bv_cvxbook_extra_exercises

516 polynomial approximation of inverse using

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: T x. The vector c ∈ Rn is the model parameter, which we want to choose. We will use a least-squares criterion, i.e., choose c to 48 minimize K J= k=1 y (k ) − c T x (k ) 2 . Here is the tricky part: some of the values of y (k) are censored; for these entries, we have only a (given) lower bound. We will re-order the data so that y (1) , . . . , y (M ) are given (i.e., uncensored), while y (M +1) , . . . , y (K ) are all censored, i.e., unknown, but larger than D, a given number. All the values of x(k) are known. (a) Explain how to find c (the model parameter) and y (M +1) , . . . , y (K ) (the censored data values) that minimize J . (b) Carry out the method of part (a) on the data values in cens_fit_data.m. Report c, the value ˆ of c found using this method. Also find cls , the least-squares estimate of c obtained by simply ignoring the censored data ˆ samples, i.e., the least-squares estimate based on the data (x(1) , y (1) ), . . . , (x(M ) , y (M ) ). The data file contains c...
View Full Document

This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

Ask a homework question - tutors are online