Definition
Plain language
Once you've thrown information away from a signal, no clever later step can put it back.
As stated in the literature
A core information-theoretic result stating that for a Markov chain X → Y → Z, the mutual information I(X;Z) ≤ I(X;Y); processing cannot increase information content.
Also called: Data Processing Inequality, DPI
Why it matters: It sets a hard ceiling on what downstream pipelines can do, formalizing why lossy steps early in a system limit everything that follows.
For example, blurring a photo and then trying any algorithm on the blurred version cannot recover information that the blur destroyed.
Heard on the show
“The tool here is the Data Processing Inequality.”Episode 020 — The Compliance Gap: Why AI Says Yes and Does No