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Unformatted text preview: oblem, since you must maximize ploss over an inﬁnitedimensional set of joint distributions. To (approximately) solve it, we discretize the values that R1
and R2 can take on, to n = 100 values r1 , . . . , rn , uniformly spaced from r1 = −30 to rn = +70.
We use the discretized marginals p(1) and p(2) for R1 and R2 , given by
(k ) pi = prob(Rk = ri ) = 2
exp −(ri − µk )2 /(2σk )
j =1 exp −(rj − µk ) /(2σk ) for k = 1, 2, i = 1, . . . , n.
Formulate the (discretized) problem as a convex optimization problem, and solve it. Report the
maximum value of ploss you ﬁnd. Plot the joint distribution that yields the maximum value of ploss
using the Matlab commands mesh and contour.
Remark. You might be surprised at both the maximum value of ploss , and the joint distribution
that achieves it.
6.11 Minimax linear ﬁtting. Consider a linear measurement model y = Ax + v , where x ∈ Rn is a
vector of parameters to be estimated, y ∈ Rm is a vector of measurements, v ∈ Rm is a set of
measurement errors, and A ∈ Rm×...
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- Fall '13
- The Aeneid