Smoothing spline

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Published on January 6, 2022 4:16:24 AM ● Video Link: https://www.youtube.com/watch?v=xQiZ1IAzqtY

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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. The most familiar example is the cubic smoothing spline, but there are many other possibilities, including for the case where



x


{\displaystyle x}
is a vector quantity.

Source: https://en.wikipedia.org/wiki/Smoothing_spline
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