Using the Semantic Information G Measure to Explain and Extend Rate-Distortion Functions and Maximum Entropy...

Area of Science:

• Information Theory
• Machine Learning
• Data Compression

Background:

• Rate-distortion theory and Maximum Entropy (ME) methods utilize Minimum Mutual Information (MMI) and ME distributions, often expressed via Bayes-like formulas with Negative Exponential Functions (NEFs) and partition functions.
• Existing rate-distortion functions face limitations including subjective distortion function definitions, difficulties in defining instance-label distortions, and inability to perform semantic data compression.

Purpose of the Study:

• To provide a novel interpretation of NEFs and partition functions within Bayes-like formulas.
• To address the limitations of traditional rate-distortion functions by introducing a semantic approach.
• To establish a framework for integrating machine learning with data compression, particularly semantic compression.

Main Methods:

• Reinterpreting NEFs as truth functions and partition functions as logical probabilities.
• Explaining Bayes-like formulas as semantic Bayes' formulas, MMI as Semantic Mutual Information (SMI), and ME as extreme ME minus SMI.
• Establishing relationships between truth functions and distortion functions, obtaining truth functions via machine learning, and using them to extend rate-distortion functions.

Main Results:

• The study explains the presence of non-probability functions in Bayes-like formulas by linking them to truth functions and logical probabilities.
• A novel approach is presented to overcome the disadvantages of traditional rate-distortion functions.
• The proposed method enables the combination of machine learning and data compression, including semantic compression, through the use of truth functions and the semantic information G measure.

Conclusions:

• The reinterpretation of information-theoretic concepts as truth functions and logical probabilities offers a new perspective on rate-distortion theory.
• The developed framework successfully extends rate-distortion functions and facilitates semantic data compression.
• Further research is needed to explore general data compression and recovery based on semantic meaning.