%% introduction

@article{mackay1992information,
  title={Information-based objective functions for active data selection},
  author={MacKay, David JC},
  journal={Neural computation},
  volume={4},
  number={4},
  pages={590--604},
  year={1992},
  publisher={MIT Press}
}


%% related work

% learning from similarity comparisons
@article{tamuz2011adaptively,
  title={Adaptively learning the crowd kernel},
  author={Tamuz, Omer and Liu, Ce and Belongie, Serge and Shamir, Ohad and Kalai, Adam Tauman},
  journal={arXiv preprint arXiv:1105.1033},
  year={2011}
}

@inproceedings{agarwal2007generalized,
  title={Generalized non-metric multidimensional scaling},
  author={Agarwal, Sameer and Wills, Josh and Cayton, Lawrence and Lanckriet, Gert and Kriegman, David and Belongie, Serge},
  booktitle={Artificial Intelligence and Statistics},
  pages={11--18},
  year={2007}
}

@inproceedings{davenport2013lost,
  title={Lost without a compass: Nonmetric triangulation and landmark multidimensional scaling},
  author={Davenport, Mark A},
  booktitle={2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)},
  pages={13--16},
  year={2013},
  organization={IEEE}
}

@inproceedings{canal2020active,
  title={Active Ordinal Querying for Tuplewise Similarity Learning.},
  author={Canal, Gregory and Fenu, Stefano and Rozell, Christopher},
  booktitle={AAAI},
  pages={3332--3340},
  year={2020}
}

@article{canal2019active,
  title={Active embedding search via noisy paired comparisons},
  author={Canal, Gregory H and Massimino, Andrew K and Davenport, Mark A and Rozell, Christopher J},
  journal={arXiv preprint arXiv:1905.04363},
  year={2019}
}

@inproceedings{jamieson2011active,
  title={Active ranking using pairwise comparisons},
  author={Jamieson, Kevin G and Nowak, Robert},
  booktitle={Advances in Neural Information Processing Systems},
  pages={2240--2248},
  year={2011}
}

%kernel PCA
@article{scholkopf1998nonlinear,
  title={Nonlinear component analysis as a kernel eigenvalue problem},
  author={Sch{\"o}lkopf, Bernhard and Smola, Alexander and M{\"u}ller, Klaus-Robert},
  journal={Neural computation},
  volume={10},
  number={5},
  pages={1299--1319},
  year={1998},
  publisher={MIT Press}
}

%t-SNE
@article{maaten2008visualizing,
  title={Visualizing data using t-SNE},
  author={Maaten, Laurens van der and Hinton, Geoffrey},
  journal={Journal of machine learning research},
  volume={9},
  number={Nov},
  pages={2579--2605},
  year={2008}
}

%LLE
@article{roweis2000nonlinear,
  title={Nonlinear dimensionality reduction by locally linear embedding},
  author={Roweis, Sam T and Saul, Lawrence K},
  journal={science},
  volume={290},
  number={5500},
  pages={2323--2326},
  year={2000},
  publisher={American Association for the Advancement of Science}
}

%ISOMAP
@article{tenenbaum2000global,
  title={A global geometric framework for nonlinear dimensionality reduction},
  author={Tenenbaum, Joshua B and De Silva, Vin and Langford, John C},
  journal={science},
  volume={290},
  number={5500},
  pages={2319--2323},
  year={2000},
  publisher={American Association for the Advancement of Science}
}


% active learning 

@techreport{settles2009active,
  title={Active learning literature survey},
  author={Settles, Burr},
  year={2009},
  institution={University of Wisconsin-Madison Department of Computer Sciences}
}

@article{olsson2009literature,
  title={A literature survey of active machine learning in the context of natural language processing},
  author={Olsson, Fredrik},
  year={2009},
  publisher={Swedish Institute of Computer Science}
}

@article{budd2019survey,
  title={A Survey on Active Learning and Human-in-the-Loop Deep Learning for Medical Image Analysis},
  author={Budd, Samuel and Robinson, Emma C and Kainz, Bernhard},
  journal={arXiv preprint arXiv:1910.02923},
  year={2019}
}

@article{long2014active,
  title={Active learning for ranking through expected loss optimization},
  author={Long, Bo and Bian, Jiang and Chapelle, Olivier and Zhang, Ya and Inagaki, Yoshiyuki and Chang, Yi},
  journal={IEEE transactions on knowledge and data engineering},
  volume={27},
  number={5},
  pages={1180--1191},
  year={2014},
  publisher={IEEE}
}

