@article{raghunathan2021synthetic,
  title={Synthetic data},
  author={Raghunathan, Trivellore E},
  journal={Annual review of statistics and its application},
  volume={8},
  pages={129--140},
  year={2021},
  publisher={Annual Reviews}
}


@article{bellovin2019privacy,
  title={Privacy and synthetic datasets},
  author={Bellovin, Steven M and Dutta, Preetam K and Reitinger, Nathan},
  journal={Stanford Technology Law Review},
  volume={22},
  pages={1},
  year={2019},
  publisher={HeinOnline}
}

@article{algorithmic2014dwork,
author = {Dwork, Cynthia and Roth, Aaron},
title = {{The Algorithmic Foundations of Differential Privacy}},
year = {2014},
publisher = {Now Publishers Inc.},
volume = {9},
number = {3–4},
journal = {Foundations and Trends in Theoretical Computer Science},
pages = {211–407},
numpages = {197}
}


@inproceedings{dwork2008differential,
  title={{Differential privacy: A survey of results}},
  author={Dwork, Cynthia},
  booktitle={International conference on theory and applications of models of computation},
  pages={1--19},
  year={2008},
  organization={Springer}
}

@inproceedings{dwork2006differential,
  title={Differential privacy},
  author={Dwork, Cynthia},
  booktitle={International colloquium on automata, languages, and programming},
  pages={1--12},
  year={2006},
  organization={Springer}
}

@article{rubin1993statistical,
  title={Statistical disclosure limitation},
  author={Rubin, Donald B},
  journal={Journal of official Statistics},
  volume={9},
  number={2},
  pages={461--468},
  year={1993}
}

@article{raghunathan2003multiple,
  title={Multiple imputation for statistical disclosure limitation},
  author={Raghunathan, Trivellore E and Reiter, Jerome P and Rubin, Donald B},
  journal={Journal of official statistics},
  volume={19},
  number={1},
  pages={1},
  year={2003},
  publisher={Statistics Sweden (SCB)}
}

@book{drechsler2011synthetic,
  title={Synthetic datasets for statistical disclosure control: theory and implementation},
  author={Drechsler, J{\"o}rg},
  volume={201},
  year={2011},
  publisher={Springer Science \& Business Media}
}

@article{raab2016practical,
  title={Practical data synthesis for large samples},
  author={Raab, Gillian M and Nowok, Beata and Dibben, Chris},
  journal={Journal of Privacy and Confidentiality},
  volume={7},
  number={3},
  pages={67--97},
  year={2016}
}

@article{reiter2005releasing,
  title={Releasing multiply imputed, synthetic public use microdata: an illustration and empirical study},
  author={Reiter, Jerome P},
  journal={Journal of the Royal Statistical Society Series A: Statistics in Society},
  volume={168},
  number={1},
  pages={185--205},
  year={2005},
  publisher={Oxford University Press}
}

@article{yan2022multifaceted,
  title={A multifaceted benchmarking of synthetic electronic health record generation models},
  author={Yan, Chao and Yan, Yao and Wan, Zhiyu and Zhang, Ziqi and Omberg, Larsson and Guinney, Justin and Mooney, Sean D and Malin, Bradley A},
  journal={Nature communications},
  volume={13},
  number={1},
  pages={7609},
  year={2022},
  publisher={Nature Publishing Group UK London}
}

@article{van2023synthetic,
  title={{Synthetic data, real errors: How (not) to publish and use synthetic data}},
  author={van Breugel, Boris and Qian, Zhaozhi and van der Schaar, Mihaela},
  journal={arXiv preprint},
  year={2023}
}

@article{zhang2020ensuring,
  title={Ensuring electronic medical record simulation through better training, modeling, and evaluation},
  author={Zhang, Ziqi and Yan, Chao and Mesa, Diego A and Sun, Jimeng and Malin, Bradley A},
  journal={Journal of the American Medical Informatics Association},
  volume={27},
  number={1},
  pages={99--108},
  year={2020},
  publisher={Oxford University Press}
}

@inproceedings{endres2022synthetic,
  title={Synthetic data generation: a comparative study},
  author={Endres, Markus and Mannarapotta Venugopal, Asha and Tran, Tung Son},
  booktitle={Proceedings of the 26th International Database Engineered Applications Symposium},
  pages={94--102},
  year={2022}
}

