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+---
+layout: post
+title: Copyvio Detector
+description: A technical writeup of some recent developments.
+---
+
+This is an in-progress technical writeup of some recent developments involving
+the [copyright violation](//en.wikipedia.org/wiki/WP:COPYVIO) detector for
+Wikipedia articles that I maintain, located at
+[tools.wmflabs.org/copyvios](//tools.wmflabs.org/copyvios). Its source code is
+available on [GitHub](//github.com/earwig/copyvios).
+
+## Determining violation confidence
+
+One of the most important aspects of the detector is not fetching and parsing
+potential sources, but figuring out the likelihood that a given article is a
+violation of a given source. We call this number, a value between 0 and 1, the
+"confidence" of a violation. Values between 0 and 0.5 are considered to
+indicate no violation (green background in results page), between 0.5 and 0.75
+a "possible" violation (yellow background), and between 0.75 and 1 a
+"suspected" violation (red background).
+
+To calculate the confidence of a violation, the copyvio detector uses the
+maximum value of two functions, one of which accounts for the size of the delta
+chain (<span>\\(\Delta\\)</span>) in relation to the article chain
+(<span>\\(A\\)</span>), and the other of which accounts for just the size of
+<span>\\(\Delta\\)</span>. This ensures a high confidence value when both
+chains are small, but not when <span>\\(A\\)</span> is significantly larger
+than <span>\\(\Delta\\)</span>.
+
+The article–delta confidence function is simply
+<span>\\(\frac{\Delta}{A}\\)</span>. Therefore, we have complete confidence of
+a violation (<span>\\(C(A, \Delta)=1\\)</span>) when the article and suspected
+source share all of their trigrams, half confidence
+(<span>\\(C(A, \Delta)=0.5\\)</span>) when the source shares half of the
+article's trigrams, and so on.
+
+The delta confidence function, <span>\\(C_{\Delta}\\)</span>, is more
+complicated because it must determine a confidence value without having
+anything to compare <span>\\(\Delta\\)</span> to. A number of confidence values
+were derived experimentally, and the function was extrapolated from there such
+that <span>\\(\lim_{Δ \to +\infty}C\_{\Delta}(\Delta) = 1\\)</span>. The
+reference points were <span>\\(\\{(0, 0), (100, 0.5), (250, 0.75), (500, 0.9),
+(1000, 0.95)\\}\\)</span>. The function is defined as follows:
+
+<div>$$C_{\Delta}(\Delta)=\begin{cases} \frac{\Delta}{\Delta+100} & \Delta\leq
+100 \\[0.5em] \frac{\Delta-25}{\Delta+50} &  100\lt \Delta\leq 250\; \\[0.5em]
+\frac{10.5\Delta-750}{10\Delta} & 250\lt \Delta\leq 500\; \\[0.5em]
+\frac{\Delta-50}{\Delta} & \Delta\gt500 \end{cases}$$</div>
+
+A graph can be viewed [here](/static/Delta Confidence Function.pdf), with the
+background colored red, yellow, and green when a violation is considered
+suspected, possible, or not present, respectively.
+
+Now that we have these two definitions, we can define the primary confidence
+function, <span>\\(C\\)</span>, as follows:
+
+<div>$$C(A, \Delta) = \max(\tfrac{\Delta}{A}, C_{\Delta}(\Delta))$$</div>
+
+By feeding <span>\\(A\\)</span> and <span>\\(\Delta\\)</span> into
+<span>\\(C\\)</span>, we get our final confidence value.
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