Fetching the paper…
Reading the bibliography…
We propose a novel approach to Bayesian analysis that is provably robust to outliers in the data and often has computational advantages over standard methods.
[author] Weiszfeld, E.E. (1936). Sur un problème de minimum dans l’espace. Tohoku Mathematical Journal. \endbibitem
1936
Earlier work this paper cites.
[author] Aronszajn, NachmanN. (1950). Theory of reproducing kernels. Transactions of the American mathematical society 68 337–404. \endbibitem
1950
Earlier work this paper cites.
[author] Box, George EPG. E. and Tiao, George CG. C. (1968). A Bayesian approach to some outlier problems. Biometrika 55 119–129. \endbibitem
1968
Earlier work this paper cites.
[author] Ostresh, L. M.L. M. (1978). On the convergence of a class of iterative methods for solving the Weber location problem. Operations Research 26 597–609. \endbibitem
1978
Earlier work this paper cites.
[author] Nemirovski, A.A. and Yudin, D.D. (1983). Problem complexity and method efficiency in optimization. \endbibitem
1983
Earlier work this paper cites.
[author] Overton, M. L.M. L. (1983). A quadratically convergent method for minimizing a sum of Euclidean norms. Mathematical Programming 27 34–63. \endbibitem
1983
Earlier work this paper cites.
[author] Kemperman, J. H. B.J. H. B. (1987). The median of a finite measure on a Banach space. Statistical Data Analysis Based on the L 1 L_{1} -norm and Related Methods, North-Holland, Amesterdam 217–230. \endbibitem
1987
Earlier work this paper cites.
[author] Chandrasekaran, R.R. and Tamir, A.A. (1990). Algebraic optimization: the Fermat-Weber location problem. Mathematical Programming 46 219–224. \endbibitem
1990
Earlier work this paper cites.
[author] Lopuhaa, Hendrik PH. P. and Rousseeuw, Peter JP. J. (1991). Breakdown points of affine equivariant estimators of multivariate location and covariance matrices. The Annals of Statistics 229–248. \endbibitem
1991
Earlier work this paper cites.
[author] Bayarri, MJM. and Berger, James OJ. O. (1994). Robust Bayesian bounds for outlier detection. Recent Advances in Statistics and Probability 175–190. \endbibitem
1994
Earlier work this paper cites.
[author] Berger, James O.J. O. (1994). An overview of robust Bayesian analysis. Test 3 5–124. With comments and a rejoinder by the author. \endbibitem
1994
Earlier work this paper cites.
[author] Sethuraman, JayaramJ. (1994). A constructive definition of Dirichlet priors. Statistica sinica 639–650. \endbibitem
1994
Earlier work this paper cites.
[author] Wong, Wing HungW. H., Shen, XiaotongX. et al. (1995). Probability Inequalities for Likelihood Ratios and Convergence Rates of Sieve MLES. The Annals of Statistics 23 339–362. \endbibitem
1995
Earlier work this paper cites.
{binproceedings}
1996
Earlier work this paper cites.
[author] van der Vaart, A. W.A. W. and Wellner, J. A.J. A. (1996). Weak convergence and empirical processes. Springer Series in Statistics. Springer-Verlag, New York. \endbibitem
1996
Earlier work this paper cites.
1996
Earlier work this paper cites.
[author] Ghosal, SubhashisS., Ghosh, Jayanta KJ. K. and Van Der Vaart, Aad WA. W. (2000). Convergence rates of posterior distributions. Annals of Statistics 28 500–531. \endbibitem
2000
Earlier work this paper cites.
[author] Van der Vaart, Aad WA. W. (2000). Asymptotic statistics. Cambridge university press. \endbibitem
2000
Earlier work this paper cites.
[author] Ghosal, SubhashisS., Ghosh, Jayanta KJ. K. and Van Der Vaart, Aad WA. W. (2000). Convergence rates of posterior distributions. Annals of Statistics 28 500–531. \endbibitem
2000
Earlier work this paper cites.
[author] Van der Vaart, Aad WA. W. (2000). Asymptotic statistics 3. Cambridge university press. \endbibitem
2000
Cited alongside, same era.
[author] Ishwaran, HemantH. and James, Lancelot FL. F. (2001). Gibbs sampling methods for stick-breaking priors. Journal of the American Statistical Association 96. \endbibitem
2001
Cited alongside, same era.
