If we simply fit a smooth curve $g(x)$ to a set of data by minimizing $RSS = \sum^n_{i=1}(y_i - g(x_i))^2$ without putting any constraints, there is a problem that we can always make $RSS$ zero simply by choosing $g$ such that it interpolates all of the $y_i$, leading to the overfitting of the data. What we want is a function $g$ that makes $RSS$ small, but that is also smooth. Instead, we can change the optimization formulation from $RSS$ to the function below: $\sum^n_{i=1}(y_i - g(x_i))^2 + \lambda \int g''(t)^2 dt$, where $\lambda$ is a nonnegative tuning parameter. The function $g$ that minimizes the formulation above is known as a smoothing spline.