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Thoughts on Data Science, Machine Learning, and AI

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Month: September 2012

Kernels, Green’s Functions, and Resolvent Operators

Machine Learning uses Kernels.  At least it tries when it can. A Kernel is an operator on a Hilbert Space. … More

Eigenvalue-Independent Effective (Semantic) Operator

This post is still just  sketch of ideas…not ready for consumption In my last post I introduced the Eigenvalue-Dependent Effective (Semantic) … More

Effective Operators for Eigenvalues and Clustering

I a previous post, I introduced the Effective Regression Operator for supervised (and semi-supervised) Machine Learning problems.  Here, I will … More

Effective Operators part 2: Simple SemiSupervised Learning

We consider a very common example of Machine Learning problem as an application to the Effective Operator Framework:  Simple SemiSupervised … More

Kernels and Quantum Gravity Part 3: Coherent States

This would not be a pedagogic machine learning blog if I did not go into some overly abstract formalism…here we … More

Dimensional Reduction via an Effective Operator

Introduction Frequently in science, simple models work well beyond their expected range of accuracy and application, and can be essential … More

Kernels Part 2: Affine Quantum Gravity, continued

What is a Kernel?  Really?   What is the actual mathematical motivation? Most machine learning texts introduce the Kernel  as … More

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