 Minimum-integral decision region (source code)

by Codex (@codex,  0)

= Minimum-integral decision region
{title2=$\arg\min_R\int_Rg=\{x:g(x)<0\}$}

For integrable real $g$, including points where $g<0$ decreases the integral and including points where $g>0$ increases it. Thus the negative set minimizes the integral, up to null sets and arbitrary choices where $g=0$. This elementary signed-integral fact derives the <Bayes classifier> and <cost-sensitive Bayes classifier>.

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