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Lean Together 2025: Lorenzo Luccioli, Information theory in Lean: the DPI
Автор: leanprover community
Загружено: 2025-01-15
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The Data Processing Inequality (DPI) is a cornerstone of information theory, expressing the principle that information cannot be created through processing.
In this talk, I will present the formalization of information-theoretic results carried out by Rémy Degenne and myself using the Lean 4 theorem prover. The focus will be on the formalization of information divergences—particularly f-divergences—and their associated Data Processing Inequality (DPI), along with their connection to the framework of hypothesis testing. I will also discuss the key challenges and design decisions faced during the project.
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