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A Framework and Benchmark for Deep Batch Active Learning for Regression

David HolzmüllerViktor ZaverkinJohannes KästnerIngo Steinwart

article2023JMLR73 citations

Presents a modular kernel-based framework, an efficient neural tangent kernel sketching technique paired with a novel clustering selection method, and an open-source 15-dataset benchmark to advance deep batch active learning for regression.

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Supervised deep learning models have achieved remarkable success across diverse predictive applications, but their performance typically depends on access to large volumes of labeled data. In many practical engineering, physical, and scientific regression problems, obtaining accurate labels requires costly physical experiments, complex numerical simulations, or intensive manual measurements. While active learning addresses this by selectively querying informative data points, evaluating neural networks sequentially after each single label is computationally prohibitive and blocks parallel workflows. Batch-mode deep active learning overcomes this bottleneck by selecting batches of unlabeled data simultaneously, yet systematic frameworks and comprehensive benchmarks for continuous regression tasks remain underdeveloped.

To address this gap, the article establishes a modular, unified framework for constructing batch active learning algorithms and introduces a standardized tabular regression benchmark to evaluate their effectiveness. The core objective is to systematically analyze and improve sample efficiency in deep regression models without requiring changes to underlying neural network architectures or training routines.

Methodologically, the framework decomposes active learning workflows into three modular components: a base kernel capturing model representations, kernel transformations for statistical modeling and efficiency, and an iterative selection method that queries candidate points. The authors evaluate this approach using an open-source benchmark of 15 large tabular regression datasets spanning up to 379 features and hundreds of thousands of candidate points. Experiments evaluate fully connected neural networks across 20 randomized splits and 16 sequential batch acquisitions, tracking metrics including root mean squared error, mean absolute error, tail quantiles, and maximum error.

The findings establish that replacing standard last-layer feature representations with a sketched, finite-width neural tangent kernel consistently improves predictive accuracy across selection strategies. Furthermore, random feature sketching drastically reduces computational overhead with negligible loss in accuracy. Crucially, the authors' newly developed clustering selection strategy—Largest Cluster Maximum Distance—consistently outperforms existing state-of-the-art methods in both root mean squared error and mean absolute error. The top-performing active learning configurations achieve the predictive accuracy of random sampling using roughly half as much labeled data, while executing batch selections in just seconds on modern hardware.

These performance gains demonstrate substantial real-world value by significantly cutting experimental labeling costs, reducing turnaround times, and boosting model reliability. Tail error improvements also suggest stronger robustness against extreme modeling failures. Additionally, the article identifies that datasets displaying higher initial prediction error variance derive the greatest relative benefit from active batch selection, offering practitioners a practical indicator for when to implement these methods.

Organizations training deep regression models on expensive data should adopt batch active learning using sketched neural tangent representations combined with balanced clustering-based selection methods. For standard accuracy targets, Largest Cluster Maximum Distance offers the best performance profile, whereas geometric distance maximization remains a strong alternative if worst-case errors or covariate shifts are primary concerns.

Confidence in these findings is bolstered by rigorous statistical testing across multiple random seeds, datasets, and activation functions. However, practitioners should note that the evaluation is confined to fully connected networks on tabular data without explicit distribution shifts between candidate and operational test sets. Further validation is warranted before generalizing these conclusions to non-tabular modalities, custom domain architectures, or streaming data environments.

Faculty of ChemistryFaculty of Mathematics and PhysicsInstitute for Stochastics and ApplicationsInstitute for Theoretical ChemistryUniversity of Stuttgartactive learningdeep batch active learningactive data selectionFrank-Wolfe optimization
arXiv: 2203.09410dholzmueller/bmdal_reg
  • Paper: Active Learning with Statistical Models, David Cohn et al. (1996). Its variance-based query criteria for locally weighted regression provide a foundation for understanding how active selection can target informative observations in continuous prediction tasks.
  • Paper: Active Learning for Convolutional Neural Networks: A Core-Set Approach, Ozan Sener et al. (2018). Its core-set formulation makes the batch-selection challenge concrete: selecting a diverse subset helps avoid redundant queries, a central concern in the source’s clustering methods.
  • Paper: Neural Network Ensembles, Cross Validation, and Active Learning, Anders Krogh et al. (1994). Its use of neural-network disagreement to guide active selection of continuous-function examples introduces a model-based selection idea that helps contextualize the source’s regression strategies.
  • Paper: A Survey of Deep Active Learning, Pengzhen Ren et al. (2020). Its survey organizes deep active learning’s batch, uncertainty, and diversity approaches, giving readers the methodological map needed to place the source’s framework and benchmark.

