Active Learning for Convolutional Neural Networks: A Core-Set Approach

Ozan SenerSilvio Savarese

article2018ICLR2,708 citations

Proposes a geometric core-set formulation for batch active learning in convolutional neural networks, providing theoretical performance bounds and an effective subset selection algorithm that significantly reduces labeling requirements for image classification.

Listen

Labeling large image datasets for training convolutional neural networks remains expensive and time-consuming, creating a practical need for methods that select the most informative points to label under a fixed budget. Existing active learning heuristics often prove ineffective for CNNs when labels are acquired in batches rather than one at a time, largely because batch sampling introduces correlations that reduce diversity.

The article sets out to reframe active learning as a core-set selection task: choosing a modest subset of unlabeled points such that a model trained on the labeled subset performs nearly as well on the remaining data as a model trained on the full set.

The authors derive a geometric upper bound on the difference in average loss between any chosen subset and the full dataset, showing that this core-set loss is controlled by the covering radius of the selected points. They convert the resulting optimization into the classic k-Center problem and solve it with a greedy 2-OPT algorithm followed by a mixed-integer program that improves robustness to outliers. Experiments compare the method against random sampling, uncertainty-based baselines, Bayesian approaches, and prior batch-mode algorithms on CIFAR-10, CIFAR-100, and SVHN under both fully supervised and weakly supervised training regimes.

The proposed core-set method consistently delivers higher classification accuracy than all baselines, often by substantial margins, and performs especially well when combined with weakly supervised models that produce richer feature spaces. Uncertainty-driven strategies, by contrast, frequently underperform random sampling once batch correlations are taken into account. The geometric coverage produced by the algorithm visibly spreads selected points more evenly across the data manifold than uncertainty sampling.

These results indicate that organizations can achieve target accuracy levels with far fewer labeled examples, lowering labeling costs and shortening project timelines without sacrificing model quality. The approach also supplies a practical way to decide how many additional labels are worth acquiring at each iteration.

Practitioners should adopt the core-set procedure, preferring the full mixed-integer solution when dataset size permits and falling back to the fast greedy approximation otherwise. Future work could explore principled ways to blend uncertainty signals with the geometric criterion and test scaling behavior on datasets larger than 50 000 images.

The main limitations are the zero-training-error assumption used to simplify the bound, which is only approximately true, and the fact that the performance guarantee weakens as the number of classes grows. Results are nevertheless consistent across three standard benchmarks and multiple random initial pools, supporting moderate-to-high confidence for image-classification tasks of similar scale.

Intel Stanford University active learning classification convolutional neural networks Active Learning Convolutional Neural Network Core‑Set Selection

arXiv: 1708.00489 ozansener/active_learning_coreset

Paper: Active Learning with Statistical Models, D. Cohn et al. (1996). This seminal paper introduces statistically optimal variance-reduction frameworks for active data selection, establishing the foundational theoretical principles for querying informative samples.
Paper: Support Vector Machine Active Learning with Applications to Text Classification, Simon Tong et al. (2001). This foundational work establishes pool-based active learning via margin and version-space query heuristics, providing essential background for understanding uncertainty-based sample selection.
Paper: Query by committee, H. Seung et al. (1992). This classic work formalizes pool-based query-by-committee active learning, which serves as a primary conceptual baseline for disagreement- and uncertainty-driven active data acquisition.
Paper: Combining active learning and semi-supervised learning using Gaussian fields and harmonic functions, Xiaojin Zhu et al. (2003). This paper establishes the core principles of combining graph-based semi-supervised structure with active learning to minimize expected classification risk.
Paper: Neural Network Ensembles, Cross Validation, and Active Learning, Anders Krogh et al. (1994). This paper derives the relationship between ensemble ambiguity and active sample selection, motivating modern disagreement-based active learning strategies.

No sufficiently relevant recommendations were found.

