\(\DeclarePairedDelimiterX{\Set}[2]{\{}{\}}{#1 \nonscript\;\delimsize\vert\nonscript\; #2}\) \( \DeclarePairedDelimiter{\set}{\{}{\}}\) \( \DeclarePairedDelimiter{\parens}{\left(}{\right)}\) \(\DeclarePairedDelimiterX{\innerproduct}[1]{\langle}{\rangle}{#1}\) \(\newcommand{\ip}[1]{\innerproduct{#1}}\) \(\newcommand{\bmat}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\barray}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\mat}[1]{\begin{matrix}#1\end{matrix}}\) \(\newcommand{\pmat}[1]{\begin{pmatrix}#1\end{pmatrix}}\) \(\newcommand{\mathword}[1]{\mathop{\textup{#1}}}\)
Needs:
Maximum Likelihood Densities
Maximum Likelihood Distributions
Needed by:
None.
Links:
Sheet PDF
Graph PDF

Data Models

Why

A distribution/density selector picks a probabilistic model for a dataset by using the maximum likelihood principle. We want to generalize this idea.1

Definition

An unsupervised data model is a function $\ell : \R ^d \to \R $ where $\ell (x)$ is the suprise of the vector $x$.2


  1. Future editions probably include a genetic approach, which moves through clustering and mixtures of Gaussians to illustrate the point more fully. ↩︎
  2. Future editions will expand. ↩︎
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