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How Statistics and Machine Learning Came To Have Two Different Kinds of Kernel Methods

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TL;DR: In statistics and machine learning, "kernel methods" refer to two different families of methods, one based on convolution, the other on hiding a basis expansion in the guise of a sum over data points. These use two different (but overlapping) sets of kernels. In both cases, the name "kernel" comes from some problems involving integrals in mathematical physics. (TL;DR of the TL;DR: Blame the mathematicians.) "Kernel" is one of those terms which is used in many distinct-but-related senses across different areas of mathematics (like "normal"). The common metaphor is "the seed (in some sense) from which some larger object or structure grows (in some sense)". In particular, in physics, there are a lot of problems which involve integral operators 𝐼 that map one function, say 𝑓 , to a new function 𝐼 𝑓 , by the relationship ( 𝐼 𝑓 ) ( 𝑥 ) = ∫ 𝑓 ( 𝑧 ) 𝐾 ( 𝑥 , 𝑧 ) 𝑑 𝑧 The inner function 𝐾 ( 𝑥 , 𝑧 ) is called the kernel of the operator. (Or at least that's what it cam

How Statistics and Machine Learning Came To Have Two Different Kinds of Kernel Methods Three-Toed Sloth Slow Takes from the Canopy (My Very Own Internet Tradition) February 27, 2026 Main How Statistics and Machine Learning Came To Have Two Different Kinds of Kernel Methods Attention conservation notice : Re-purposed teaching materials, about a confusing point of terminology in two arcane disciplines. This is amateur history of science, which will not help you learn or practice those disciplines, even if you wanted to (which you don't). Also, it was written for an advanced undergraduate class i

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