Cover for Active Learning for Convolutional Neural Networks: A Core-Set Approach

Abstract

Convolutional neural networks (CNNs) have been successfully applied to many recognition and learning tasks using a universal recipe; training a deep model on a very large dataset of supervised examples. However, this approach is rather restrictive in practice since collecting a large set of labeled images is very expensive. One way to ease this problem is coming up with smart ways for choosing images to be labelled from a very large collection (ie. active learning).

Our empirical study suggests that many of the active learning heuristics in the literature are not effective when applied to CNNs in batch setting. Inspired by these limitations, we define the problem of active learning as core-set selection, ie. choosing set of points such that a model learned over the selected subset is competitive for the remaining data points. We further present a theoretical result characterizing the performance of any selected subset using the geometry of the datapoints. As an active learning algorithm, we choose the subset which is expected to yield best result according to our characterization. Our experiments show that the proposed method significantly outperforms existing approaches in image classification experiments by a large margin.

1 introduction
2 Related Work
3 Problem Definition
4 Method
4.1 Active Learning as a Set Cover
4.2 Core-Sets for CNNs
4.3 Solving the k-Center Problem
4.4 Implementation Details
5 Experimental Results
6 Conclusion
References
A Proof for Lemma 1
B Proof for Theorem 1

Knowls

Knowl 1 — Risk Decomposition and Core-Set Formulation for Batch Active Learning
model/method
In pool-based batch active learning for classification over an input space $\mathcal{X}$ and label space $\mathcal{Y} = \{1, \dots, C\}$ , the learner starts with an initial randomly labeled pool $s^0 \subset [n]$ with $|s^0| = m$ and a large set of unlabeled data points $\{x_i\}_{i \in [n]}$ , and selects a subset $s^1 \subset [n] \setminus s^0$ with query budget $|s^1| \le b$ to be labeled by an oracle. The true population risk of the model parameters $A_s$ trained on the labeled subset $s = s^0 \cup s^1$ under loss $l(\cdot, \cdot; A_s)$ is upper-bounded by three components:

$\mathbb{E}_{(x,y)\sim p_{\mathcal{Z}}}[l(x, y; A_s)] \le \left|\mathbb{E}_{(x,y)\sim p_{\mathcal{Z}}}[l(x, y; A_s)] - \frac{1}{n}\sum_{i\in[n]} l(x_i, y_i; A_s)\right| + \frac{1}{|s|}\sum_{j\in s} l(x_j, y_j; A_s) + \left|\frac{1}{n}\sum_{i\in[n]} l(x_i, y_i; A_s) - \frac{1}{|s|}\sum_{j\in s} l(x_j, y_j; A_s)\right|$

where the terms correspond respectively to the Generalization Error over the entire dataset $[n]$ , the Training Error on the chosen labeled subset $s$ , and the Core-Set Loss (the difference between average empirical loss over all data points and the average empirical loss over the labeled subset).

Because overparameterized convolutional neural networks (CNNs) achieve near-zero training error on small labeled sets and generalize well over visual tasks, population risk minimization is dominated by core-set loss minimization, formalizing batch active learning as:

$\min_{s^1 : |s^1| \le b} \left| \frac{1}{n} \sum_{i \in [n]} l(x_i, y_i; A_{s^0 \cup s^1}) - \frac{1}{|s^0 \cup s^1|} \sum_{j \in s^0 \cup s^1} l(x_j, y_j; A_{s^0 \cup s^1}) \right|$
Knowl 2 — Upper Bound on CNN Core-Set Loss via Covering Radius
theoretical result
Let $n$ independent and identically distributed samples $\{x_i, y_i\}_{i \in [n]}$ be drawn from distribution $p_{\mathcal{Z}}$ over $\mathcal{X} \times \mathcal{Y}$ for a $C$ -class classification problem. Suppose the loss function $l(\cdot, y; w)$ is $\lambda^l$ -Lipschitz continuous for all labels $y \in \mathcal{Y}$ and parameters $w$ , and bounded by $L$ . Let the class posterior regression functions $\eta_c(x) = p(y=c \mid x)$ be $\lambda^\eta$ -Lipschitz continuous for all $c \in \{1, \dots, C\}$ . If the chosen labeled set $s \subseteq [n]$ forms a $\delta_s$ -cover of the full dataset $\{x_i, y_i\}_{i \in [n]}$ under distance metric $\Delta$ (i.e., $\max_{i \in [n]} \min_{j \in s} \Delta(x_i, x_j) \le \delta_s$ ), and the classifier achieves zero training loss on the labeled subset ( $l(x_j, y_j; A_s) = 0$ for all $j \in s$ ), then with probability at least $1 - \gamma$ :