@inproceedings{wan2017variational,
  title={Variational autoencoder based synthetic data generation for imbalanced learning},
  author={Wan, Zhiqiang and Zhang, Yazhou and He, Haibo},
  booktitle={{2017 IEEE symposium series on computational intelligence (SSCI)}},
  pages={1--7},
  year={2017},
  organization={IEEE}
}

@inproceedings{brain1999effect,
  title={On the effect of data set size on bias and variance in classification learning},
  author={Brain, Damien and Webb, Geoffrey I},
  booktitle={{Proceedings of the Fourth Australian Knowledge Acquisition Workshop, University of New South Wales}},
  pages={117--128},
  year={1999}
}

@inproceedings{liu2022goggle,
  title={{GOGGLE}: Generative modelling for tabular data by learning relational structure},
  author={Liu, Tennison and Qian, Zhaozhi and Berrevoets, Jeroen and van der Schaar, Mihaela},
  booktitle={{The Eleventh International Conference on Learning Representations}},
  year={2022}
}

@article{chen2021synthetic,
author = {Chen, Richard and Lu, Ming and Chen, Tiffany and Williamson, Drew and Mahmood, Faisal},
year = {2021},
pages = {1-5},
title = {Synthetic data in machine learning for medicine and healthcare},
volume = {5},
journal = {Nature Biomedical Engineering}
}

@article{hernandez2022synthetic,
  title={{Synthetic data generation for tabular health records: A systematic review}},
  author={Hernandez, Mikel and Epelde, Gorka and Alberdi, Ane and Cilla, Rodrigo and Rankin, Debbie},
  journal={Neurocomputing},
  volume={493},
  pages={28--45},
  year={2022},
  publisher={Elsevier}
}

@inproceedings{stadler2022synthetic,
  title={Synthetic data--anonymisation groundhog day},
  author={Stadler, Theresa and Oprisanu, Bristena and Troncoso, Carmela},
  booktitle={31st USENIX Security Symposium (USENIX Security 22)},
  pages={1451--1468},
  year={2022}
}

@article{xu2019modeling,
  title={Modeling tabular data using conditional {GAN}},
  author={Xu, Lei and Skoularidou, Maria and Cuesta-Infante, Alfredo and Veeramachaneni, Kalyan},
  journal={Advances in neural information processing systems},
  volume={32},
  year={2019}
}

@article{odaibo2019tutorial,
  title={{Tutorial: Deriving the standard variational autoencoder (vae) loss function}},
  author={Odaibo, Stephen},
  journal={arXiv preprint arXiv:1907.08956},
  year={2019}
}

@article{goodfellow2014generative,
  title={Generative adversarial nets},
  author={Goodfellow, Ian and Pouget-Abadie, Jean and Mirza, Mehdi and Xu, Bing and Warde-Farley, David and Ozair, Sherjil and Courville, Aaron and Bengio, Yoshua},
  journal={Advances in neural information processing systems},
  volume={27},
  year={2014}
}


@Article{synthpop2016,
    title = {{Synthpop}: Bespoke Creation of Synthetic Data in {R}},
    author = {Beata Nowok and Gillian M. Raab and Chris Dibben},
    journal = {Journal of Statistical Software},
    year = {2016},
    volume = {74},
    number = {11},
    pages = {1--26},
  }


@book{boos2013essential,
  title={Essential statistical inference: theory and methods},
  author={Boos, Dennis D and Stefanski, Leonard A},
  volume={591},
  year={2013},
  publisher={Springer}
}


@article{greene2000econometric,
  title={Econometric analysis 4th edition},
  author={Greene, William H},
  journal={International edition, New Jersey: Prentice Hall},
  pages={201--215},
  year={2000}
}

@book{python,
 author = {Van Rossum, Guido and Drake, Fred L.},
 title = {Python 3 Reference Manual},
 year = {2009},
 isbn = {1441412697},
 publisher = {CreateSpace},
 address = {Scotts Valley, CA}
}

@article{kingma2013auto,
  title={Auto-encoding variational bayes},
  author={Kingma, Diederik P and Welling, Max},
  journal={arXiv preprint},
  year={2013}
}

