Homogenizing Entropy Across Different Environmental Conditions: A Universally Applicable Method for Transforming Continuous Variables
نویسندگان
چکیده
In classical information theory, a causal relationship between two variables is typically modelled by assuming that, for every possible state of one the variables, there exists particular distribution states second variable. Let us call these and caused respectively. We shall assume that both are continuous one-dimensional. this work we consider procedure to transform each variable, using transformations differentiable strictly increasing. increasing transformations. Any (as defined here) associated with channel capacity, which maximum rate could be sent if was used as signalling system. Channel capacity unaffected when changed use For any show always way variable such entropy independent value Furthermore, resulting universal has an absolute equal relationship. This observation may useful in statistical applications. Also, relationship, it implies ‘natural’ also additional constraints on natural transformation leads transformed properties might expected from well-engineered measuring device.
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2023
ISSN: ['0018-9448', '1557-9654']
DOI: https://doi.org/10.1109/tit.2022.3217387