No sufficiently relevant recommendations were found.

Cover for A Framework and Benchmark for Deep Batch Active Learning for Regression

Abstract

The acquisition of labels for supervised learning can be expensive. To improve the sample efficiency of neural network regression, we study active learning methods that adaptively select batches of unlabeled data for labeling. We present a framework for constructing such methods out of (network-dependent) base kernels, kernel transformations, and selection methods. Our framework encompasses many existing Bayesian methods based on Gaussian process approximations of neural networks as well as non-Bayesian methods. Additionally, we propose to replace the commonly used last-layer features with sketched finite-width neural tangent kernels and to combine them with a novel clustering method. To evaluate different methods, we introduce an open-source benchmark consisting of 15 large tabular regression data sets. Our proposed method outperforms the state-of-the-art on our benchmark, scales to large data sets, and works out-of-the-box without adjusting the network architecture or training code. We provide open-source code that includes efficient implementations of all kernels, kernel transformations, and selection methods, and can be used for reproducing our results.

Topics

active learning

Keywords

deep batch active learningactive data selectionFrank-Wolfe optimizationimage regression data setsBayesian Deep Learningempirical kernelsemi-supervised learningdeep neural networks

Table of Contents

  • 1. Introduction
  • 1.1 Contributions
  • 2. Problem Setting
  • 2.1 Regression with Fully-Connected Neural Networks
  • 2.2 Batch Mode Active Learning
  • 3. Related Work
  • 3.1 Uncertainty Measures and Kernel Approximations
  • 3.2 Selection Methods
  • 3.3 Data Sets
  • 4. Kernels
  • 4.1 Base Kernels
  • 4.1.1 Linear Kernel
  • 4.1.3 Last-layer Kernel
  • 4.1.4 Infinite-width NNGP
  • 4.2 Kernel Transformations
  • 4.2.1 Scaling
  • 4.2.2 Gaussian Process Posterior Transformation
  • 4.2.3 Sketching
  • 4.2.4 Ensembling
  • 4.2.5 ACS Random Features Transformation
  • 4.2.6 ACS Gradient Transformation
  • 4.3 Discussion
  • 5. Selection Methods
  • 5.1 Iterative Selection Methods
  • 5.2 Specific Methods
  • 5.2.1 Random Selection
  • 5.2.2 Naive Active Learning
  • 5.2.3 Greedy Determinant Maximization
  • 5.2.4 Greedy total uncertainty minimization
  • 5.2.5 Frank-Wolfe optimization
  • 5.2.6 Greedy distance maximization
  • 5.2.7 k-means++ seeding
  • 5.2.8 Largest cluster maximum distance
  • 5.2.9 Other options
  • 5.3 Discussion
  • 6. Experiments
  • 6.1 Comparison to Existing Methods
  • 6.2 Evaluated Combinations
  • 6.3 Best Kernels and Modes for each Selection Method
  • 6.4 Comparison of Selection Methods
  • 6.5 When should BMDAL be Applied?
  • 7. Conclusion
  • 7.1 Limitations
  • 7.2 Remaining Questions
  • Acknowledgments
  • Appendix A. Overview
  • Appendix B. Details on Base Kernels
  • B.1 NNGP Kernel
  • Appendix C. Details on Kernel Transformations
  • C.1 Gaussian Process Posterior Transformation
  • C.2 Sketching
  • C.3 ACS Random Features Transformation
  • Appendix D. Details on Selection Methods
  • D.1 Iterative Selection Scheme
  • D.2 Random
  • D.3 MaxDiag
  • D.4 MaxDet
  • D.4.1 Equivalence of MaxDet to Non-batch Mode Active Learning With Fixed Kernel
  • D.4.2 Equivalence of MaxDet to BatchBALD on a GP
  • D.4.3 Equivalence of MaxDet to the P-greedy Algorithm
  • D.4.4 Relation to the Greedy Algorithm for D-optimal Design
  • D.4.5 Kernel-space Implementation of MaxDet
  • D.4.6 Feature-space Implementation of MaxDet
  • D.5 Bait
  • D.5.2 Forward Version
  • D.5.3 Forward-Backward Version
  • D.6 FrankWolfe
  • D.7 MaxDist
  • D.8 KMeansPP
  • D.9 LCMD
  • Appendix E. Details on Experiments
  • E.1 Data Sets
  • E.2 Preprocessing
  • E.3 Neural Network Configuration
  • E.4 Results
  • References