@inproceedings{alaa2022faithful,
  title={{How faithful is your synthetic data? Sample-level metrics for evaluating and auditing generative models}},
  author={Alaa, Ahmed and Van Breugel, Boris and Saveliev, Evgeny S and van der Schaar, Mihaela},
  booktitle={{International Conference on Machine Learning}},
  pages={290--306},
  year={2022},
  organization={PMLR}
}

@book{lehmann2006theory,
  title={Theory of point estimation},
  author={Lehmann, Erich L and Casella, George},
  year={2006},
  publisher={Springer Science \& Business Media}
}

@book{van2000asymptotic,
  title={Asymptotic statistics},
  author={Van der Vaart, Aad W},
  volume={3},
  year={2000},
  publisher={Cambridge university press}
}

@article{vansteelandt2022assumption,
  title={Assumption-lean inference for generalised linear model parameters},
  author={Vansteelandt, Stijn and Dukes, Oliver},
  journal={Journal of the Royal Statistical Society Series B: Statistical Methodology},
  volume={84},
  number={3},
  pages={657--685},
  year={2022},
  publisher={Oxford University Press}
}


@inproceedings{ankan2015pgmpy,
  title={pgmpy: Probabilistic graphical models using {Python}},
  author={Ankan, Ankur and Panda, Abinash},
  booktitle={{Proceedings of the 14th Python in Science Conference (SCIPY 2015)}},
  year={2015}
}

@online{ForwardSampling,
  author = {Kuleshov, Volodymyr and Ermon, Stefano},
  title = {Sampling methods},
  year = 2023,
  url = {https://ermongroup.github.io/cs228-notes/inference/sampling/},
  urldate = {2023-09-08}
}

@book{pearl2011BN,
    title={Bayesian Networks},
    author={Pearl, Judea},
    year = {2011}
}


@book{kutner2005applied,
  title={Applied linear statistical models},
  author={Kutner, Michael H and Nachtsheim, Christopher J and Neter, John and Li, William},
  volume={5},
  year={2005},
  publisher={McGraw-Hill Irwin Boston}
}

@article{ghosheh2022review,
  title={{A review of Generative Adversarial Networks for Electronic Health Records: applications, evaluation measures and data sources}},
  author={Ghosheh, Ghadeer and Li, Jin and Zhu, Tingting},
  journal={arXiv preprint},
  year={2022}
}

@article{gelman2014beyond,
  title={Beyond power calculations: Assessing type S (sign) and type M (magnitude) errors},
  author={Gelman, Andrew and Carlin, John},
  journal={Perspectives on Psychological Science},
  volume={9},
  number={6},
  pages={641--651},
  year={2014},
  publisher={Sage Publications Sage CA: Los Angeles, CA}
}

@article{Synthcity,
  author = {Qian, Zhaozhi and Cebere, Bogdan-Constantin and van der Schaar, Mihaela},
  title = {Synthcity: facilitating innovative use cases of synthetic data in different data modalities},
  year = {2023},
  journal = {arXiv preprint}
}

@inproceedings{assefa2021finance,
author = {Assefa, Samuel A. and Dervovic, Danial and Mahfouz, Mahmoud and Tillman, Robert E. and Reddy, Prashant and Veloso, Manuela},
title = {{Generating Synthetic Data in Finance: Opportunities, Challenges and Pitfalls}},
year = {2021},
publisher = {Association for Computing Machinery},
booktitle = {{Proceedings of the First ACM International Conference on AI in Finance}},
articleno = {44},
numpages = {8},
location = {New York, New York},
series = {ICAIF '20}
}

@article{tao2021benchmarking,
  author       = {Yuchao Tao and
                  Ryan McKenna and
                  Michael Hay and
                  Ashwin Machanavajjhala and
                  Gerome Miklau},
  title        = {{Benchmarking Differentially Private Synthetic Data Generation Algorithms}},
  journal      = {arXiv preprint},
  year         = {2021},
}

@article{bourou2021tabular,
author = {Bourou, Stavroula and El Saer, Andreas and Velivasaki, Terpsichori‐Helen and Voulkidis, Artemis and Zahariadis, Theodore},
year = {2021},
pages = {375},
title = {{A Review of Tabular Data Synthesis Using {GANs} on an {IDS} Dataset}},
volume = {12},
journal = {Information}
}