$\left| \frac{1}{n} \sum_{i \in [n]} l(x_i, y_i; A_s) - \frac{1}{|s|} \sum_{j \in s} l(x_j, y_j; A_s) \right| \le \delta_s (\lambda^l + \lambda^\eta L C) + \sqrt{\frac{L^2 \log(1/\gamma)}{2n}}$

This result demonstrates that the core-set loss depends directly on the covering radius $\delta_s$ and an $\mathcal{O}(1/\sqrt{n})$ term that depends only on the total number of dataset points $n$ . Consequently, querying a new label reduces the core-set loss if and only if it decreases the geometric covering radius $\delta_s$ .
Knowl 3 — Lipschitz Continuity of Convolutional Neural Networks with $l_2$ Softmax Loss
theoretical result
Consider a convolutional neural network with $n_c$ convolutional layers (interspersed with ReLU non-linearities and max-pooling operations) and $n_{fc}$ fully connected layers defined over $C$ classes. Let $\alpha = \max_{j, d} \sum_i |w_{i,j}^d|$ represent the maximum sum of input weights per neuron across any layer $d$ . When the classification loss function $l(x, y; w)$ is defined as the $l_2$ norm between the one-hot class probability vector and the network's softmax output vector, the loss function is $\lambda^l$ -Lipschitz continuous with respect to input $x$ under the $l_2$ norm for fixed class probabilities and network parameters $w$ , with:

$\lambda^l = \frac{\sqrt{C - 1}}{C} \alpha^{n_c + n_{fc}}$

This verifies that standard CNN architectures satisfy the Lipschitz continuity requirement needed to bound the active learning core-set loss by the covering radius.
Knowl 4 — Robust $k$-Center Active Selection via Mixed Integer Programming
algorithm
To find an active learning query batch $s^1$ of size $b$ that minimizes the covering radius while tolerating up to $\Xi$ outliers, binary search over the covering radius $\delta \in [\delta_{\text{2-OPT}} / 2, \delta_{\text{2-OPT}}]$ is performed using a Mixed Integer Program (MIP) feasibility test $\text{Feasible}(b, s^0, \delta, \Xi)$ .

The decision variables in $\text{Feasible}(b, s^0, \delta, \Xi)$ are binary: $u_i \in \{0, 1\}$ indicates whether sample $i$ is selected as a center, $\omega_{i,j} \in \{0, 1\}$ indicates whether sample $i$ is covered by center $j$ , and $\xi_{i,j} \in \{0, 1\}$ indicates whether sample $i$ is an uncovered outlier assigned to $j$ at distance $\Delta(x_i, x_j) > \delta$ :

