On the Application of McDiarmid's Inequality to Complex Systems

Abstract

Abstract.McDiarmid's inequality has recently been proposed as a tool for setting margin requirements for complex systems. If F is the bounded output of a complex system, depending on a vector of n bounded inputs, this inequality provides a bound BF ( ), such that the probability of a deviation exceeding BF ( ) is less than . I compare this bound with the absolute bound, based on the range of F . I show that when n eff , the effective number of independent variates, is small, and when is small, the absolute bound is smaller than BF ( ), while also providing a smaller probability of exceeding the bound, i.e., zero instead of . Thus, for BF ( ) to be useful, the number of inputs must be large, with a small dependence on any single input, which is consistent with the usual guidance for application of concentration-of-measure results. When the number of inputs is small, or when a small number of inputs account for much of the uncertainty, the absolute bounds will provide better results. The use of absolute bounds is equivalent to the original formulation of the method of quantification of margins and uncertainties (QMU).

A systematic review on detection and adaptation of concept drift in streaming data using machine learning techniques

“…This method is modular and may be used in conjunction with any underlying classifier to give an extra layer of concept drift detection. Pesaranghader et al (2018) introduced the McDiarmid Drift Detection Method (MDDM), which detects concept drift using McDiarmid's inequality (Wallstrom, 2017). The MDDM method works by sliding a window over model performance and assigning weights to window elements.…”

“…Pesaranghader et al (2018) introduced the McDiarmid Drift Detection Method (MDDM), which detects concept drift using McDiarmid's inequality (Wallstrom, 2017). The MDDM method works by sliding a window over model performance and assigning weights to window elements.…”