Invariance explains multiplicative and exponential skedactic functions

• Main Authors: Kreinovich V., Kosheleva O., Nguyen H., Sriboonchitta S.
• Format: Book Series
• Published: 2017
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84952684545&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/42518
• Institution: Chiang Mai University

© Springer International Publishing Switzerland 2016. In many situations, we have an (approximately) linear dependence between several quantities.(Formula presented.) The variance v=σ 2 of the corresponding approximation error (Formula presented.) often depends on the values of the quantities x 1 ,…,x n : v= v(x 1 ,…,x n ); the function describing this dependence is known as the skedactic function. Empirically, two classes of skedactic functions are most successful: multiplicative functions (Formula presented.) and exponential functions (Formula presented.).In this paper, we use natural invariance ideas to provide a possible theoretical explanation for this empirical success; we explain why in some situations multiplicative skedactic functions work better and in some exponential ones. We also come up with a general class of invariant skedactic function that includes both multiplicative and exponential functions as particular cases.