@Article{rajabi2022tabfairgan,
AUTHOR = {Rajabi, Amirarsalan and Garibay, Ozlem Ozmen},
TITLE = {{{TabFairGAN}: Fair Tabular Data Generation with Generative Adversarial Networks}},
JOURNAL = {Machine Learning and Knowledge Extraction},
VOLUME = {4},
YEAR = {2022},
NUMBER = {2},
PAGES = {488--501},
ISSN = {2504-4990}
}


@Article{figueira2022survey,
AUTHOR = {Figueira, Alvaro and Vaz, Bruno},
TITLE = {{Survey on Synthetic Data Generation, Evaluation Methods and GANs}},
JOURNAL = {Mathematics},
VOLUME = {10},
YEAR = {2022},
NUMBER = {15},
ARTICLE-NUMBER = {2733},
ISSN = {2227-7390}
}

@article{chale2022intrusion,
title = {Generating realistic cyber data for training and evaluating machine learning classifiers for network intrusion detection systems},
journal = {Expert Systems with Applications},
volume = {207},
pages = {117936},
year = {2022},
issn = {0957-4174},
author = {Marc Chalé and Nathaniel D. Bastian}
}

@article{el2020seven,
  title={Seven ways to evaluate the utility of synthetic data},
  author={El Emam, Khaled},
  journal={IEEE Security \& Privacy},
  volume={18},
  number={4},
  pages={56--59},
  year={2020},
  publisher={IEEE}
}

@article{kaloskampis2020synthetic,
  title={Synthetic data in the civil service},
  author={Kaloskampis, Ioannis and Joshi, Chaitanya and Cheung, Catrin and Nolan, Louisa},
  journal={Significance},
  volume={17},
  number={6},
  pages={18--23},
  year={2020},
  publisher={Oxford University Press}
}

@book{van2011targeted,
  title={Targeted learning: causal inference for observational and experimental data},
  author={Van der Laan, Mark J and Rose, Sherri},
  volume={4},
  year={2011},
  publisher={Springer}
}

@incollection{SALASPARRA2023195,
title = {Chapter 32 - {Basic science statistics}},
booktitle = {Translational Surgery},
publisher = {Academic Press},
pages = {195-199},
year = {2023},
series = {Handbook for Designing and Conducting Clinical and Translational Research},
author = {Ruben D. Salas-Parra and Kenny J. Castro-Ochoa and David A. Machado-Aranda},
}

@inproceedings{
    SDV,
    title={The Synthetic data vault},
    author={Patki, Neha and Wedge, Roy and Veeramachaneni, Kalyan},
    booktitle={{IEEE International Conference on Data Science and Advanced Analytics (DSAA)}},
    year={2016},
    pages={399-410},
}

@inproceedings{optuna_2019,
    title={{Optuna: A Next-generation Hyperparameter Optimization Framework}},
    author={Akiba, Takuya and Sano, Shotaro and Yanase, Toshihiko and Ohta, Takeru and Koyama, Masanori},
    booktitle={{Proceedings of the 25th {ACM} {SIGKDD} International Conference on Knowledge Discovery and Data Mining}},
    year={2019}
}

@ARTICLE{chowliu,
  author={Chow, C. and Liu, C.},
  journal={IEEE Transactions on Information Theory}, 
  title={Approximating discrete probability distributions with dependence trees}, 
  year={1968},
  volume={14},
  number={3},
  pages={462-467}
}

@misc{misc_adult_2,
  author       = {Becker,Barry and Kohavi,Ronny},
  title        = {{Adult}},
  year         = {1996},
  howpublished = {UCI Machine Learning Repository}
}

@book{brickel1993efficient,
    author = {Bickel, Peter and Klaassen, Chris and Ritov, Ya'acov and Wellner, Jon},
    year = {1993},
    title = {{Efficient and Adaptive Estimation for Semiparametric Models}},
    volume = {4},
    publisher = {Baltimore Johns Hopkins University Press}
}

