Knot
Topic of Smooth means, part of Smoothing
Knot
| Type | Topic |
| Taught in | Smooth means |
| Part | Smoothing |
| Questions using it | 3 |
A point where the pieces of a spline join. A smoothing spline puts a knot at every distinct x; in practice a smaller set, often ten equally spaced points or the deciles of x, is used.
In Smooth means
From Smooth means
Putting a knot at every x_i is expensive, and \lambda itself changes meaning when you change the likelihood. In practice we use a smaller set of knots, ten equally spaced between the smallest and largest x being the usual default, or knots at the deciles if the x values pile up at one end. More knots are available when the sample is in the thousands. And we do not quote \lambda. Cross-validation hides a fraction of the sample, fits on the rest, and scores the hidden points, rotating which fraction is hidden. The software reports the smoothness as an equivalent degrees of freedom: the polynomial degree the curve is about as flexible as. As \lambda\to\infty that degrees of freedom falls to 1, a straight line, which is the ordinary GLM. As \lambda\to 0 the fit interpolates, and if no x values are tied it interpolates perfectly. Interpolation fits noise. It does not predict the next point.
Used in
- Taught in Smooth means
- Also used in Additive smooths
- Questions that use it (3) — Q36 (answer) · Question 19 (answer) · C31
- All 5 questions on Smooth means
See also
Roughness penalty · Cubic smoothing spline · Spline · Lidar data · Kyphosis data