$\sum_j u_j = |s^0| + b, \quad \sum_{i,j} \xi_{i,j} \le \Xi$ $\sum_j \omega_{i,j} = 1 \quad \forall i \in [n], \quad \omega_{i,j} \le u_j \quad \forall i, j \in [n]$ $u_i = 1 \quad \forall i \in s^0, \quad u_i \in \{0, 1\} \quad \forall i \in [n]$ $\omega_{i,j} = \xi_{i,j} \quad \forall i, j \text{ such that } \Delta(x_i, x_j) > \delta$
Input: Data points $\{x_i\}_{i \in [n]}$ , existing pool $s^0$ , budget $b$ , outlier bound $\Xi$ , metric $\Delta$
Initialize: $s_g = \text{k-Center-Greedy}(\{x_i\}, s^0, b)$
$\delta_{\text{2-OPT}} = \max_i \min_{j \in s_g} \Delta(x_i, x_j)$
$lb = \delta_{\text{2-OPT}} / 2$
$ub = \delta_{\text{2-OPT}}$
repeat
    if $\text{Feasible}(b, s^0, (lb + ub) / 2, \Xi)$ then
         $ub = \max_{i, j \mid \Delta(x_i, x_j) \le (lb + ub) / 2} \Delta(x_i, x_j)$
    else
         $lb = \min_{i, j \mid \Delta(x_i, x_j) \ge (lb + ub) / 2} \Delta(x_i, x_j)$
    end if
until $ub = lb$
return $\{i \mid u_i = 1\} \setminus s^0$
Knowl 5 — Greedy 2-OPT Approximation for $k$-Center Active Learning
algorithm
Minimizing the covering radius $\min_{s^1 : |s^1| \le b} \max_i \min_{j \in s^0 \cup s^1} \Delta(x_i, x_j)$ is equivalent to the minimax facility location ( $k$ -Center) problem, which is NP-hard. The greedy farthest-first traversal provides a 2-OPT polynomial-time approximation guarantee such that $\max_i \min_{j \in s^0 \cup s^1} \Delta(x_i, x_j) \le 2 \times \text{OPT}$ .
Input: Data points $\{x_i\}_{i \in [n]}$ , existing labeled pool $s^0$ , query budget $b$ , distance metric $\Delta(\cdot, \cdot)$
Initialize: $s = s^0$
repeat
$u = \arg\max_{i \in [n] \setminus s} \min_{j \in s} \Delta(x_i, x_j)$
$s = s \cup \{u\}$
until $|s| = |s^0| + b$
return $s \setminus s^0$
The algorithm repeatedly queries the data point whose distance to its closest existing center in $s$ is maximal, producing a diversified subset that serves either as a standalone selection or as a bounded initialization for the exact MIP solver.
Knowl 6 — Experimental Implementation for CNN Core-Set Selection
experimental setup
The core-set batch active learning framework is implemented as follows:
- Distance Metric: The metric $\Delta(x_i, x_j)$ is computed as the $l_2$ Euclidean distance between the feature activations of the final fully-connected pre-softmax layer of the CNN.
- Network Architecture: VGG-16 is used for all experiments. Convolutional filters are initialized according to the He normal initialization scheme.
- Optimization: The networks are trained using RMSProp with a learning rate of $10^{-3}$ in TensorFlow. The CNN is retrained from scratch at each active learning round after querying new labeled examples.
- Weakly-Supervised Model: Ladder networks are utilized in weakly-supervised active learning experiments to leverage representations learned jointly from labeled and unlabeled points.
- Robust MIP Parameters: The outlier threshold in the mixed integer program is set to $\Xi = 10^{-4} \times n$ , where $n$ is the number of unlabeled points, and feasibility is checked using the Gurobi optimization framework.
Knowl 7 — Active Classification Performance on CIFAR and SVHN Benchmarks
empirical result
The core-set active learning approach was evaluated on CIFAR-10, CIFAR-100, and SVHN across sequential batch labeling rounds starting from uniform random initial subsets:
- In the weakly-supervised regime (using Ladder networks), the core-set method outperformed all baselines—including Random sampling, Empirical Uncertainty (entropy, BALD, Variation Ratios), Deep Bayesian Active Learning (DBAL with Monte Carlo dropout), Oracle Uncertainty, $k$ -Median clustering, BMDR, and CEAL—by a large margin across all three datasets.
- In the fully-supervised regime, the core-set approach consistently achieved higher classification accuracy for given labeling budgets than all competing baselines.
- The performance improvement of core-set selection was higher in the weakly-supervised setting than in the fully-supervised setting because semi-supervised representation learning yields more accurate feature geometries for computing $\Delta(x_i, x_j)$ .
- The margin of improvement was smaller on CIFAR-100 than on CIFAR-10 and SVHN, aligning with the theoretical core-set bound where error scales linearly with the class count $C$ .
Knowl 8 — Spatial Redundancy and Failure of Batch Uncertainty Sampling
empirical result
Standard uncertainty-based active learning heuristics (such as maximum entropy, BALD, Variation Ratios, Monte Carlo dropout DBAL, and even an Oracle uncertainty sampler using true loss values) fail to match or outperform uniform random sampling when applied to CNNs in batch acquisition mode.

