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  "body": "\n## Summary\n\nA smoothing spline is the function that best balances closeness to noisy data against roughness, measured by the integral of the squared second derivative.\nThe balance is set by a smoothing parameter $\\lambda \u003e 0$.\nThe minimizer turns out to be a natural [[cubic spline|V42H0R3EKX]] with knots at the data points.\nSmoothing splines are a basic tool of nonparametric regression and data smoothing.\n\n## Explanations\n\n### L1 human\n\nImagine noisy measurements scattered around an unknown smooth curve.\nPassing a curve through every point copies the noise, while a straight line may miss the shape.\nA smoothing spline pays a price for missing the points and a price for bending, and takes the curve with the smallest total price.\nA small $\\lambda$ gives a wiggly curve close to the data, and a large $\\lambda$ gives a curve close to the [[least squares|0BYTQ4X1HC]] line.\n",
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