@article{demystifying2022hines,
  author       = {Hines, Oliver and Dukes, Oliver and Diaz-Ordaz, Karla and Vansteelandt, Stijn},
  journal      = {AMERICAN STATISTICIAN},
  number       = {3},
  pages        = {292--304},
  title        = {Demystifying statistical learning based on efficient influence functions},
  volume       = {76},
  year         = {2022},
}

@article{espinosa_2023,
AUTHOR = {Espinosa, Erica and Figueira, Alvaro},
TITLE = {{On the Quality of Synthetic Generated Tabular Data}},
JOURNAL = {Mathematics},
VOLUME = {11},
YEAR = {2023},
NUMBER = {15},
ARTICLE-NUMBER = {3278},
ISSN = {2227-7390}
}


@article{drechsler30yearsof,
  title={30 Years of Synthetic Data},
  author={Drechsler, Joerg and Haensch, Anna-Carolina},
  journal={arXiv preprint arXiv:2304.02107},
  year={2023}
}

@article{reiter2009estimating,
  title={Estimating risks of identification disclosure in partially synthetic data},
  author={Reiter, Jerome P and Mitra, Robin},
  journal={Journal of Privacy and Confidentiality},
  volume={1},
  number={1},
  year={2009}
}

@article{drechsler2009disclosure,
  title={Disclosure risk and data utility for partially synthetic data: An empirical study using the German IAB Establishment Survey},
  author={Drechsler, Jorg and Reiter, JP},
  journal={Journal of Official Statistics},
  volume={25},
  number={4},
  pages={589--603},
  year={2009},
  publisher={Statistics Sweden (SCB)}
}

@article{reiter2010releasing,
  title={Releasing multiply-imputed synthetic data generated in two stages to protect confidentiality},
  author={Reiter, Jerome P and Drechsler, J{\"o}rg},
  journal={Statistica Sinica},
  pages={405--421},
  year={2010},
  publisher={JSTOR}
}

@inproceedings{wilde2021foundations,
  title={Foundations of Bayesian learning from synthetic data},
  author={Wilde, Harrison and Jewson, Jack and Vollmer, Sebastian and Holmes, Chris},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={541--549},
  year={2021},
  organization={PMLR}
}

@inproceedings{raisa2023noise,
  title={Noise-Aware Statistical Inference with Differentially Private Synthetic Data},
  author={R{\"a}is{\"a}, Ossi and J{\"a}lk{\"o}, Joonas and Kaski, Samuel and Honkela, Antti},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={3620--3643},
  year={2023},
  organization={PMLR}
}

@article{klein2015likelihood,
  title={Likelihood based finite sample inference for singly imputed synthetic data under the multivariate normal and multiple linear regression models},
  author={Klein, Martin and Sinha, Bimal},
  journal={Journal of Privacy and Confidentiality},
  volume={7},
  number={1},
  year={2015}
}

@misc{ghalebikesabi2022mitigating,
      title={Mitigating Statistical Bias within Differentially Private Synthetic Data}, 
      author={Sahra Ghalebikesabi and Harrison Wilde and Jack Jewson and Arnaud Doucet and Sebastian Vollmer and Chris Holmes},
      year={2022},
      eprint={2108.10934},
      archivePrefix={arXiv},
      primaryClass={stat.ML}
}

@book{van_der_laan_targeted_2011,
	Address = {New York, NY},
	Author = {van der Laan, Mark J. and Rose, Sherri},
	Doi = {10.1007/978-1-4419-9782-1},
	Isbn = {978-1-4419-9781-4 978-1-4419-9782-1},
	Publisher = {Springer New York},
	Series = {Springer {Series} in {Statistics}},
	Title = {Targeted {Learning}},
	Year = {2011},
	Bdsk-Url-1 = {http://link.springer.com/10.1007/978-1-4419-9782-1},
	Bdsk-Url-2 = {http://dx.doi.org/10.1007/978-1-4419-9782-1}}

