202416901 このページの About > Technical Details に、以前から漠然と気になっていた「ノイズがある場合のロバストな二分探索」に対する一つの答えが書いてあった。回答後にしかこの部分に辿りつけないので引用する (デザイン上の理由で隠す意図はないと思う。あったらごめん)。
Technical Details
The test asks you to categorize colors sequentially. Colors are often represented in HSL (hue, saturation, lightness) color space. Hue 120 is green, and hue 240 is blue. The test focuses on blue-green hues between 150 and 210. The test assumes that your responses between blue and green are represented by a sigmoid curve. It sequentially fits that sigmoid curve to your responses:
p(response = blue | hue) = σ(slope (hue - threshold))
This is equivalent to a logistic regression model. The test uses a maximum-a-posteriori (MAP) estimation algorithm (specifically, a second order Newton method implemented in pure JS, no calls to a backend) to fit the sigmoid curve to your responses, with a vague prior on the scale and offset parameters. It uses the fitted curve to determine which color will be presented next. It tries to be smart about where it samples new points, focusing on regions where you're predicted to be intermediately confident in your responses. To improve the validity of the results, it randomizes which points it samples, and uses a noise mask to mitigate visual adaptation.
It's a curve fit, not a binary search. In theory, if you feel like you're guessing in the middle shades, or even guessing incorrectly, that should be fine. If you're inconsistent in the middle, the curve fit should be able to recover, although your estimated threshold will have larger error bars.
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