Title: Enhancing Deep Batch Active Learning for Regression with Imperfect Data Guided Selection
Venue: NeurIPS 2025
Accepted: yes
Keywords: Batch mode deep active learning; Auxiliary data; Regression
Abstract: Active learning (AL) reduces annotation costs by  selecting the most informative samples based on both model sensitivity and predictive uncertainty. While sensitivity can be measured through parameter gradients in an unsupervised manner, predictive uncertainty can hardly be estimated without true labels especially for  regression tasks, reducing the informativeness of actively selected samples. This paper proposes the concept of \textit{auxiliary data} to aid the uncertainty estimation for regression tasks. With detailed theoretical analysis, we reveal that auxiliary data, despite potential distribution shifts, can provide a promising uncertainty surrogate when properly weighted. Such finding inspires our design of AGBAL, a novel AL framework that recalibrates auxiliary data losses through density ratio weighting to obtain reliable uncertainty estimates for sample selection. Extensive experiments show that AGBAL consistently outperforms existing approaches without auxiliary data across diverse synthetic and real-world datasets.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes an active learning approach that leverages auxiliary data (data that is distributionally shifted but relevant) to help with predicting sample uncertainty. The approach uses this data to estimate density ratio between auxiliary and target data distributions, compute model's loss on auxiliary data, and then apply density ratio weighting to obtain approximation of true loss. The paper then verifies their approach through theoretical analysis based on Neural Tangent Kernel theory. Results show strong performance of their approch.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n* Intuitive yet innovative active learning approach to using auxiliary data \n* Well-supported analysis of their proposed approach \n* Writing and motivation is clear throughout the paper\n* Empirical results show consistent improvement with their proposed approach and appendix has very thorough experimentation ablations\n\nWeaknesses:\n* Lack of mentions/comparison against prior work that also make use of auxiliary data for active learning (eg \"Active Transfer Learning under Model Shift\" [2014])\n* As mentioned in paper's limitations, unsure how NTK analysis translates to real-world applications as it assumes infinite-width network approximation\n* Lack of clarity on experiments compute resource. While the paper runs many experiments, it is unclear how costly their proposed approach is in terms of compute resources and time.\n\nQUESTIONS:\n1. How does your method compare against prior works that also use auxiliary data in active learning?\n2. How does your method compare against baselines in terms of compute resources and time?\n3. Are there any sort of analysis or arguments that can be extended to understand how the proposed approach may translate to real-world applications?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-06"}

comments: SUMMARY:
The paper addresses a long standing problem that in order to know to the gradient for gradients which are required for active learning one usually needs to know the labels if not relaying on strong model assumptions. The paper attempts to solve this egg and chicken problem using similarly, but different, auxiliary data, for which the labels are known. Trough that, the problem is transferred from knowing $p(x,y)$ to knowing $r(x,y)\coloneqq \frac{p(x,y)}{q(x,y)}$.

STRENGTHS AND WEAKNESSES:
**Strengths**
1. The problem is important and the mathematics looks sound (I did not check proofs).
2. The core idea is original interesting.
3. Experimental results are encouraging.

**Weaknesses**
1. It is not clear for me what is the meaning of the theoretical result, what it guarantees and in which practical conditions.  
2. The theoretical result is only applicable for in the infinite width regime. 
3. The paper only deals with the square loss.
 
(Points 2 and 3 are pointed out as  limitations by the authors in the checklist)

QUESTIONS:
1. Why we need to assume $\hat{r}$ is independent of $X_i',Y_i' \sim Q$ (line 153) and why is it reasonable  to assume so.
2. Line 90: (a) Is $\mathcal A$ a function that takes in its second argument an **infinite** training set from $(\mathcal{X}\times\mathcal{Y})^\mathbb{N}$; (b) why does $\mathcal A$ needs the initial parameter in its first argument, how is it been used in the rest of the paper?
3. Why do we need to expect that the estimation.
4. Line 162: why do we expect $\rho$ to be small?
5. What is the  limit of $\mathbb{E}[\hat{\phi}_2(\hat{\theta},x_0)]$ ?
6. Table 1: why is lower AUC better (usually larger is better)?