Qualitative analysis using 2D t-SNE projections of CNN feature embeddings shows that uncertainty-based acquisition selects queries that are strongly correlated and clustered along localized decision boundaries, leaving wide expanses of the data space uncovered. In contrast, core-set selection systematically covers the entire geometry of the dataset, preventing redundant query acquisition.

Knowl 9 — Runtime and Performance Tradeoff of Exact MIP versus Greedy $k$-Center

data/table

To analyze the computational cost of the exact mixed integer programming (MIP) solver compared to the greedy 2-OPT approximation, runtimes were recorded on a system with an Intel Core i7-5930K CPU @ 3.50GHz and 64 GB RAM for a dataset of $n = 50\text{k}$ images with an initial labeled pool $|s^0| = 10\text{k}$ and query budget $b = 5\text{k}$ .

Solving the MIP via binary search requires $360.23$ seconds total ( $104.2$ s to form pairwise distances and $244.03$ s across MIP iterations), whereas the greedy 2-OPT heuristic requires only $2.0$ seconds. On CIFAR-100, the exact MIP provides a consistent accuracy advantage over greedy selection (e.g., $0.45$ vs. $0.43$ at $20\text{k}$ labeled samples, and $0.54$ vs. $0.52$ at $30\text{k}$ labeled samples). However, greedy 2-OPT still outperforms all non-core-set baselines, demonstrating that the greedy variant provides an effective, scalable active learning solution for massive datasets where integer programming is computationally prohibitive.

Coverage note — No substantial contributed material was omitted.

