Research map / Probabilistic and scientific modeling / Variational and generative sampling
ReTaSA: A Nonparametric Functional Estimation Approach for Addressing Continuous Target Shift
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Proposes ReTaSA, a Tikhonov-regularized nonparametric (kernel-based) method that estimates the continuous target-shift importance weight by solving an ill-posed integral equation via a linear system, with consistency and convergence-rate guarantees.
Problem
Target shift in regression, where the continuous target y has different marginals in source and target while p(x|y) is invariant; importance weights for continuous y require solving an ill-posed Fredholm integral equation of the first kind.
Approach
Reformulates the continuous importance weight as the solution of an integral equation T rho = eta, and solves it with Tikhonov regularization using kernel density estimates of conditional expectation operators, yielding an optimization-free closed-form linear-system estimator with theoretical consistency rates (unlike KMM and L2IWE, which require QCQP).
Key results
- Proves consistency of the regularized importance weight estimator in weighted L2 norm, with an explicit O_p rate in regularization alpha, bandwidth h, and sample sizes n and m (for beta >= 2).
- Reports that ReTaSA surpasses KMM and L2IWE in estimation accuracy and computational efficiency on synthetic and real-world datasets (specific numbers not given in the provided text).
Limitations
- Consistency requires decaying bandwidth and regularization parameters and sample-size conditions that become costly in high dimensions.
- Hyperparameter (bandwidth and regularization) selection is left largely unspecified in the text.
- Assumes support of target density is contained in source support and densities bounded away from zero.
Experimental setup
Datasets: synthetic data real-world datasets (unnamed in text)
Metrics: estimation accuracy of importance weights computational efficiency
Baselines: KMM L2IWE
Builds on: Black-box shift estimation KMM L2IWE
Closest papers by meaning
- Towards a Unified Analysis of Kernel-based Methods Under Covariate Shift (NeurIPS 2023 · similarity 0.85)
- Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift (ICLR 2025 · similarity 0.84)
- Evaluating Robustness to Dataset Shift via Parametric Robustness Sets (NeurIPS 2022 · similarity 0.84)
- Out of the Ordinary: Spectrally Adapting Regression for Covariate Shift (ICML 2024 · similarity 0.83)
- Learning from Interval Targets (NeurIPS 2025 · similarity 0.83)
- Optimizing importance weighting in the presence of sub-population shifts (ICLR 2025 · similarity 0.82)
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