LIMITATIONS:
Yes, in the checklist.
TITLE: Official Review
CLARITY: 2
IMPACT: 2
ORIGINALITY: 4
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper focuses on deep batch active learning for regression tasks where obtaining labels is typically costly, and the objective is to identify a small set of informative unlabeled instances to label, thereby improving the predictive performance of deep learning models. The active selection process typically relies on measures such as model sensitivity and predictive uncertainty. While model sensitivity can be estimated using only unlabeled data, obtaining reliable uncertainty estimates can be markedly challenged by the scarcity of available labeled data. To address this, the paper proposes leveraging auxiliary data, typically drawn from a different distribution than the target task, to guide the active selection process. Although such auxiliary data cannot be directly used to train deep learning models for the main task of interest, the paper shows that they can be used to efficiently estimate the predictive uncertainty to guide the AL process. The proposed method approximates the model's loss by first estimating the density ratio between the auxiliary and main/target data distributions, then computing the model’s loss on the auxiliary data, and finally applying a density ratio weighting scheme. Numerical tests on both synthetic and real-world datasets demonstrate that incorporating auxiliary data in this manner leads to improved performance over the gradient kernel-based BMDAL method, which does not use auxiliary data. The proposed approach is further supported by theoretical analysis via the notion of neural tangent kernels.\n\nSTRENGTHS AND WEAKNESSES:\nSTRENGTHS \n\n(S1) The idea of judiciously leveraging auxiliary data to obtain reliable estimates of the model predictive uncertainty that can readily guide the active selection process seems interesting, intuitive, and effective. \n\n(S2) The background, motivation and key concepts of the proposed method are well presented in general. \n\n(S3) The proposed approach is supported by a well-motivated theoretical analysis. \n\n(S4) The literature review is comprehensive. \n\n\nWEAKNESSES\n\n(W1) The paper does not provide an analysis or discussion of the computational complexity of the proposed method, and it does not report the running time of the proposed method compared to the baselines that do not process auxiliary data in the numerical evaluation. Since leveraging and processing auxiliary data using the density ratio weighting approach introduces additional computational overhead, in my opinion it is important to discuss this additional complexity and show the running time demonstrating the trade-off between prediction performance and running time. \n\n(W2) The proposed method is not compared against effective model predictive uncertainty estimation approaches that can be used for AL; see e.g. [1], [2]. Such an additional test/comparison both in terms of prediction performance and running time, in my opinion is important to further demonstrate the benefits of the proposed approach.  \n\n[1] Lakshminarayanan, B., Pritzel, A., & Blundell, C. (2017). Simple and scalable predictive uncertainty estimation using deep ensembles. Advances in neural information processing systems, 30.\n\n[2] Gal, Y., & Ghahramani, Z. (2016, June). Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In International conference on machine learning (pp. 1050-1059). PMLR.\n\nQUESTIONS:\nPlease refer to weaknesses W1,W2 above. In addition, some questions are listed below:\n\nQ1. What are the properties of the auxiliary dataset relative to the target dataset of the main task, so that the proposed method can be effective?\n\nQ2. What is the role of the size of the auxiliary dataset in the performance of the proposed approach?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes AGBAL (Auxiliary data Guided Batch Active Learning), a new framework for regression-based active learning that incorporates imperfect auxiliary data to better estimate predictive uncertainty. Unlike prior methods which rely heavily on model gradients alone, AGBAL estimates the expected loss gradient by weighting auxiliary data losses using a density ratio between auxiliary and target distributions. The estimated gradient is then used to define an auxiliary-data-guided gradient kernel, improving sample selection strategies. The method is theoretically grounded with derivations based on NTK (Neural Tangent Kernel) theory and evaluated on synthetic and real-world regression datasets, showing consistent performance gains over conventional approaches.