An extension of the Hoeffding inequality to unbounded random variables

Bentkus, V.

doi:10.1007/s10986-008-9007-7

Cited by 17 publications

(16 citation statements)

References 21 publications

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“…The proof of (4.4) is completed. The extension (4.5) to convex functions is classical (see, for example, Proposition 3 in Bentkus [4] or the proof of Theorem 3.3 in Klein, Ma and Privault [14]).…”

Section: Proofs Of the Results Of Sections 2 And 4 91 Proofs Of Secmentioning

confidence: 99%

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Concentration inequalities for separately convex functions

Marchina¹

2018

Bernoulli

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Section: Proofs Of the Results Of Sections 2 And 4 91 Proofs Of Secmentioning

confidence: 99%

“…Consequently, for any convex function ϕ, Remark 4.5. The special case 0 ≤ X ≤ st ψ was considered by Bentkus [4,5]. In [6], Bentkus obtained similar results in the situation where X ≤ st ψ and the variance of X is known.…”

Section: Lemma 43 Let Assumption (41) Hold Let ζ Q Be As In Definmentioning

confidence: 89%

Concentration inequalities for separately convex functions

Marchina¹

2018

Bernoulli

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“…Assumption 2 is for ease of our proofs. Standard techniques as in [11], [12] can be applied to generalize the bounds when Assumption 2 does not hold.…”

Section: Sequentiality and Adaptivity Gainsmentioning

confidence: 99%

“…i, j En P3 VNN(P) ;::: ---'-b ,-= max min min max L Aa(1-ex)Da Jqfllqj ) · AEA(A) iEn ]f.i aE[O, I ] aEA ::; 0.5 max min min L AaD(qfllq j ) · (12)AEA(A) iEn ]f.i aEACombining(10),(12), we have the assertion of Proposition 1.…”

mentioning

confidence: 99%

Active hypothesis testing: Sequentiality and adaptivity gains

Naghshvar

Javidi

2012

2012 46th Annual Conference on Information Sciences and Systems (CISS)

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Consider a decision maker who is responsible to collect observations so as to enhance his information in a speedy manner about an underlying phenomena of interest. The policies under which the decision maker selects sensing actions can be categorized based on the following two factors: i) sequential vs. non-sequential; ii) adaptive vs. non-adaptive. Non-sequential policies collect a fixed number of observation samples and make the final decision afterwards; while under sequential policies, the sample size is not known initially and is determined by the observation outcomes. Under adaptive policies, the decision maker relies on the previous collected samples to select the next sensing action; while under non-adaptive policies, the actions are selected independent of the past observation outcomes.In this paper, performance bounds are provided for the policies in each category. Using these bounds, sequentiality gain and adaptivity gain, i.e., the gains of sequential and adaptive selection of actions are characterized.

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“…As a matter of fact, exploiting unbounded loss functions would require additional hypotheses to hold in order to derive bounds ranging between slow and fast convergence[2,21,45].…”

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confidence: 99%

Global Rademacher Complexity Bounds: From Slow to Fast Convergence Rates

Oneto

Ghio

Ridella

et al. 2015

Neural Process Lett

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Previousworksinliteratureshowedthatperformanceestimationsoflearningpro- cedures can be characterized by a convergence rate ranging between O(n^(−1)) (fast rate) and O(n^(−1/2)) (slow rate). In order to derive such result, some assumptions on the prob- lem are required; moreover, even when convergence is fast, the constants characterizing the bounds are often quite loose. In this work, we prove new Rademacher complexity (RC) based bounds, which do not require any additional assumptions for achieving a fast convergence rate O(n^(−1)) in the optimistic case and a slow rate O(n^(−1/2)) in the general case. At the same time, they are characterized by smaller constants with respect to other state-of-the-art RC fast converging alternatives in literature. The results proposed in this work are obtained by exploiting the fundamental work of Talagrand on concentration inequalities for product mea- sures and empirical processes. As a further issue, we also provide the extension of the results to the semi-supervised learning framework, showing how additional unlabeled samples allow improving the tightness of the derived bound

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An extension of the Hoeffding inequality to unbounded random variables

Cited by 17 publications

References 21 publications

Concentration inequalities for separately convex functions

Concentration inequalities for separately convex functions

Active hypothesis testing: Sequentiality and adaptivity gains

Global Rademacher Complexity Bounds: From Slow to Fast Convergence Rates

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