bv_cvxbook_extra_exercises

In this exercise we consider the problem of

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Unformatted text preview: lumns of matrices X and Y, respectively. Find the thickness of the maximum thickness separating slab. Solve the problem above for 100 or so values of λ over an appropriate range (we recommend log spacing). For each value, 63 record the separation slab thickness 2/ a 2 and card(a), the cardinality of a (i.e., the number of nonzero entries). In computing the cardinality, you can count an entry aj of a as zero if it satisfies |aj | ≤ 10−4 . Plot these data with slab thickness on the vertical axis and cardinality on the horizontal axis. Use this data to choose a set of 10 features out of the 50 in the data. Give the indices of the features you choose. You may have several choices of sets of features here; you can just choose one. Then find the maximum thickness separating slab that uses only the chosen features. (This is standard practice: once you’ve chosen the features you’re going to use, you optimize again, using only those features, and without the ℓ1 regularization. 7.7 Th...
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