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This paper is focused on dimension-free PAC-Bayesian bounds, under weak polynomial moment assumptions, allowing for heavy tailed sample distributions.
[author] Kato, T.T. (1982). A Short Introduction to Perturbation Theory for Linear Operators. Springer-Verlag, New York. \endbibitem
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[author] Catoni, O.O. (2004). Statistical Learning Theory and Stochastic Optimization, Lectures on Probability Theory and Statistics, École d’Été de Probabilités de Saint-Flour XXXI – 2001. Lecture Notes in Mathematics 1851. Springer pages 1–269. \endbibitem
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[author] Bickel, P. J.P. J., Ritov, Y.Y. and Tsybakov, A.A. (2009). Simultaneous analysis of Lasso and Dantzig selector. Annals of Statistics 37 1705–1732. \endbibitem
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[author] Catoni, O.O. (2012). Challenging the empirical mean and empirical variance: a deviation study. Ann. Inst. Henri Poincaré 48 1148-1185. \endbibitem
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[author] Minsker, S.S. (2015). Geometric Median and Robust Estimation in Banach Spaces. Bernoulli 4 2308–2335. \endbibitem
2015
Cited alongside, same era.
[author] Catoni, O.O. (2016). PAC-Bayesian bounds for the Gram matrix and least squares regression with a random design. preprint on ArXiv. \endbibitem
2016
Cited alongside, same era.
[author] Minsker, S.S. (2016). Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entries. Annals of Statistics, to appear. \endbibitem
2016
Cited alongside, same era.
[author] Giulini, I.I. (2017a). Robust dimension-free Gram operator estimates. Bernoulli, to appear. \endbibitem
Cited in the paper.
[author] Giulini, I.I. (2017b). Robust PCA and pairs of projections in a Hilbert space. Electron. J. Statist. 11 3903–3926. 10.1214/17-EJS1343 \endbibitem
Cited in the paper.
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2017
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[author] Joly, E.E., Lugosi, G.G. and Oliveira, R. I.R. I. (2017). On the estimation of the mean of a random vector. Electronic Journal of Statistics 11 440–451. \endbibitem
2017
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[author] Lugosi, G.G. and Mendelson, S.S. (2017). Sub-Gaussian estimators of the mean of a random vector. Annals of Statistics, to appear. \endbibitem
2017
Closest in time.
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