Knowls

  1. Knowl 1 — Composable kernel framework for batch active learning

    model/method

    The paper represents a pool-based batch active-learning method as three components: a base kernel, a sequence of kernel transformations, and a selection rule. The base kernel measures similarity between inputs and may depend on a trained neural network; transformations can, for example, encode posterior uncertainty or reduce feature dimension; the selection rule uses the resulting kernel to choose a batch from the unlabeled pool. This composition includes Bayesian approaches based on Gaussian-process or Laplace approximations as well as geometric selection methods, and allows the same kernel to be paired with different selection rules.

    Two modes distinguish how a method accounts for information already in the labeled data. In P mode, informativeness is incorporated through a kernel transformed using the current training inputs. In TP mode, selection promotes diversity from the union of the training inputs and the batch selected so far. The selection rule receives the kernel, training inputs, pool inputs, and requested batch size; it does not directly receive training labels.

  2. Knowl 2 — LCMD: deterministic selection from the largest distance-weighted cluster

    algorithm

    LCMD (largest cluster maximum distance) is a deterministic, iterative selection method intended to promote both diversity and representativity of the pool. Let kk be a positive semidefinite kernel and define the induced distance dk(x,x′)=k(x,x)+k(x′,x′)−2k(x,x′)d_k(x,x')=\sqrt{k(x,x)+k(x',x')-2k(x,x')}. Let XremX_{\mathrm{rem}} be the pool points not yet selected, and let XselX_{\mathrm{sel}} contain already selected points. In TP mode, XselX_{\mathrm{sel}} initially contains the labeled training inputs; in P mode it is initially empty.

    Input: Kernel kk, initial selected set XselX_{\mathrm{sel}}, pool XpoolX_{\mathrm{pool}}, batch size NbatchN_{\mathrm{batch}}
    Output: A batch XbatchX_{\mathrm{batch}} of NbatchN_{\mathrm{batch}} pool points
    Set XbatchX_{\mathrm{batch}} to the empty set
    If XselX_{\mathrm{sel}} is empty, add to XbatchX_{\mathrm{batch}} the remaining point maximizing k(x,x)k(x,x)
    While ∣Xbatch∣<Nbatch|X_{\mathrm{batch}}| < N_{\mathrm{batch}}:
        Set Xrem=Xpool∖XbatchX_{\mathrm{rem}} = X_{\mathrm{pool}} \setminus X_{\mathrm{batch}}
        For each xx in XremX_{\mathrm{rem}}, assign xx to a nearest center c(x)c(x) in Xsel∪XbatchX_{\mathrm{sel}} \cup X_{\mathrm{batch}}
        For each center zz in Xsel∪XbatchX_{\mathrm{sel}} \cup X_{\mathrm{batch}}, compute
            s(z)=∑x∈Xrem:c(x)=zdk(x,z)2s(z) = \sum_{x \in X_{\mathrm{rem}}: c(x)=z} d_k(x,z)^2
        Find a center z∗z^* with maximum s(z)s(z)
        Add to XbatchX_{\mathrm{batch}} a point in the cluster of z∗z^* maximizing dk(x,z∗)d_k(x,z^*)
    Return XbatchX_{\mathrm{batch}}

    Ties may be resolved arbitrarily. The cluster score is the sum of squared distances of its remaining points to its center, so the method focuses on a cluster with substantial distance-weighted mass, then chooses its most distant point. With NpoolN_{\mathrm{pool}} pool points, NselN_{\mathrm{sel}} selected or initial-center points, and kernel-evaluation time TkT_k, the stated runtime is O(NpoolNsel(Tk+1))O(N_{\mathrm{pool}}N_{\mathrm{sel}}(T_k+1)) and memory use is O(Ncand)O(N_{\mathrm{cand}}), where Ncand=Npool+∣Xsel∣N_{\mathrm{cand}}=N_{\mathrm{pool}}+|X_{\mathrm{sel}}|.