[author] Dudley, Richard MR. M. (2002). Real analysis and probability 74. Cambridge University Press. \endbibitem
2002
Cited alongside, same era.
[author] Bose, P.P., Maheshwari, A.A. and Morin, P.P. (2003). Fast approximations for sums of distances, clustering, and the Fermat–Weber problem. Computational Geometry 24 135–146. \endbibitem
2003
Cited alongside, same era.
[author] Svensen, MarkusM. and Bishop, Christopher MC. M. (2005). Robust Bayesian mixture modelling. Neurocomputing 64 235–252. \endbibitem
2005
{binproceedings}
2012
Later among the works it cites.
[author] Ahn, SungjinS., Korattikara, AnoopA. and Welling, MaxM. (2012). Bayesian posterior sampling via stochastic gradient Fisher scoring. Proceedings of the 29th International Conference on Machine Learning (ICML-12). \endbibitem
2012
Later among the works it cites.
[author] Cardot, HervéH., Cénac, PeggyP. and Zitt, Pierre-AndréP.-A. (2012). Recursive estimation of the conditional geometric median in Hilbert spaces. Electronic Journal of Statistics 6 2535–2562. \endbibitem
2012
Later among the works it cites.
[author] Beck, AmirA. and Sabach, ShohamS. (2013). Weiszfeld’s method: old and new results. Preprint. Available at https://iew3.technion.ac.il/Home/Users/becka/Weiszfeld_review-v3.pdf . \endbibitem
2013
Later among the works it cites.
{binproceedings}
2013
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
[author] Bishop, Christopher M.C. M. (2006). Pattern recognition and machine learning. Springer, New York. \endbibitem
2006
Cited alongside, same era.
[author] Rasmussen, Carl EdwardC. E. and Williams, Christopher KIC. K. (2006). Gaussian processes for machine learning. the MIT Press 2. \endbibitem
2006
Cited alongside, same era.
[author] Dunson, David BD. B. and Xing, ChuanhuaC. (2009). Nonparametric Bayes modeling of multivariate categorical data. Journal of the American Statistical Association 104 1042–1051. \endbibitem
2009
Cited alongside, same era.
[author] Huber, Peter J.P. J. and Ronchetti, Elvezio M.E. M. (2009). Robust statistics, second ed. Wiley Series in Probability and Statistics. John Wiley & Sons Inc. \endbibitem
2009
Cited alongside, same era.
2009
Cited alongside, same era.
[author] Dunson, David BD. B. and Xing, ChuanhuaC. (2009). Nonparametric Bayes modeling of multivariate categorical data. Journal of the American Statistical Association 104 1042–1051. \endbibitem
2009
Cited alongside, same era.
{binproceedings}
2010
Cited alongside, same era.
[author] Cardot, HervéH., Cénac, PeggyP. and Zitt, Pierre-AndréP.-A. (2013). Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm. Bernoulli 19 18–43. \endbibitem
2013
Later among the works it cites.
[author] Fournier, N.N. and Guillin, A.A. (2013). On the rate of convergence in Wasserstein distance of the empirical measure. ArXiv e-prints. \endbibitem
2013
Later among the works it cites.
[author] Hoffman, Matthew D.M. D., Blei, David M.D. M., Wang, ChongC. and Paisley, JohnJ. (2013). Stochastic Variational Inference. Journal of Machine Learning Research 14 1303-1347. \endbibitem
2013
Later among the works it cites.
2013
Later among the works it cites.
2013
Later among the works it cites.
2013
Later among the works it cites.
[author] GroupLens Research (2013). MovieLens Data Sets. \endbibitem
2013
Later among the works it cites.
[author] Scott, Steven LS. L., Blocker, Alexander WA. W., Bonassi, Fernando VF. V., Chipman, Hugh AH. A., George, Edward IE. I. and McCulloch, Robert ER. E. (2013). Bayes and big data: the consensus Monte Carlo algorithm. \endbibitem
2013
Later among the works it cites.
2013
Later among the works it cites.
2013
Later among the works it cites.
[author] Boissard, EmmanuelE. and Le Gouic, ThibautT. (2014). On the mean speed of convergence of empirical and occupation measures in Wasserstein distance. Ann. Inst. H. Poincaré Probab. Statist. 50 539–563. \endbibitem
2014
Closest in time.
[author] Minsker, StanislavS. (2015). Geometric median and robust estimation in Banach spaces. Bernoulli 21 2308–2335. \endbibitem
2015
Closest in time.