@article{ren2020survey,
  title={A Survey of Deep Active Learning},
  author={Ren, Pengzhen and Xiao, Yun and Chang, Xiaojun and Huang, Po-Yao and Li, Zhihui and Chen, Xiaojiang and Wang, Xin},
  journal={arXiv preprint arXiv:2009.00236},
  year={2020}
}

% embedding learning
@article{kendall1938new,
  title={A new measure of rank correlation},
  author={Kendall, Maurice},
  journal={Biometrika},
  volume={30},
  number={1/2},
  pages={81--93},
  year={1938}
}

@inproceedings{ghosh2019landmark,
  title={Landmark Ordinal Embedding},
  author={Ghosh, Nikhil and Chen, Yuxin and Yue, Yisong},
  booktitle={Advances in Neural Information Processing Systems},
  pages={11506--11515},
  year={2019}
}

@inproceedings{ma2019robust,
  title={Robust ordinal embedding from contaminated relative comparisons},
  author={Ma, Ke and Xu, Qianqian and Cao, Xiaochun},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={33},
  pages={7908--7915},
  year={2019}
}

@article{kruskal1964multidimensional,
  title={Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis},
  author={Kruskal, Joseph B},
  journal={Psychometrika},
  volume={29},
  number={1},
  pages={1--27},
  year={1964},
  publisher={Springer}
}

@article{kruskal1964nonmetric,
  title={Nonmetric multidimensional scaling: a numerical method},
  author={Kruskal, Joseph B},
  journal={Psychometrika},
  volume={29},
  number={2},
  pages={115--129},
  year={1964},
  publisher={Springer-Verlag}
}

@article{shepard1962analysis1,
  title={The analysis of proximities: multidimensional scaling with an unknown distance function. I.},
  author={Shepard, Roger N},
  journal={Psychometrika},
  volume={27},
  number={2},
  pages={125--140},
  year={1962},
  publisher={Springer}
}

@article{shepard1962analysis2,
  title={The analysis of proximities: Multidimensional scaling with an unknown distance function. II},
  author={Shepard, Roger N},
  journal={Psychometrika},
  volume={27},
  number={3},
  pages={219--246},
  year={1962},
  publisher={Springer}
}

@inproceedings{kleindessner2017kernel,
  title={Kernel functions based on triplet comparisons},
  author={Kleindessner, Matth{\"a}us and von Luxburg, Ulrike},
  booktitle={Advances in neural information processing systems},
  pages={6807--6817},
  year={2017}
}

@inproceedings{terada2014local,
  title={Local ordinal embedding},
  author={Terada, Yoshikazu and Luxburg, Ulrike},
  booktitle={International Conference on Machine Learning},
  pages={847--855},
  year={2014}
}

@inproceedings{jamieson2011low,
  title={Low-dimensional embedding using adaptively selected ordinal data},
  author={Jamieson, Kevin G and Nowak, Robert D},
  booktitle={2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)},
  pages={1077--1084},
  year={2011},
  organization={IEEE}
}

@inproceedings{jain2016finite,
  title={Finite sample prediction and recovery bounds for ordinal embedding},
  author={Jain, Lalit and Jamieson, Kevin G and Nowak, Rob},
  booktitle={Advances in neural information processing systems},
  pages={2711--2719},
  year={2016}
}

@inproceedings{van2012stochastic,
  title={Stochastic triplet embedding},
  author={Van Der Maaten, Laurens and Weinberger, Kilian},
  booktitle={2012 IEEE International Workshop on Machine Learning for Signal Processing},
  pages={1--6},
  year={2012},
  organization={IEEE}
}

@article{van2014accelerating,
  title={Accelerating t-SNE using tree-based algorithms},
  author={Van Der Maaten, Laurens},
  journal={The Journal of Machine Learning Research},
  volume={15},
  number={1},
  pages={3221--3245},
  year={2014},
  publisher={JMLR. org}
}

@inproceedings{o2016localizing,
  title={Localizing users and items from paired comparisons},
  author={O'Shaughnessy, Matthew R and Davenport, Mark A},
  booktitle={2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP)},
  pages={1--6},
  year={2016},
  organization={IEEE}
}

@inproceedings{sankaranarayanan2016triplet,
  title={Triplet probabilistic embedding for face verification and clustering},
  author={Sankaranarayanan, Swami and Alavi, Azadeh and Castillo, Carlos D and Chellappa, Rama},
  booktitle={2016 IEEE 8th international conference on biometrics theory, applications and systems (BTAS)},
  pages={1--8},
  year={2016},
  organization={IEEE}
}

