Convex Formulations for Fair Principal Component Analysis

Though there is a growing body of literature on fairness for supervised learning, the problem of incorporating fairness into unsupervised learning has been less well-studied. This paper studies fairness in the context of principal component analysis (PCA). We first present a definition of fairness for dimensionality reduction, and our definition can be interpreted as saying that a reduction is fair if information about a protected class (e.g., race or gender) cannot be inferred from the dimensionality-reduced data points. Next, we develop convex optimization formulations that can improve the fairness (with respect to our definition) of PCA and kernel PCA. These formulations are semidefinite programs (SDP's), and we demonstrate the effectiveness of our formulations using several datasets. We conclude by showing how our approach can be used to perform a fair (with respect to age) clustering of health data that may be used to set health insurance rates.

[1]  Michael I. Jordan,et al.  A Direct Formulation for Sparse Pca Using Semidefinite Programming , 2004, SIAM Rev..

[2]  P. Massart,et al.  Concentration inequalities and model selection , 2007 .

[3]  Blake Lemoine,et al.  Mitigating Unwanted Biases with Adversarial Learning , 2018, AIES.

[4]  Martin J. Wainwright,et al.  High-Dimensional Statistics , 2019 .

[5]  Sven Tuzovic,et al.  Leveraging pushed Self-tracking in the Health Insurance Industry: How do Individuals perceive Smart Wearables offered by Insurance Organization? , 2017, ECIS.

[6]  Zhe Zhao,et al.  Data Decisions and Theoretical Implications when Adversarially Learning Fair Representations , 2017, ArXiv.

[7]  Roberto Todeschini,et al.  Quantitative Structure − Activity Relationship Models for Ready Biodegradability of Chemicals , 2013 .

[8]  Pablo A. Parrilo,et al.  Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization , 2007, SIAM Rev..

[9]  M. Kearns,et al.  Fairness in Criminal Justice Risk Assessments: The State of the Art , 2017, Sociological Methods & Research.

[10]  M. Blair,et al.  Video Game Telemetry as a Critical Tool in the Study of Complex Skill Learning , 2013, PloS one.

[11]  Rekha R. Thomas,et al.  Semidefinite Optimization and Convex Algebraic Geometry , 2012 .

[12]  Toon Calders,et al.  Building Classifiers with Independency Constraints , 2009, 2009 IEEE International Conference on Data Mining Workshops.

[13]  R. Tibshirani,et al.  Sparse Principal Component Analysis , 2006 .

[14]  Alexandra Chouldechova,et al.  Fair prediction with disparate impact: A study of bias in recidivism prediction instruments , 2016, Big Data.

[15]  Richard S. Johannes,et al.  Using the ADAP Learning Algorithm to Forecast the Onset of Diabetes Mellitus , 1988 .

[16]  Nathan Srebro,et al.  Equality of Opportunity in Supervised Learning , 2016, NIPS.

[17]  Carlos Eduardo Scheidegger,et al.  Certifying and Removing Disparate Impact , 2014, KDD.

[18]  Nathan Srebro,et al.  Stochastic Optimization of PCA with Capped MSG , 2013, NIPS.

[19]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[20]  Evgueni A. Haroutunian,et al.  Information Theory and Statistics , 2011, International Encyclopedia of Statistical Science.

[21]  Kush R. Varshney,et al.  Optimized Pre-Processing for Discrimination Prevention , 2017, NIPS.

[22]  M. Feinleib.  National Center for Health Statistics (NCHS) , 2005 .

[23]  Amit Kumar,et al.  Clustering with Spectral Norm and the k-Means Algorithm , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[24]  Athanasios Tsanas,et al.  Accurate quantitative estimation of energy performance of residential buildings using statistical machine learning tools , 2012 .

[25]  Jon A. Wellner,et al.  Empirical Processes with Applications to Statistics. , 1988 .

[26]  Ken Goldberg,et al.  Objectively Measured Baseline Physical Activity Patterns in Women in the mPED Trial: Cluster Analysis , 2018, JMIR public health and surveillance.

[27]  Toniann Pitassi,et al.  Learning Fair Representations , 2013, ICML.

[28]  Charu C. Aggarwal,et al.  On the Surprising Behavior of Distance Metrics in High Dimensional Spaces , 2001, ICDT.

[29]  Toniann Pitassi,et al.  Fairness through awareness , 2011, ITCS '12.

[30]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[31]  Petr Savický,et al.  Methods for multidimensional event classification: A case study using images from a Cherenkov gamma-ray telescope , 2004 .

[32]  A. Bauman,et al.  Environmental and policy interventions to promote physical activity. , 1998, American journal of preventive medicine.

[33]  Matt Olfat,et al.  Spectral Algorithms for Computing Fair Support Vector Machines , 2017, AISTATS.

[34]  Christopher T. Lowenkamp,et al.  False Positives, False Negatives, and False Analyses: A Rejoinder to "Machine Bias: There's Software Used across the Country to Predict Future Criminals. and It's Biased against Blacks" , 2016 .

[35]  I-Cheng Yeh,et al.  The comparisons of data mining techniques for the predictive accuracy of probability of default of credit card clients , 2009, Expert Syst. Appl..

[36]  Silvio Lattanzi,et al.  Fair Clustering Through Fairlets , 2018, NIPS.

[37]  Tong Wang,et al.  Learning to Detect Patterns of Crime , 2013, ECML/PKDD.

[38]  Krishna P. Gummadi,et al.  Fairness Constraints: Mechanisms for Fair Classification , 2015, AISTATS.

[39]  Paul Horton,et al.  A Probabilistic Classification System for Predicting the Cellular Localization Sites of Proteins , 1996, ISMB.

[40]  Paulo Cortez,et al.  Modeling wine preferences by data mining from physicochemical properties , 2009, Decis. Support Syst..

[41]  Indre Zliobaite,et al.  On the relation between accuracy and fairness in binary classification , 2015, ArXiv.

[42]  Andrew D. Selbst,et al.  Big Data's Disparate Impact , 2016 .