  3. Knowl 3 — Finite-width neural tangent kernel as a neural-network-dependent similarity

    model/method

    For a trained neural network fθT:Rd→Rf_{\theta_T}:\mathbb{R}^d\to\mathbb{R} with parameter vector θT\theta_T, the full-gradient feature map is ϕgrad(x)=∇θfθT(x)\phi_{\mathrm{grad}}(x)=\nabla_\theta f_{\theta_T}(x), and its kernel is the finite-width neural tangent kernel

    kgrad(x,x′)=⟨∇θfθT(x),∇θfθT(x′)⟩.k_{\mathrm{grad}}(x,x')=\langle \nabla_\theta f_{\theta_T}(x),\nabla_\theta f_{\theta_T}(x')\rangle.

    This kernel measures similarity in the network's parameter-gradient features at the trained parameters; it is motivated by the first-order linearization of the network around θT\theta_T. In a fully connected network, the full parameter-gradient feature need not be explicitly formed to evaluate the kernel: each layer contributes a product of an inner product between its augmented input activations and an inner product between output derivatives with respect to that layer's preactivations. Summing these products over layers yields the full-gradient kernel. For a network with LL layers of hidden width mm, cached activations and derivatives permit reducing the kernel-evaluation cost from Θ(m2L)\Theta(m^2L) to Θ(mL)\Theta(mL), with a corresponding reduction for stored precomputed features. The paper's experiments use a sketched version of this trained, finite-width kernel rather than the commonly used last-layer-only feature kernel.

  4. Knowl 4 — Gaussian sketching preserves kernel distances with a dimension-independent feature bound

    theoretical result

    For a finite-dimensional kernel with feature map ϕ:Rd→Rdfeat\phi:\mathbb{R}^d\to\mathbb{R}^{d_{\mathrm{feat}}}, a Gaussian sketch with pp features is ϕsketch(x)=p−1/2Uϕ(x)\phi_{\mathrm{sketch}}(x)=p^{-1/2}U\phi(x), where U∈Rp×dfeatU\in\mathbb{R}^{p\times d_{\mathrm{feat}}} has independent standard-normal entries. The induced kernel is an unbiased estimate of the original kernel. Define dk(x,x′)=∥ϕ(x)−ϕ(x′)∥2d_k(x,x')=\|\phi(x)-\phi(x')\|_2 and let X⊂RdX\subset\mathbb{R}^d be finite. For ε,δ∈(0,1)\varepsilon,\delta\in(0,1), if

    p≥8log⁡(∣X∣2/δ)ε2,p\geq \frac{8\log(|X|^2/\delta)}{\varepsilon^2},

    then, with probability at least 1−δ1-\delta, every pair in XX satisfies

    (1−ε)dk(x,x′)≤dksketch(x,x′)≤(1+ε)dk(x,x′).(1-\varepsilon)d_k(x,x')\leq d_{k_{\mathrm{sketch}}}(x,x')\leq(1+\varepsilon)d_k(x,x').

    The feature-count bound does not depend on the original feature dimension dfeatd_{\mathrm{feat}}. For a product of kernels, the paper also gives an efficient sketch: independently sketch the two factor feature maps to pp dimensions, take their element-wise product, and multiply by p\sqrt{p}. This avoids materializing the tensor-product feature space. In the benchmark, sketching the finite-width neural tangent kernel to 512 features retains its selection accuracy while substantially reducing runtime.

  5. Knowl 5 — Posterior kernel transformation and automatic scale normalization

    equation

    Given a kernel kk with feature map ϕ\phi, training inputs XtrainX_{\mathrm{train}} of size NtrainN_{\mathrm{train}}, and assumed Gaussian observation-noise variance σ2>0\sigma^2>0, the paper uses a Gaussian-process posterior covariance transformation. Before conditioning, the kernel can be rescaled to give it mean unit diagonal on the training inputs:

    kscale(x,x′)=λ2k(x,x′),λ=(1Ntrain∑x∈Xtraink(x,x))−1/2.k_{\mathrm{scale}}(x,x')=\lambda^2 k(x,x'),\qquad \lambda=\left(\frac{1}{N_{\mathrm{train}}}\sum_{x\in X_{\mathrm{train}}}k(x,x)\right)^{-1/2}.

    For a feature map ϕ\phi of the kernel being transformed, the posterior covariance of the latent function is

    kpost(x,x′)=ϕ(x)⊤(σ−2ϕ(Xtrain)⊤ϕ(Xtrain)+I)−1ϕ(x′),k_{\mathrm{post}}(x,x')=\phi(x)^\top\left(\sigma^{-2}\phi(X_{\mathrm{train}})^\top\phi(X_{\mathrm{train}})+I\right)^{-1}\phi(x'),

    where ϕ(Xtrain)\phi(X_{\mathrm{train}}) is the matrix whose rows are the training-input feature vectors and II is the identity matrix of the matching feature dimension. The transformed covariance depends on training inputs but not on their observed labels. For the last-layer kernel this is Bayesian linear regression on the network's last-layer features; applying the same transformation to the full-gradient kernel gives a generalized Gauss–Newton/Laplace-style approximation under the paper's stated linearization assumptions.

