Some compact notations for concentration inequalities and user-friendly results
This work provides incremental improvements for researchers and practitioners in probability theory and machine learning by streamlining the application of concentration inequalities.
The paper tackled the problem of simplifying probabilistic analysis by introducing compact notations for concentration inequalities, resulting in user-friendly expressions that describe typical sizes and tails of random variables without heavy constants.
This paper presents compact notations for concentration inequalities and convenient results to streamline probabilistic analysis. The new expressions describe the typical sizes and tails of random variables, allowing for simple operations without heavy use of inessential constants. They bridge classical asymptotic notations and modern non-asymptotic tail bounds together. Examples of different kinds demonstrate their efficacy.