References

1.Martin Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, et al. Tensorflow: Large-scale machine learning on heterogeneous distributed systems. arXiv:1603.04467, 2016.
2.C. Berlind and R. Urner. Active nearest neighbors in changing environments. In ICML, 2015.
3.Klaus Brinker. Incorporating diversity in active learning with support vector machines. In ICML, volume 3, pp. 59–66, 2003.
4.William J Cook, William H Cunningham, William R Pulleyblank, and Alexander Schrijver. Combinatorial optimization, volume 605. Springer, 1998.
5.Sanjoy Dasgupta. Analysis of a greedy active learning strategy. In NIPS, 2004.
6.Sanjoy Dasgupta. Analysis of a greedy active learning strategy. In L. K. Saul, Y. Weiss, and L. Bottou (eds.), Advances in Neural Information Processing Systems 17, pp. 337–344. MIT Press, 2005. URL http://papers.nips.cc/paper/2636-analysis-of-a-greedy-active-learning-strategy.pdf.
7.Begüm Demir, Claudio Persello, and Lorenzo Bruzzone. Batch-mode active-learning methods for the interactive classification of remote sensing images. IEEE Transactions on Geoscience and Remote Sensing, 49(3):1014–1031, 2011.
8.Jeff Donahue, Philipp Krähenbühl, and Trevor Darrell. Adversarial feature learning. arXiv:1605.09782, 2016.
9.Vincent Dumoulin, Ishmael Belghazi, Ben Poole, Alex Lamb, Martin Arjovsky, Olivier Mastropietro, and Aaron Courville. Adversarially learned inference. arXiv:1606.00704, 2016.
10.Ehsan Elhamifar, Guillermo Sapiro, Allen Yang, and S Shankar Sasrty. A convex optimization framework for active learning. In ICCV, 2013.
11.Yoav Freund, H Sebastian Seung, Eli Shamir, and Naftali Tishby. Selective sampling using the query by committee algorithm. Machine learning, 28(2-3), 1997.
12.Yarin Gal and Zoubin Ghahramani. Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In International Conference on Machine Learning, 2016.
13.Yarin Gal, Riashat Islam, and Zoubin Ghahramani. Deep bayesian active learning with image data. arXiv preprint arXiv:1703.02910, 2017.
14.Ravi Ganti and Alexander Gray. Upal: Unbiased pool based active learning. In Artificial Intelligence and Statistics, pp. 422–431, 2012.
15.Daniel Golovin and Andreas Krause. Adaptive submodularity: Theory and applications in active learning and stochastic optimization. Journal of Artificial Intelligence Research, 42:427–486, 2011.
16.Alon Gonen, Sivan Sabato, and Shai Shalev-Shwartz. Efficient active learning of halfspaces: an aggressive approach. The Journal of Machine Learning Research, 14(1):2583–2615, 2013.
17.Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In NIPS, 2014.
18.Andrew Guillory and Jeff Bilmes. Interactive submodular set cover. arXiv:1002.3345, 2010.
19.Yuhong Guo. Active instance sampling via matrix partition. In Advances in Neural Information Processing Systems, pp. 802–810, 2010.
20.Yuhong Guo and Dale Schuurmans. Discriminative batch mode active learning. In Advances in neural information processing systems, pp. 593–600, 2008.
21.Steve Hanneke. A bound on the label complexity of agnostic active learning. In Proceedings of the 24th international conference on Machine learning, pp. 353–360. ACM, 2007.
22.Sariel Har-Peled and Akash Kushal. Smaller coresets for k-median and k-means clustering. In Annual Symposium on Computational geometry. ACM, 2005.
23.Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016.
24.Steven CH Hoi, Rong Jin, Jianke Zhu, and Michael R Lyu. Batch mode active learning and its application to medical image classification. In Proceedings of the 23rd international conference on Machine learning, pp. 417–424. ACM, 2006.
25.Gurobi Optimization Inc. Gurobi optimizer reference manual, 2016. URL http://www.gurobi.com.
26.Ajay J Joshi, Fatih Porikli, and Nikolaos Papanikolopoulos. Multi-class active learning for image classification. In CVPR, 2009.
27.A. J. Joshiy, F. Porikli, and N. Papanikolopoulos. Multi-class batch-mode active learning for image classification. In 2010 IEEE International Conference on Robotics and Automation, pp. 1873–1878, May 2010. doi: 10.1109/ROBOT.2010.5509293.
28.Ashish Kapoor, Kristen Grauman, Raquel Urtasun, and Trevor Darrell. Active learning with gaussian processes for object categorization. In ICCV, 2007.
29.Alex Krizhevsky and Geoffrey Hinton. Learning multiple layers of features from tiny images. 2009.
30.Xin Li and Yuhong Guo. Adaptive active learning for image classification. In CVPR, 2013.
31.Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of Machine Learning Research, 9(Nov):2579–2605, 2008.
32.David JC MacKay. Information-based objective functions for active data selection. Neural computation, 4(4):590–604, 1992.
33.Andrew Kachites McCallumzy and Kamal Nigamy. Employing em and pool-based active learning for text classification. In ICML, 1998.
34.Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng. Reading digits in natural images with unsupervised feature learning. In NIPS workshop on deep learning and unsupervised feature learning, volume 2011, pp. 5, 2011.
35.Alec Radford, Luke Metz, and Soumith Chintala. Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv:1511.06434, 2015.
36.Antti Rasmus, Mathias Berglund, Mikko Honkala, Harri Valpola, and Tapani Raiko. Semi-supervised learning with ladder networks. In NIPS, 2015.
37.Nicholas Roy and Andrew McCallum. Toward optimal active learning through monte carlo estimation of error reduction. ICML, 2001.
38.Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen. Improved techniques for training gans. In NIPS, 2016.
39.Burr Settles. Active learning literature survey. University of Wisconsin, Madison, 52(55-66):11, 2010.
40.Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv:1409.1556, 2014.
41.Fabian Stark, Caner Hazırbas, Rudolph Triebel, and Daniel Cremers. Captcha recognition with active deep learning. In GCPR Workshop on New Challenges in Neural Computation, 2015.
42.Simon Tong and Daphne Koller. Support vector machine active learning with applications to text classification. JMLR, 2(Nov):45–66, 2001.
43.Ivor W Tsang, James T Kwok, and Pak-Ming Cheung. Core vector machines: Fast svm training on very large data sets. JMLR, 6(Apr):363–392, 2005.
44.Keze Wang, Dongyu Zhang, Ya Li, Ruimao Zhang, and Liang Lin. Cost-effective active learning for deep image classification. Transactions on Circuits and Systems for Video Technology, 2016.
45.Zheng Wang and Jieping Ye. Querying discriminative and representative samples for batch mode active learning. ACM Transactions on Knowledge Discovery from Data (TKDD), 9(3):17, 2015.
46.Kai Wei, Yuzong Liu, Katrin Kirchhoff, and Jeff A Bilmes. Using document summarization techniques for speech data subset selection. In HLT-NAACL, 2013.
47.Kai Wei, Rishabh K Iyer, and Jeff A Bilmes. Submodularity in data subset selection and active learning. In ICML, 2015.
48.Gert W Wolf. Facility location: concepts, models, algorithms and case studies., 2011.
49.Huan Xu and Shie Mannor. Robustness and generalization. Machine learning, 86(3):391–423, 2012.
50.Yi Yang, Zhigang Ma, Feiping Nie, Xiaojun Chang, and Alexander G Hauptmann. Multi-class active learning by uncertainty sampling with diversity maximization. International Journal of Computer Vision, 113(2):113–127, 2015.
51.Kai Yu, Jinbo Bi, and Volker Tresp. Active learning via transductive experimental design. In Proceedings of the 23rd international conference on Machine learning, pp. 1081–1088. ACM, 2006.