  6. Knowl 6 — Benchmark design and neural-network training protocol

    experimental setup

    The benchmark contains 15 large tabular regression datasets: sgemm, wec_sydney, ct_slices, kegg_undir, online_video, query, poker, road, mlr_knn_rng, fried, diamonds, methane, stock, protein, and sarcos. Their input dimensions range from 2 to 379, and initial pool sizes range from 31,335 to 198,720. The evaluated regressor is a fully connected neural network with two hidden layers of 512 units each. Networks are trained with Adam for 256 epochs using mini-batches of 256 and early stopping on a 1,024-example validation set. The main results use ReLU; most comparisons were also repeated with SiLU.

    Each active-learning run starts with 256 labeled training examples and acquires 16 batches of 256 examples. The authors repeat runs 20 times with different initializations and data splits. They measure test MAE, RMSE, the 95% and 99% error quantiles, and maximum error, averaging logarithms of each metric across repetitions and, where specified, datasets and acquisition steps. Posterior-based methods use σ2=10−6\sigma^2=10^{-6}; sketched kernels and random-feature transformations target 512 features. The benchmark was designed for scalable pool-based comparisons without changing the network architecture or training procedure.

  7. Knowl 7 — LCMD with the sketched full-gradient kernel beats literature baselines on mean log RMSE

    empirical result

    On the 15-dataset benchmark, the proposed combination LCMD-TP with the 512-feature sketched finite-width neural tangent kernel achieved the lowest averaged logarithmic RMSE among the compared methods, for both ReLU and SiLU networks. The table reports the mean log RMSE averaged across datasets, repetitions, and active-learning steps; lower values indicate lower RMSE. The compared methods were adapted to regression within the paper's kernel framework.

    Method ReLU SiLU
    Random (no active learning) -1.401 -1.406
    BALD with last-layer GP -1.285 -1.300
    BatchBALD with last-layer GP -1.463 -1.467
    Bait -1.541 -1.522
    ACS-FW -1.439 -1.437
    Core-Set / FF-Active -1.491 -1.515
    BADGE with last-layer GP uncertainty -1.530 -1.484
    LCMD-TP with kgrad→sketch(512)k_{\mathrm{grad}\to\mathrm{sketch}(512)} -1.590 -1.597

    The corresponding LCMD configuration was not just better than random selection: it also improved on the best reported literature baseline in this comparison, Bait for ReLU and Bait for SiLU.

  8. Knowl 8 — Best-performing kernel and mode vary by selection rule

    data/table

    The authors selected a kernel and P/TP mode for each selection method using average log RMSE on the ReLU benchmark. These configurations show that selection-rule comparisons depend on kernel choice: LCMD-TP paired with the sketched full-gradient kernel was best overall, while posterior-based transformations or ACS transformations were selected for several other rules. Average selection time is seconds per batch across datasets and acquisition steps on an NVIDIA RTX 3090; mean log RMSE is averaged across datasets, repetitions, and steps.

    Selection rule Selected kernel Mean log RMSE Time (s)
    Random none -1.401 0.001
    MaxDiag kgrad→sketch(512)→acs−rf(512)k_{\mathrm{grad}\to\mathrm{sketch}(512)\to\mathrm{acs-rf}(512)} -1.370 0.650
    MaxDet-P kgrad→sketch(512)→Xtraink_{\mathrm{grad}\to\mathrm{sketch}(512)\to X_{\mathrm{train}}} -1.512 0.770
    Bait-F-P kgrad→sketch(512)→Xtraink_{\mathrm{grad}\to\mathrm{sketch}(512)\to X_{\mathrm{train}}} -1.585 1.508
    FrankWolfe-P kgrad→sketch(512)→acs−rf−hyper(512)k_{\mathrm{grad}\to\mathrm{sketch}(512)\to\mathrm{acs-rf-hyper}(512)} -1.542 0.823
    MaxDist-P kgrad→sketch(512)→Xtraink_{\mathrm{grad}\to\mathrm{sketch}(512)\to X_{\mathrm{train}}} -1.514 0.713
    KMeansPP-P kgrad→sketch(512)→acs−rf(512)k_{\mathrm{grad}\to\mathrm{sketch}(512)\to\mathrm{acs-rf}(512)} -1.569 0.836
    LCMD-TP kgrad→sketch(512)k_{\mathrm{grad}\to\mathrm{sketch}(512)} -1.590 0.981

