New-Type Hoeffding's Inequalities and Application in Tail Bounds
It is well known that Hoeffding's inequality has a lot of applications in the signal and information processing fields. How to improve Hoeffding's inequality and find the refinements of its applications have always attracted much attentions. An improvement of Hoeffding inequality was recently given by Hertz \cite{r1}. Eventhough such an improvement is not so big, it still can be used to update many known results with original Hoeffding's inequality, especially for Hoeffding-Azuma inequality for martingales. However, the results in original Hoeffding's inequality and its refinement one by Hertz only considered the first order moment of random variables. In this paper, we present a new type of Hoeffding's inequalities, where the high order moments of random variables are taken into account. It can get some considerable improvements in the tail bounds evaluation compared with the known results. It is expected that the developed new type Hoeffding's inequalities could get more interesting applications in some related fields that use Hoeffding's results.
Code (0)
등록된 구현이 없습니다.
Tasks
Vocal Bursts Type PredictionSimilar Papers 제목 키워드 기반
Distribution-dependent concentration inequalities for tighter generalization bounds
Concentration inequalities are indispensable tools for studying the generalization capacity of learning models. Hoeffding's and McDiarmid's inequalities are commonly used, giving bounds independent of the data distributi…
Generalization BoundsLearning TheoryOn the Non-asymptotic and Sharp Lower Tail Bounds of Random Variables
The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds …
Generalization Bounds for Representative Domain Adaptation
In this paper, we propose a novel framework to analyze the theoretical properties of the learning process for a representative type of domain adaptation, which combines data from multiple sources and one target (or brief…
Domain AdaptationGeneralization BoundsVocal Bursts Type PredictionFinite sample bounds for barycenter estimation in geodesic spaces
We study the problem of estimating the barycenter of a distribution given i.i.d. data in a geodesic space. Assuming an upper curvature bound in Alexandrov's sense and a support condition ensuring the strong geodesic conv…
PAC-Bayes Mini-tutorial: A Continuous Union Bound
When I first encountered PAC-Bayesian concentration inequalities they seemed to me to be rather disconnected from good old-fashioned results like Hoeffding's and Bernstein's inequalities. But, at least for one flavour of…
BIG-bench Machine LearningRelation