Quantum State

December 22, 2019

This is a very short primer on quantum mechanics, and the bare minimum that needs to be explained in order to understand what QM is about. My goal is to provide some conceptual punchlines with minimal prereqs. The formalism of QM is filled with technicalities and complications, which I try to point out where possible. Keep in mind I am glossing over a ton of details. The focus of this post is to introduce two equivalent views on quantum state is: Quantum states are $L^2$-normalized complex-valued functions over classical configuration space. Quantum states are unit vectors residing in a complex Hilbert space, $\mathcal{H}$. …

Bias-Variance Decomposition

July 14, 2019

All about the bias-variance decomposition as it pertains to machine learning. All you need to know: $$ \begin{align*} & \mathbb{E}_D[(f(x; D) - y(x))^2] \qquad\quad\ \textrm{Avg. error}\\ & = (\mathbb{E}_D[f(x; D)] - y(x))^2 \qquad \textrm{Bias}_y(f)^2\\ &\phantom{=}\, + \mathbb{V}_D[f(x; D)] \qquad\qquad\quad\ \, \textrm{Variance}(f)\\ \end{align*} $$ …