Smoothing spline
Smoothing splines are function estimates, f ^ ( x ) {\displaystyle {\hat {f}}(x)} , obtained from a set of noisy observations y i {\displaystyle y_{i}} of the target f ( x i ) {\displaystyle f(x_{i})} , in order to balance a measure of goodness of fit of f ^ ( x i ) {\displaystyle {\hat {f}}(x_{i})} to y i {\displaystyle y_{i}} with a derivative based measure of the smoothness of f ^ ( x ) {\displaystyle {\hat {f}}(x)} . They provide a means for smoothing noisy x i , y i {\displaystyle x_{i},y_{i}} data.