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61.182 Informaatiotekn. ek II, spring 1997

Exercise problems

(Ch. 4, Ripley)

7. Ripley uses the term "Projection Pursuit Regression" for discriminant functions of the form of eq. (4.6), p. 126. Discuss the similarity of this with the conventional Multi-Layer Perceptron classifiers.

(Ch. 6, Ripley)

8. Assume a set of points consisting of n points (vectors) tex2html_wrap_inline21 . The kernel estimator for the density is


with K(.) the kernel function. A natural condition for any estimate for the density function would be that


Show that this holds asymptotically, when tex2html_wrap_inline29 where tex2html_wrap_inline31 is the Dirac delta dunction.

Esa Alhoniemi
Fri Apr 11 10:26:43 DST 1997