive projection for selective knowledge transfer. The key idea is to decouple transfer at two levels: first, we construct a source-guided hierarchical prior that aggregates information across sources using data-driven weights, capturing global alignment between each source and the target; second, we refine this borrowing through a posterior-projection step that operates at the feature level, selectively retaining coordinates that exhibit local agreement with the target signal. This two-stage design enables the method to simultaneously perform source selection and feature selection, thereby mitigating negative transfer while preserving interpretability. ProjectionTL provides a principled approach to integrating heterogeneous data across domains, bridging statistical modeling and modern machine learning paradigms for robust and interpretable transfer. Through simulations and real-world biomedical applications, we demonstrate improved accuracy, stability, and interpretability compared to existing methods. Our framework offers a scalable and generalizable strategy for trustworthy cross-domain learning in high-dimensional settings.
Deep unsupervised domain adaptation (Deep UDA) methods successfully leverage rich labeled data in a source domain to boost the performance on related but unlabeled data in a target domain. However, algorithm comparison is cumbersome in Deep UDA due to the absence of accurate and standardized model selection method, posing an obstacle to further advances in the field. Existing model selection methods for Deep UDA are either highly biased, restricted, unstable, or even controversial (requiring labeled target data). To this end, we propose \textit{Deep Embedded Validation} (\textbf{DEV}), which embeds adapted feature representation into the validation procedure to obtain unbiased estimation of the target risk with bounded variance. The variance is further reduced by the technique of control variate. The efficacy of the method has been justified both theoretically and empirically.