Self-Normalized Processes
By Victor H. de la Peña, Tze Leung Lai, Qi-Man Shao. 2009
110 citations recorded by the source corpus.
Subfields: Artificial Intelligence, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d2d1d49d1218cfcced2ea35707ef8fe4be9fb4ec
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Victor Chernozhukov
- Alexandre Belloni
- Christian Hansen
- D. Chetverikov
- Kengo Kato
- Corinna Cortes
- Mehryar Mohri
- Lie Wang
In Mathematical Physics
- Christian Hansen
- Wouter M. Koolen
- Lie Wang
- Kengo Kato
- Aditya Gopalan
- Emilie Kaufmann
- Victor Chernozhukov
- Aurélien Garivier
Citations in the corpus
- Relative deviation learning bounds and generalization with unbounded loss functions (2013, background): “Self-normalized processes have attracted attention in other domains as well, outside of the Machine Learning community, for instance in [39] and [8].”
- High-dimensional econometrics and regularized GMM (2018, background): “ 2 i, and D n;:= (n 1 P n i=1 E[j˘ ij 2+])1=(2+). Then uniformly in 0 xn 2(2+) =D n;, P(S n=V nx) 1 ( x) 1 Kn =2D2+ n; (1 + x) 2+; where Kis a universal constant. Proof. SeeTheorem7.4in[57]ortheoriginalpaper,[80]. Notethattheformulationinthese sources requires that n 1 P n i=1 E[˘ 2 i ] = 1 but it ”
- On Kernelized Multi-armed Bandits (2017, methodology): “Specifically, the method of mixtures (de la Pena et al., 2009) or Laplace method, as dubbed by Maillard (2016) (Lemma 5.2), fails to hold in infinite dimension.”
- Pivotal estimation via square-root Lasso in nonparametric regression (2011, background): “nikov’s result adds uniformity and relaxes the moment assumption. We refer to [28] for proofs. A.3. Moderate Deviations for Self-Normalized Sums. We shall beusingthe following result – Theorem 7.4 in [12]. Let X1,...,Xn be independent, mean-zero variables, and Sn = Xn i=1 Xi, V 2 n = Xn i=1 X2 i . F”
- Sequential Test for the Lowest Mean: From Thompson to Murphy Sampling (2018, methodology): “From there, the proof easily follows from a combination of Chernoff method and Doob inequality: Inequality (7) is then obtained by optimizing over λ , carefully picking η and inverting the bound.”