@article{chernozhukov_double/debiased_2018,
author = {Chernozhukov, Victor and Chetverikov, Denis and Demirer, Mert and Duflo, Esther and Hansen, Christian and Newey, Whitney and Robins, James},
    title = "{Double/debiased machine learning for treatment and structural parameters}",
    journal = {The Econometrics Journal},
    volume = {21},
    number = {1},
    pages = {C1-C68},
    year = {2018},
    abstract = "{We revisit the classic semi?parametric problem of inference on a low?dimensional parameter ?0 in the presence of high?dimensional nuisance parameters ?0. We depart from the classical setting by allowing for ?0 to be so high?dimensional that the traditional assumptions (e.g. Donsker properties) that limit complexity of the parameter space for this object break down. To estimate ?0, we consider the use of statistical or machine learning (ML) methods, which are particularly well suited to estimation in modern, very high?dimensional cases. ML methods perform well by employing regularization to reduce variance and trading off regularization bias with overfitting in practice. However, both regularization bias and overfitting in estimating ?0 cause a heavy bias in estimators of ?0 that are obtained by naively plugging ML estimators of ?0 into estimating equations for ?0. This bias results in the naive estimator failing to be N?1/2 consistent, where N is the sample size. We show that the impact of regularization bias and overfitting on estimation of the parameter of interest ?0 can be removed by using two simple, yet critical, ingredients: (1) using Neyman?orthogonal moments/scores that have reduced sensitivity with respect to nuisance parameters to estimate ?0; (2) making use of cross?fitting, which provides an efficient form of data?splitting. We call the resulting set of methods double or debiased ML (DML). We verify that DML delivers point estimators that concentrate in an N?1/2?neighbourhood of the true parameter values and are approximately unbiased and normally distributed, which allows construction of valid confidence statements. The generic statistical theory of DML is elementary and simultaneously relies on only weak theoretical requirements, which will admit the use of a broad array of modern ML methods for estimating the nuisance parameters, such as random forests, lasso, ridge, deep neural nets, boosted trees, and various hybrids and ensembles of these methods. We illustrate the general theory by applying it to provide theoretical properties of the following: DML applied to learn the main regression parameter in a partially linear regression model; DML applied to learn the coefficient on an endogenous variable in a partially linear instrumental variables model; DML applied to learn the average treatment effect and the average treatment effect on the treated under unconfoundedness; DML applied to learn the local average treatment effect in an instrumental variables setting. In addition to these theoretical applications, we also illustrate the use of DML in three empirical examples.}",
    issn = {1368-4221},
    doi = {10.1111/ectj.12097},
    eprint = {https://academic.oup.com/ectj/article-pdf/21/1/C1/27684918/ectj00c1.pdf},
}

@article{ohm2009broken,
  title={Broken promises of privacy: Responding to the surprising failure of anonymization},
  author={Ohm, Paul},
  journal={UCLA l. Rev.},
  volume={57},
  pages={1701},
  year={2009},
  publisher={HeinOnline}
}

@article{zhang2017privbayes,
  title={Privbayes: Private data release via bayesian networks},
  author={Zhang, Jun and Cormode, Graham and Procopiuc, Cecilia M and Srivastava, Divesh and Xiao, Xiaokui},
  journal={ACM Transactions on Database Systems (TODS)},
  volume={42},
  number={4},
  pages={1--41},
  year={2017},
  publisher={ACM New York, NY, USA}
}

@inproceedings{jordon2018pate,
  title={PATE-GAN: Generating synthetic data with differential privacy guarantees},
  author={Jordon, James and Yoon, Jinsung and Van Der Schaar, Mihaela},
  booktitle={International conference on learning representations},
  year={2018}
}

@article{xie2018differentially,
  title={Differentially private generative adversarial network},
  author={Xie, Liyang and Lin, Kaixiang and Wang, Shu and Wang, Fei and Zhou, Jiayu},
  journal={arXiv preprint arXiv:1802.06739},
  year={2018}
}

@article{akiya2024comparison,
  title={A Comparison of Synthetic Data Generation Techniques for Control Group Survival Data in Oncology Clinical Trials: Simulation Study.},
  author={Akiya, Ippei and Ishihara, Takuma and Yamamoto, Keiichi},
  journal={JMIR Medical Informatics},
  year={2024}
}

@article{el2024evaluation,
  title={An evaluation of the replicability of analyses using synthetic health data},
  author={El Emam, Khaled and Mosquera, Lucy and Fang, Xi and El-Hussuna, Alaa},
  journal={Scientific Reports},
  volume={14},
  number={1},
  pages={6978},
  year={2024},
  publisher={Nature Publishing Group UK London}
}