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n- Novelty: The idea of leveraging auxiliary (distribution-shifted) data via density ratio-weighted gradient approximation is conceptually fresh and well-motivated for regression tasks, where predictive uncertainty is hard to estimate without labels.\n- Theoretical Rigor: The authors provide solid mathematical grounding, including an NTK-based analysis showing how the auxiliary-guided gradient approximates the true expected loss gradient.\n- Empirical Effectiveness: Extensive experiments on multiple datasets and across various selection strategies demonstrate that AGBAL consistently improves MSE and convergence over baseline methods.\n\nWeaknesses\n- Dependency on Auxiliary Data Quality: The method assumes the availability of auxiliary data that is not only relevant to the target task but also sufficiently high quality. As shown in the authors’ own ablation study (Fig. 2), performance deteriorates when the auxiliary data distribution is heavily shifted. In practice, ensuring auxiliary data quality may be non-trivial.\n- Resemblance to Importance Sampling: The core mechanism of re-weighting auxiliary losses by a density ratio is reminiscent of importance sampling in off-policy learning or domain adaptation. While the authors mention this connection, a clearer differentiation—conceptually or in results—is needed.\n- Bias in Target Labeled Set (Lₜ): The estimation of the density ratio relies on the labeled target dataset Lₜ, which is obtained through active learning. However, such data is typically biased, as AL tends to over-sample uncertain or diverse examples. This raises concerns about the validity of the density ratio estimation and the generalizability of the reweighted losses.\n- Auxiliary Uncertainty Estimation is Still Model-Dependent: Although the method avoids relying solely on model gradients, the uncertainty estimation through auxiliary loss still depends on a trained model, and errors or biases in that model can propagate into the selection process.\n- Borderline Scalability: The full method requires training and maintaining auxiliary loss estimators, density ratio estimators, and selection kernels, which could add computational burden compared to simpler gradient-based AL strategies.\n- Readability: Certain sections of the paper-particulary Section 2.3- are difficult to follow. The exposition is mathematically dense and lacks intuition-building commentary. The derivation involving NTK-based decomposition of loss gradient estimation is correct but could benefit from clearer structure, step-wise annotations, or illustrative figures.\n- Scalability and Complexity: The full pipeline involves model training, auxiliary data loss computation, density ratio estimation, and guided kernel construction. The practical cost of running AGBAL is not clearly discussed, making it less attractive for low-resource or fast-iteration settings.\n\nQUESTIONS:\n1. How robust is AGBAL to mislabeled or low-quality auxiliary data? Can performance degrade catastrophically if auxiliary data is noisy, even if the density ratio is correctly estimated?\n2. How is AGBAL fundamentally different from importance sampling or domain adaptation weighting schemes? Could this approach be viewed as an instance of transfer-active learning with a known source domain?\n3. Given that Lₜ is actively selected and thus biased, how reliable is it as a reference for estimating the density ratio or surrogate gradients? Would using a small, randomly labeled validation set instead improve stability?\n4. Could the auxiliary data be adversarially exploited? Since the method uses them for uncertainty estimation, poorly aligned auxiliary data could potentially misguide the acquisition function.\n5. Can this framework be extended to classification tasks, or is it strictly limited to regression? The kernel-based formulation and surrogate gradient approximation might generalize.\n\nLIMITATIONS:\n- Biased Labeled Set (Lₜ): The framework assumes Lₜ to be a reliable proxy for the target distribution, but active learning selection is inherently biased.\n- Data Quality Sensitivity: The performance is highly sensitive to the quality of the auxiliary dataset and the correctness of the density ratio estimation.\n- Distribution Matching Assumption: The method assumes that the auxiliary distribution is absolutely continuous with respect to the target distribution, which may not hold in real-world cases (e.g., outlier auxiliary sources).", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-03"}