A Likelihood Ratio Approach for Probabilistic Inequalities
This provides a novel theoretical framework for statisticians and machine learning researchers working on concentration bounds, though it appears incremental rather than paradigm-shifting.
The authors tackled the problem of deriving probabilistic concentration inequalities by proposing a new likelihood ratio approach that is more general and powerful than classical methods like Chernoff bounds, resulting in new inequalities that cannot be obtained through existing techniques.
We propose a new approach for deriving probabilistic inequalities based on bounding likelihood ratios. We demonstrate that this approach is more general and powerful than the classical method frequently used for deriving concentration inequalities such as Chernoff bounds. We discover that the proposed approach is inherently related to statistical concepts such as monotone likelihood ratio, maximum likelihood, and the method of moments for parameter estimation. A connection between the proposed approach and the large deviation theory is also established. We show that, without using moment generating functions, tightest possible concentration inequalities may be readily derived by the proposed approach. We have derived new concentration inequalities using the proposed approach, which cannot be obtained by the classical approach based on moment generating functions.