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@article{rosenbaum1983central,
  title={The central role of the propensity score in observational studies for causal effects},
  author={Rosenbaum, Paul R and Rubin, Donald B},
  journal={Biometrika},
  volume={70},
  number={1},
  pages={41--55},
  year={1983},
  publisher={Oxford University Press}
}

@article{austin2011introduction,
  title={An introduction to propensity score methods for reducing the effects of confounding in observational studies},
  author={Austin, Peter C},
  journal={Multivariate behavioral research},
  volume={46},
  number={3},
  pages={399--424},
  year={2011},
  publisher={Taylor \& Francis}
}

@book{pearl2000,
  author = 	 {J.~Pearl},
  title = 	 {Causality: Models, Reasoning, and Inference},
  publisher = 	 {Cambridge University Press},
  year = 	 {2000}
}

@article{pearl1995empirical,
  title={Causal diagrams for empirical research},
  author={Pearl, Judea},
  journal={Biometrika},
  volume={82},
  number={4},
  pages={669--688},
  year={1995},
  publisher={Oxford University Press}
}


@article{brennan2009evaluating,
  title={Evaluating the predictive validity of the COMPAS risk and needs assessment system},
  author={Brennan, Tim and Dieterich, William and Ehret, Beate},
  journal={Criminal Justice and Behavior},
  volume={36},
  number={1},
  pages={21--40},
  year={2009},
  publisher={Sage Publications Sage CA: Los Angeles, CA}
}


@article{hernan2004structural,
  title={A structural approach to selection bias},
  author={Hern{\'a}n, Miguel A and Hern{\'a}ndez-D{\'\i}az, Sonia and Robins, James M},
  journal={Epidemiology},
  volume={15},
  number={5},
  pages={615--625},
  year={2004},
  publisher={LWW}
}

@inproceedings{DBLP:conf/icml/Kusner0LS19,
  author    = {Matt J. Kusner and
               Chris Russell and
               Joshua R. Loftus and
               Ricardo Silva},
  title     = {Making Decisions that Reduce Discriminatory Impacts},
  booktitle = {{ICML}},
  series    = {Proceedings of Machine Learning Research},
  volume    = {97},
  pages     = {3591--3600},
  publisher = {{PMLR}},
  year      = {2019}
}

@inproceedings{tolan2019why,
	Acmid = {3326705},
	Address = {New York, NY, USA},
	Author = {Tolan, Song\"{u}l and Miron, Marius and G\'{o}mez, Emilia and Castillo, Carlos},
	Booktitle = {Proceedings of the Seventeenth International Conference on Artificial Intelligence and Law},
	Date-Added = {2019-08-02 06:37:23 +0000},
	Date-Modified = {2019-08-02 06:38:23 +0000},
	Doi = {10.1145/3322640.3326705},
	Isbn = {978-1-4503-6754-7},
	Keywords = {algorithmic bias, algorithmic fairness, criminal recidivism, machine learning, risk assessment},
	Location = {Montreal, QC, Canada},
	Numpages = {10},
	Pages = {83--92},
	Publisher = {ACM},
	Series = {ICAIL '19},
	Title = {Why Machine Learning May Lead to Unfairness: Evidence from Risk Assessment for Juvenile Justice in Catalonia},
	Url = {http://doi.acm.org/10.1145/3322640.3326705},
	Year = {2019}
	}

@article{pearl2010introduction,
	Author = {Pearl, Judea},
	Journal = {The international journal of biostatistics},
	Number = {2},
	Publisher = {De Gruyter},
	Title = {An introduction to causal inference},
	Volume = {6},
	Year = {2010}}

@book{bookofwhy,
  title={The book of why: the new science of cause and effect},
  author={Pearl, Judea and Mackenzie, Dana},
  year={2018},
  publisher={Basic Books},
  address = {New York, USA}
}

@inproceedings{lakkaraju2017selective,
	Acmid = {3098066},
	Address = {New York, NY, USA},
	Author = {Lakkaraju, Himabindu and Kleinberg, Jon and Leskovec, Jure and Ludwig, Jens and Mullainathan, Sendhil},
	Booktitle = {Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining},
	Doi = {10.1145/3097983.3098066},
	Isbn = {978-1-4503-4887-4},
	Keywords = {evaluating machine learning algorithms, selective labels, unmeasured confounders, unobservables},
	Location = {Halifax, NS, Canada},
	Numpages = {10},
	Pages = {275--284},
	Publisher = {ACM},
	Series = {KDD '17},
	Title = {The Selective Labels Problem: Evaluating Algorithmic Predictions in the Presence of Unobservables},
	Url = {http://doi.acm.org/10.1145/3097983.3098066},
	Year = {2017},
	Bdsk-Url-1 = {http://doi.acm.org/10.1145/3097983.3098066},
	Bdsk-Url-2 = {http://dx.doi.org/10.1145/3097983.3098066}}

@article{jung2018algorithmic,
	Author = {Jung, Jongbin and Shroff, Ravi and Feller, Avi and Goel, Sharad},
	Date-Added = {2019-08-02 06:37:23 +0000},
	Date-Modified = {2019-08-02 06:37:23 +0000},
	Journal = {arXiv preprint arXiv:1805.01868},
	Title = {Algorithmic decision making in the presence of unmeasured confounding},
	Year = {2018}}

@article{dearteaga2018learning,
	Author = {De-Arteaga, Maria and Dubrawski, Artur and Chouldechova, Alexandra},
	Date-Added = {2019-08-02 06:37:23 +0000},
	Date-Modified = {2019-08-02 06:37:23 +0000},
	Journal = {arXiv preprint arXiv:1807.00905},
	Title = {Learning under selective labels in the presence of expert consistency},
	Year = {2018}}

@article{ohagan1979outlier,
  title={On outlier rejection phenomena in Bayes inference},
  author={O'Hagan, Anthony},
  journal={Journal of the Royal Statistical Society: Series B (Methodological)},
  volume={41},
  number={3},
  pages={358--367},
  year={1979},
  publisher={Wiley Online Library}
}

@inproceedings{bareinboim2012controlling,
  title={Controlling selection bias in causal inference},
  author={Bareinboim, Elias and Pearl, Judea},
  booktitle={Artificial Intelligence and Statistics},
  pages={100--108},
  year={2012}
}

@misc{kleinberg2016inherent,
    title={Inherent Trade-Offs in the Fair Determination of Risk Scores},
    author={Jon Kleinberg and Sendhil Mullainathan and Manish Raghavan},
    year={2016},
    eprint={1609.05807},
    archivePrefix={arXiv},
    primaryClass={cs.LG}
}

@article{angwin2016machine, 
  title={Machine Bias}, 
  url={https://www.propublica.org/article/machine-bias-risk-assessments-in-criminal-sentencing}, 
  journal={ProPublica}, 
  author={Julia Angwin and Jeff Larson and Surya Mattu and Lauren Kirchner}
} 

@article{mccandless2007bayesian,
  title={Bayesian sensitivity analysis for unmeasured confounding in observational studies},
  author={McCandless, Lawrence C and Gustafson, Paul and Levy, Adrian},
  journal={Statistics in medicine},
  volume={26},
  number={11},
  pages={2331--2347},
  year={2007},
  publisher={Wiley Online Library}
}