MACHINE LEARNING TECHNIQUES - LASA

103
Note that since we never have the projections ( x
i
)
We can however once more exploit the kernel trick to compute f . Using
M
φ , we cannot compute explicitly w in (5.71).
*
i
( ) = ∑( i
− i ) ( ) ( )
w,
φ x α α φ x φ x
i=
1
M
*
i
∑( αi
αi
) k( x x)
= −
i=
1
, ,
we can compute an estimate of our regression function through:
M
*
i
( ) ( αi
αi
) ( , )
f x = ∑ − k x x + b
(5.73)
i=
1
Observe that the computation costs for the regression function grow linearly with the number
M of datapoints. As for SVM, computation can be reduced importantly if one reduces the number
of datapoints for which the elements in the sum are non-zero, the so-called support vectors. This
*
is the case when ( αi
αi
)
*
− = 0. Note that for all points within the e-insensitive tube α = α = 0 (so
as to satisfy the KKT conditions given in (5.72).
i
i
© A.G.Billard 2004 – Last Update March 2011