@InProceedings{Wah_2014_CVPR,
    author = {Wah, Catherine and Van Horn, Grant and Branson, Steve and Maji, Subhransu and Perona, Pietro and Belongie, Serge},
    title = {Similarity Comparisons for Interactive Fine-Grained Categorization},
    booktitle = {Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
    month = {June},
    year = {2014}
}

@inproceedings{kajino2012convex,
  title={A convex formulation for learning from crowds},
  author={Kajino, Hiroshi and Tsuboi, Yuta and Kashima, Hisashi},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  year={2012}
}

@inproceedings{andre2014crowd,
  title={Crowd synthesis: Extracting categories and clusters from complex data},
  author={Andr{\'e}, Paul and Kittur, Aniket and Dow, Steven P},
  booktitle={Proceedings of the 17th ACM conference on Computer supported cooperative work \& social computing},
  pages={989--998},
  year={2014}
}

@InProceedings{Veit_2017_CVPR,
author = {Veit, Andreas and Belongie, Serge and Karaletsos, Theofanis},
title = {Conditional Similarity Networks},
booktitle = {Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {July},
year = {2017}
}

@inproceedings{amid2015multiview,
  title={Multiview triplet embedding: Learning attributes in multiple maps},
  author={Amid, Ehsan and Ukkonen, Antti},
  booktitle={International Conference on Machine Learning},
  pages={1472--1480},
  year={2015},
  organization={PMLR}
}

@article{karaletsos2015bayesian,
  title={Bayesian representation learning with oracle constraints},
  author={Karaletsos, Theofanis and Belongie, Serge and R{\"a}tsch, Gunnar},
  journal={arXiv preprint arXiv:1506.05011},
  year={2015}
}

@inproceedings{vasileva2018learning,
  title={Learning type-aware embeddings for fashion compatibility},
  author={Vasileva, Mariya I and Plummer, Bryan A and Dusad, Krishna and Rajpal, Shreya and Kumar, Ranjitha and Forsyth, David},
  booktitle={Proceedings of the European Conference on Computer Vision (ECCV)},
  pages={390--405},
  year={2018}
}



% classification

@inproceedings{joshi2009multi,
  title={Multi-class active learning for image classification},
  author={Joshi, Ajay J and Porikli, Fatih and Papanikolopoulos, Nikolaos},
  booktitle={2009 IEEE Conference on Computer Vision and Pattern Recognition},
  pages={2372--2379},
  year={2009},
  organization={IEEE}
}

@article{tuia2009active,
  title={Active learning methods for remote sensing image classification},
  author={Tuia, Devis and Ratle, Fr{\'e}d{\'e}ric and Pacifici, Fabio and Kanevski, Mikhail F and Emery, William J},
  journal={IEEE Transactions on Geoscience and Remote Sensing},
  volume={47},
  number={7},
  pages={2218--2232},
  year={2009},
  publisher={IEEE}
}

@article{houlsby2011bayesian,
  title={Bayesian active learning for classification and preference learning},
  author={Houlsby, Neil and Husz{\'a}r, Ferenc and Ghahramani, Zoubin and Lengyel, M{\'a}t{\'e}},
  journal={arXiv preprint arXiv:1112.5745},
  year={2011}
}

@inproceedings{kapoor2007active,
  title={Active learning with gaussian processes for object categorization},
  author={Kapoor, Ashish and Grauman, Kristen and Urtasun, Raquel and Darrell, Trevor},
  booktitle={2007 IEEE 11th International Conference on Computer Vision},
  pages={1--8},
  year={2007},
  organization={IEEE}
}

@article{tong2001support,
  title={Support vector machine active learning with applications to text classification},
  author={Tong, Simon and Koller, Daphne},
  journal={Journal of machine learning research},
  volume={2},
  number={Nov},
  pages={45--66},
  year={2001}
}

@inproceedings{li2012multi,
  title={Multi-domain active learning for text classification},
  author={Li, Lianghao and Jin, Xiaoming and Pan, Sinno Jialin and Sun, Jian-Tao},
  booktitle={Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining},
  pages={1086--1094},
  year={2012}
}

@inproceedings{gal2017deep,
  title={Deep bayesian active learning with image data},
  author={Gal, Yarin and Islam, Riashat and Ghahramani, Zoubin},
  booktitle={International Conference on Machine Learning},
  pages={1183--1192},
  year={2017},
  organization={PMLR}
}

@article{wang2016cost,
  title={Cost-effective active learning for deep image classification},
  author={Wang, Keze and Zhang, Dongyu and Li, Ya and Zhang, Ruimao and Lin, Liang},
  journal={IEEE Transactions on Circuits and Systems for Video Technology},
  volume={27},
  number={12},
  pages={2591--2600},
  year={2016},
  publisher={IEEE}
}

