Smoothing splines are function estimates, f ^ {\displaystyle {\hat {f}}}, obtained from a set of noisy observations y i {\displaystyle y_{i}} of the target f {\displaystyle f}, in order to balance a measure of goodness of fit of f ^ {\displaystyle {\hat {f}}} to y i {\displaystyle y_{i}} with a derivative based measure of the smoothness of f ^ {\displaystyle {\hat {f}}}. Wikipedia