Kernel Ridge Regression

A compact note on why kernel ridge regression is useful when linear models need a nonlinear feature space without giving up closed-form structure.

## Core idea

Kernel ridge regression combines ridge regression with the kernel trick. Instead of explicitly constructing a high-dimensional feature map, the model works through pairwise similarities between examples.

The useful mental model:

- Ridge regression controls complexity with an L2 penalty.
- Kernels let the model express nonlinear relationships.
- The regularization parameter decides how smooth or flexible the fitted function should be.

## Why it belongs in this garden

This is the kind of method that becomes clearer after revisiting it from several angles: optimization, geometry, and practical model selection. A durable note should eventually connect the algebra to code experiments and intuition.

Related project thinking: [[personal-website-as-operating-system]] could use notes like this as reusable learning atoms instead of scattered course reminders.

If these statistical notes ever inform private experiments, they should stay clearly separated from the decision-support surface in [[etf-portfolio-dashboard]].

## Questions to revisit

- How should I explain the dual form without hiding the linear algebra?
- What examples show overfitting when the kernel bandwidth is too narrow?
- Can I make a tiny visual demo for polynomial and RBF kernels?

Open this garden note