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Linear regression is one of the most prevalent techniques in machine learning, however, it is also common to use linear regression for its \emph{explanatory} capabilities rather than label prediction.
Solution of incorrectly formulated problems and the regularization method
Tikhonov, A. N · 1963
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Ridge regression: Biased estimation for nonorthogonal problems
Hoerl, A. E. and Kennard, R. W · 1970
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Linear statistical inference and its applications
Rao, C. Radhakrishna · 1973
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On lower bounds for the smallest eigenvalue of a hermitian positive-definite matrix
Ma, E. M. and Zarowski, Christopher J · 1995
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Adaptive estimation of a quadratic functional by model selection
Laurent, B. and Massart, P · 2000
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Linear Model Theory: Univariate, Multivariate, and Mixed Models
Muller, Keith E. and Stewart, Paul W · 2006
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Improved approx. algs for large matrices via random projections
Sarlós, T · 2006
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Zhou, S., Lafferty, J., and Wasserman, L · 2007
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What can we learn privately?
Kasiviswanathan, S., Lee, H., Nissim, K., Raskhodnikova, S., and Smith, A · 2008
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Statistical Methods for the Social Sciences
Agresti, A. and Finlay, B · 2009
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Differential privacy and robust statistics
Dwork, C. and Lei, J · 2009
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Smallest singular value of a random rectangular matrix
Rudelson, Mark and Vershynin, Roman · 2009
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Differential privacy for clinical trial data: Preliminary evaluations
Vu, D. and Slavkovic, A · 2009
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Differentially private empirical risk minimization
Chaudhuri, Kamalika, Monteleoni, Claire, and Sarwate, Anand D · 2011
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Privacy-preserving statistical estimation with optimal convergence rates
Smith, Adam D · 2011
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Mixture of gaussian models and bayes error under differential privacy
Xi, B., Kantarcioglu, M., and Inan, A · 2011
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The Johnson-Lindenstrauss transform itself preserves differential privacy
Blocki, J., Blum, A., Datta, A., and Sheffet, O · 2012
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Differentially private feature selection via stability arguments, and the robustness of the lasso
Thakurta, Abhradeep and Smith, Adam · 2013
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Privacy-preserving data sharing for genome-wide association studies
Uhler, Caroline, Slavkovic, Aleksandra B., and Fienberg, Stephen E · 2013
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Private empirical risk minimization: Efficient algorithms and tight error bounds
Bassily, R., Smith, A., and Thakurta, A · 2014
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Analyze gauss - optimal bounds for privacy preserving principal component analysis
Dwork, Cynthia, Talwar, Kunal, Thakurta, Abhradeep, and Zhang, Li · 2014
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Impact of HbA1c measurement on hospital readmission rates: Analysis of 70,000 clinical database patient records
Strack, B., DeShazo, J., Gennings, C., Olmo, J., Ventura, S., Cios, K., and Clore, J · 2014
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Convergence rates for differentially private statistical estimation
Chaudhuri, Kamalika and Hsu, Daniel J · 2012
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Private convex optimization for empirical risk minimization with applications to high-dimensional regression
Kifer, Daniel, Smith, Adam D., and Thakurta, Abhradeep · 2012
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Topics in Random Matrix Theory
Tao, T · 2012
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Local privacy and statistical minimax rates
Duchi, John C., Jordan, Michael I., and Wainwright, Martin J · 2013
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Our data, ourselves: Privacy via distributed noise generation
Dwork, Cynthia, Kenthapadi, Krishnaram, McSherry, Frank, Mironov, Ilya, and Naor, Moni
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Calibrating noise to sensitivity in private data analysis
Dwork, Cynthia, Mcsherry, Frank, Nissim, Kobbi, and Smith, Adam
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Dwork, Cynthia, Su, Weijie, and Zhang, Li · 2015
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Private approximations of the 2nd-moment matrix using existing techniques in linear regression
Sheffet, O · 2015
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Private multiplicative weights beyond linear queries
Ullman, J · 2015
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Differentially private hypothesis testing, revisited
Wang, Yue, Lee, Jaewoo, and Kifer, Daniel · 2015
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Differentially private chi-squared hypothesis testing: Goodness of fit and independence testing
Rogers, Ryan M., Vadhan, Salil P., Lim, Hyun-Woo, and Gaboardi, Marco · 2016
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