    Here, kgradk_{\mathrm{grad}} is the finite-width full-gradient kernel, “sketch(512)” reduces its feature map to 512 dimensions, and XtrainX_{\mathrm{train}} denotes the rescale-then-posterior transformation. P and TP denote pool-only and training-plus-pool selection modes, respectively.

  9. Knowl 9 — Performance patterns across metrics, datasets, and batch sizes

    empirical result

    Across the benchmark, replacing the last-layer feature kernel with the finite-width full-gradient kernel generally improved results across selection methods, and sketching that kernel to 512 features preserved accuracy while making selection faster. LCMD-TP with this sketched kernel reduced RMSE relative to random selection on 13 of 15 datasets and matched or outperformed the other selected active-learning methods on 8 of 15 datasets. In aggregate learning curves, the strongest active-learning methods reached random selection's average RMSE with about half as many labeled examples; for maximum error they needed even fewer. LCMD-TP performed best overall for MAE, RMSE, and the 95% quantile, while MaxDist, MaxDet, and Bait-F were among the strongest for maximum error.

    With a fixed final training-set size of 4,352, MaxDiag was particularly sensitive to acquisition batch size. The other compared methods showed almost no degradation through batch sizes of 1,024; the paper notes that this threshold may depend on training-set size and feature dimension. On these datasets, the initial-training-set ratio RMSE/MAE was strongly associated with the benefit of LCMD-TP over random selection: the reported Pearson correlation between error-distribution variation and relative sample-efficiency gain was approximately 0.880.88. This association is an empirical observation on the benchmark, not a guarantee for other datasets.

  10. Knowl 10 — Limits on generalizing the benchmark findings

    limitation

    The empirical conclusions come from large tabular regression datasets and fully connected neural networks, primarily with ReLU or SiLU activations. The paper states that it is unclear whether the findings transfer to substantially different applications such as drug discovery or atomistic machine learning, to smaller tabular datasets, or to newer tabular-network architectures. The benchmark also contains no distribution shift between the pool and test data, so it does not establish how the methods compare when those distributions differ.

Coverage note — The paper's detailed implementations and comparisons of established selection methods and the full per-dataset appendix results are omitted because they support the framework and benchmark rather than constitute separate new contributions.

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Citation

MLA
Holzmüller, D., et al. “A Framework and Benchmark for Deep Batch Active Learning for Regression”. Journal of Machine Learning Research, vol. 24, no. 164, 2023, pp. 1–1, https://www.jmlr.org/papers/v24/22-0937.html.
APA
Holzmüller, D., Zaverkin, V., Kästner, J., & Steinwart, I. (2023). A Framework and Benchmark for Deep Batch Active Learning for Regression. Journal of Machine Learning Research, 24(164), 1–81. https://www.jmlr.org/papers/v24/22-0937.html
Chicago
Holzmüller, D., V. Zaverkin, J. Kästner, and I. Steinwart. 2023. “A Framework and Benchmark for Deep Batch Active Learning for Regression”. Journal of Machine Learning Research 24 (164): 1–81. https://www.jmlr.org/papers/v24/22-0937.html.
Harvard
Holzmüller, D. et al. (2023) “A Framework and Benchmark for Deep Batch Active Learning for Regression”, Journal of Machine Learning Research, 24(164), pp. 1–81. Available at: https://www.jmlr.org/papers/v24/22-0937.html.
Vancouver
1. Holzmüller D, Zaverkin V, Kästner J, Steinwart I (2023) A Framework and Benchmark for Deep Batch Active Learning for Regression. Journal of Machine Learning Research 24:1–81

BibTeX

@article{JMLR:v24:22-0937,
  author  = {David Holzmüller and Viktor Zaverkin and Johannes Kästner and Ingo Steinwart},
  title   = {A Framework and Benchmark for Deep Batch Active Learning for Regression},
  journal = {Journal of Machine Learning Research},
  year    = {2023},
  volume  = {24},
  number  = {164},
  pages   = {1--81},
  url     = {http://jmlr.org/papers/v24/22-0937.html}
}
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