Abstract
We present the method of optimistic estimation, a novel paradigm that seeks to incorporate robustness to errors-in-variables biases directly into the estimation objective function. This approach protects parameter estimates in statistical models from data set corruption. We apply the optimistic paradigm to estimation of linear regression, logistic regression, and Ising graphical models in the presence of noise and demonstrate that more accurate predictions of the model parameters can be obtained.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Fertis, A.: A robust optimization approach to statistical estimation problems. Ph.D. thesis, MIT (2009)
Bertsimas, D., Sim, M.: The price of robustness. Oper. Res. 52(1), 35–53 (2004)
Bertsimas, D., Brown, D., Caramanis, C.: Theory and applications of robust optimization. SIAM Rev. 53(3), 464–501 (2011)
Gabrel, V., Murat, C., Thiele, A.: Recent advances in robust optimization: an overview. Eur. J. Oper. Res. 235(3), 471–483 (2014)
Brofos, J., Shu, R.: Optimistic and parallel Ising model estimation. Dartmouth CS Technical report. TR2015-766 (2015)
Ghaoui, L., Lebret, H.: Robust solutions to least-squares problems with uncertain data. SIAM J. Matrix Anal. Appl. 18(4), 1035–1064 (1997)
Xu, H., Caramanis, C., Mannor, S.: Robust regression and lasso. IEEE Trans. Inform. Theor. 56, 3561–3574 (2010)
Kindermann, R., Snell, J.L.: Markov Random Fields and Their Applications. Contemporary Mathematics, vol. 1. American Mathematical Society, Providence (1980)
Wainwright, M.J., Jordan, M.I.: Graphical models, exponential families, and variational inference. Found. Trends Mach. Learn. 1(1), 62 (2008)
Boyd, S., Vandenberghe, L.: Algorithms for Convex Optimization. Cambridge University Press, Cambridge (2009)
Acknowledgments
The authors wish to thank Abigail Gertner and Jason Ventrella of The MITRE Corporation for helpful comments and recommendations. The author’s affiliation with The MITRE Corporation is provided for identification purposes only, and is not intended to convey or imply MITRE’s concurrence with, or support for, the positions, opinions or viewpoints expressed by the author. Approved for Public Release; Distribution Unlimited. Case Number 16-0621.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Brofos, J., Shu, R., Zhang, F. (2016). The Optimistic Method for Model Estimation. In: Boström, H., Knobbe, A., Soares, C., Papapetrou, P. (eds) Advances in Intelligent Data Analysis XV. IDA 2016. Lecture Notes in Computer Science(), vol 9897. Springer, Cham. https://doi.org/10.1007/978-3-319-46349-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-46349-0_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-46348-3
Online ISBN: 978-3-319-46349-0
eBook Packages: Computer ScienceComputer Science (R0)