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[scikit-learn 0.18 User Guide 1. Supervised Learning](http://qiita.com/nazoking@github/items/267f2371757516f8c168#1-%E6%95%99%E5%B8%AB%E4%BB%98 From% E3% 81% 8D% E5% AD% A6% E7% BF% 92)

1.15. Isotonic regression

The IsotonicRegression () class adapts non-decreasing functions to the data. It solves the following problems:

minimize \sum_i w_i (y_i - \hat{y}_i)^2

subject\ to\ \hat{y}_{min} = \hat{y}_1 \le \hat{y}_2 ... \le \hat{y}_n = \hat{y}_{max}

Each $ w_i $ is strictly positive and each $ y_i $ is any real number. This produces a vector of non-decreasing elements that are the least approximate with respect to the mean square error. In practice, this list of elements forms a function that is piecewise linear.

[scikit-learn 0.18 User Guide 1. Supervised Learning](http://qiita.com/nazoking@github/items/267f2371757516f8c168#1-%E6%95%99%E5%B8%AB%E4%BB%98 From% E3% 81% 8D% E5% AD% A6% E7% BF% 92)

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