@article{song2019combining,
  title={Combining MixMatch and Active Learning for Better Accuracy with Fewer Labels},
  author={Song, Shuang and Berthelot, David and Rostamizadeh, Afshin},
  journal={arXiv preprint arXiv:1912.00594},
  year={2019}
}

@article{sener2017active,
  title={Active learning for convolutional neural networks: A core-set approach},
  author={Sener, Ozan and Savarese, Silvio},
  journal={arXiv preprint arXiv:1708.00489},
  year={2017}
}

@inproceedings{kirsch2019batchbald,
  title={Batchbald: Efficient and diverse batch acquisition for deep bayesian active learning},
  author={Kirsch, Andreas and van Amersfoort, Joost and Gal, Yarin},
  booktitle={Advances in Neural Information Processing Systems},
  pages={7026--7037},
  year={2019}
}

@inproceedings{pinsler2019bayesian,
  title={Bayesian batch active learning as sparse subset approximation},
  author={Pinsler, Robert and Gordon, Jonathan and Nalisnick, Eric and Hern{\'a}ndez-Lobato, Jos{\'e} Miguel},
  booktitle={Advances in Neural Information Processing Systems},
  pages={6359--6370},
  year={2019}
}

@article{gao2019consistency,
  title={Consistency-Based Semi-Supervised Active Learning: Towards Minimizing Labeling Cost},
  author={Gao, Mingfei and Zhang, Zizhao and Yu, Guo and Arik, Sercan O and Davis, Larry S and Pfister, Tomas},
  journal={arXiv preprint arXiv:1910.07153},
  year={2019}
}

@inproceedings{zhang2017active,
  title={Active discriminative text representation learning},
  author={Zhang, Ye and Lease, Matthew and Wallace, Byron},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  year={2017}
}

@inproceedings{gao2018active,
  title={Active discriminative network representation learning},
  author={Gao, Li and Yang, Hong and Zhou, Chuan and Wu, Jia and Pan, Shirui and Hu, Yue},
  booktitle={IJCAI International Joint Conference on Artificial Intelligence},
  year={2018}
}

@inproceedings{hoffer2015deep,
  title={Deep metric learning using triplet network},
  author={Hoffer, Elad and Ailon, Nir},
  booktitle={International Workshop on Similarity-Based Pattern Recognition},
  pages={84--92},
  year={2015},
  organization={Springer}
}

%% observation model

@book{train2009discrete,
  title={Discrete choice methods with simulation},
  author={Train, Kenneth E},
  year={2009},
  publisher={Cambridge university press}
}

@article{tversky1981framing,
  title={The framing of decisions and the psychology of choice},
  author={Tversky, Amos and Kahneman, Daniel},
  journal={science},
  volume={211},
  number={4481},
  pages={453--458},
  year={1981},
  publisher={American Association for the Advancement of Science}
}

@article{rosenfeld2019predicting,
  title={Predicting Choice with Set-Dependent Aggregation},
  author={Rosenfeld, Nir and Oshiba, Kojin and Singer, Yaron},
  journal={arXiv preprint arXiv:1906.06365},
  year={2019}
}

@misc{luce1959individual,
  title={Individual choice behavior, 1959},
  author={Luce, R Duncan},
  year={1959},
  publisher={New York: John Wiley \& Sons}
}

@article{cover1991elements,
  title={Elements of Information Theory John Wiley \& Sons},
  author={Cover, Thomas M and Thomas, Joy A},
  journal={New York},
  volume={68},
  pages={69--73},
  year={1991}
}

@article{miller1956magical,
  title={The magical number seven, plus or minus two: Some limits on our capacity for processing information.},
  author={Miller, George A},
  journal={Psychological review},
  volume={63},
  number={2},
  pages={81},
  year={1956},
  publisher={American Psychological Association}
}

@article{kendall1948rank,
  title={Rank correlation methods.},
  author={Kendall, Maurice George},
  year={1948},
  publisher={Griffin}
}

@inproceedings{kumari2020batch,
  title={Batch Decorrelation for Active Metric Learning},
  author={Kumari, Priyadarshini and Goru, Ritesh and Chaudhuri, Siddhartha and Chaudhuri, Subhasis},
  booktitle={IJCAI},
  year={2020}
}

@inproceedings{wilber2014cost,
  title={Cost-effective hits for relative similarity comparisons},
  author={Wilber, Michael and Kwak, Iljung and Belongie, Serge},
  booktitle={Proceedings of the AAAI Conference on Human Computation and Crowdsourcing},
  year={2014}
}

