These are the censored data values we wish to t a set

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Unformatted text preview: de. Is X convex? Now we will examine what happens when the measurements are occasionally in error, i.e., for a few i we have no relation between x and yi . More precisely suppose that Ifault is a subset of {1, . . . , K }, and that yi = Ax + vi with vi ∞ ≤ α (as above) for i ∈ Ifault , but for i ∈ Ifault , there is no relation between x and yi . The set Ifault is the set of times of the faulty measurements. Suppose you know that Ifault has at most J elements, i.e., out of K measurements, at most J are faulty. You do not know Ifault ; you know only a bound on its cardinality (size). For what values of J is X , the set of x consistent with the measurements, convex? 5.12 Least-squares with some permuted measurements. We want to estimate a vector x ∈ Rn , given some linear measurements of x corrupted with Gaussian noise. Here’s the catch: some of the measurements have been permuted. More precisely, our measurement vector y ∈ Rm has the form y = P (Ax + v ), 47 where vi are IID N (0, 1) measurement noises, x ∈ Rn is the vector...
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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.

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