Citation

MLA

Şener, O., and S. Savarese. “Active Learning for Convolutional Neural Networks: A Core-Set Approach”. International Conference on Learning Representations, 2018, https://openreview.net/pdf?id=H1aIuk-RW.

APA

Şener, O., & Savarese, S. (2018). Active Learning for Convolutional Neural Networks: A Core-Set Approach. International Conference on Learning Representations. https://openreview.net/pdf?id=H1aIuk-RW

Chicago

Şener, O., and S. Savarese. 2018. “Active Learning for Convolutional Neural Networks: A Core-Set Approach”. International Conference on Learning Representations. https://openreview.net/pdf?id=H1aIuk-RW.

Harvard

Şener, O. and Savarese, S. (2018) “Active Learning for Convolutional Neural Networks: A Core-Set Approach”, International Conference on Learning Representations [Preprint]. Available at: https://openreview.net/pdf?id=H1aIuk-RW.

Vancouver

1. Şener O, Savarese S (2018) Active Learning for Convolutional Neural Networks: A Core-Set Approach. International Conference on Learning Representations

BibTeX

@article{sener2018active,
  title = {Active Learning for Convolutional Neural Networks: A Core-Set Approach},
  author = {Şener, Ozan and Savarese, Silvio},
  year = {2018},
  journal = {International Conference on Learning Representations},
  url = {https://openreview.net/pdf?id=H1aIuk-RW}
}

Metadata:DOI registry

Source Code

This paper has an official code repository available. Click below to access the source code.

View Repository

Access the Paper

This paper is available from its original source. Click below to access the PDF.

Open PDF

License: Authors

Distance Matrix	Greedy (2-OPT)	MIP (iteration)	MIP (total)	Total Runtime
104.2 s	2.0 s	7.5 s	244.03 s	360.23 s

Active Learning for Convolutional Neural Networks: A Core-Set Approach

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — Risk Decomposition and Core-Set Formulation for Batch Active Learning

Knowl 2 — Upper Bound on CNN Core-Set Loss via Covering Radius

Knowl 3 — Lipschitz Continuity of Convolutional Neural Networks with $l_2$ Softmax Loss

Knowl 4 — Robust $k$-Center Active Selection via Mixed Integer Programming

Knowl 5 — Greedy 2-OPT Approximation for $k$-Center Active Learning

Knowl 6 — Experimental Implementation for CNN Core-Set Selection

Knowl 7 — Active Classification Performance on CIFAR and SVHN Benchmarks