@article{kaya2019deep,
  title={Deep metric learning: A survey},
  author={Kaya, Mahmut and Bilge, Hasan {\c{S}}akir},
  journal={Symmetry},
  volume={11},
  number={9},
  pages={1066},
  year={2019},
  publisher={Multidisciplinary Digital Publishing Institute}
}

@inproceedings{weinberger2006distance,
  title={Distance metric learning for large margin nearest neighbor classification},
  author={Weinberger, Kilian Q and Blitzer, John and Saul, Lawrence K},
  booktitle={Advances in neural information processing systems},
  pages={1473--1480},
  year={2006}
}

@inproceedings{ge2018deep,
  title={Deep metric learning with hierarchical triplet loss},
  author={Ge, Weifeng},
  booktitle={Proceedings of the European Conference on Computer Vision (ECCV)},
  pages={269--285},
  year={2018}
}

@inproceedings{chen2017beyond,
  title={Beyond triplet loss: a deep quadruplet network for person re-identification},
  author={Chen, Weihua and Chen, Xiaotang and Zhang, Jianguo and Huang, Kaiqi},
  booktitle={Proceedings of the IEEE conference on computer vision and pattern recognition},
  pages={403--412},
  year={2017}
}

@inproceedings{davis2007information,
  title={Information-theoretic metric learning},
  author={Davis, Jason V and Kulis, Brian and Jain, Prateek and Sra, Suvrit and Dhillon, Inderjit S},
  booktitle={Proceedings of the 24th international conference on Machine learning},
  pages={209--216},
  year={2007}
}

@article{heim2015active,
  title={Active perceptual similarity modeling with auxiliary information},
  author={Heim, Eric and Berger, Matthew and Seversky, Lee and Hauskrecht, Milos},
  journal={arXiv preprint arXiv:1511.02254},
  year={2015}
}

@article{lohaus2019uncertainty,
  title={Uncertainty estimates for ordinal embeddings},
  author={Lohaus, Michael and Hennig, Philipp and von Luxburg, Ulrike},
  journal={arXiv preprint arXiv:1906.11655},
  year={2019}
}

@article{sohn2020fixmatch,
  title={Fixmatch: Simplifying semi-supervised learning with consistency and confidence},
  author={Sohn, Kihyuk and Berthelot, David and Li, Chun-Liang and Zhang, Zizhao and Carlini, Nicholas and Cubuk, Ekin D and Kurakin, Alex and Zhang, Han and Raffel, Colin},
  journal={arXiv preprint arXiv:2001.07685},
  year={2020}
}

% MNIST dataset
@article{lecun1998gradient,
  title={Gradient-based learning applied to document recognition},
  author={LeCun, Yann and Bottou, L{\'e}on and Bengio, Yoshua and Haffner, Patrick},
  journal={Proceedings of the IEEE},
  volume={86},
  number={11},
  pages={2278--2324},
  year={1998},
  publisher={Ieee}
}

% CIFAR-10 dataset
@article{krizhevsky2009learning,
  title={Learning multiple layers of features from tiny images},
  author={Krizhevsky, Alex and Hinton, Geoffrey and others},
  year={2009},
  publisher={Citeseer}
}

% SVHN dataset
@article{netzer2011reading,
  title={Reading digits in natural images with unsupervised feature learning},
  author={Netzer, Yuval and Wang, Tao and Coates, Adam and Bissacco, Alessandro and Wu, Bo and Ng, Andrew Y},
  year={2011}
}

% Plackett-Luce model
@misc{turner2018introduction,
  title={Introduction to PlackettLuce},
  author={Turner, Heather and van Etten, Jacob and Firth, David and Kosmidis, Ioannis},
  year={2018}
}

% resnet 18
@inproceedings{he2016deep,
  title={Deep residual learning for image recognition},
  author={He, Kaiming and Zhang, Xiangyu and Ren, Shaoqing and Sun, Jian},
  booktitle={Proceedings of the IEEE conference on computer vision and pattern recognition},
  pages={770--778},
  year={2016}
}

% umap
@article{mcinnes2018umap,
  title={Umap: Uniform manifold approximation and projection for dimension reduction},
  author={McInnes, Leland and Healy, John and Melville, James},
  journal={arXiv preprint arXiv:1802.03426},
  year={2018}
}

% normal assumption

@article{mackay1986probabilistic,
  title={A probabilistic model for the multidimensional scaling of proximity and preference data},
  author={MacKay, David B and Zinnes, Joseph L},
  journal={Marketing Science},
  volume={5},
  number={4},
  pages={325--344},
  year={1986},
  publisher={INFORMS}
}