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Abstract:
We apply a general algorithm for merging prediction
strategies (the Aggregating Algorithm) to the problem of linear
regression with the square loss; our main assumption is that the
response variable is bounded. It turns out that for this particular
problem the Aggregating Algorithm resembles, but is different from,
the well-known ridge estimation procedure. From general results
about the Aggregating Algorithm we deduce a guaranteed bound on the
difference between our algorithm's performance and the best, in
some sense, linear regression function's performance. We show that
the AA attains the optimal constant in our bound, whereas the
constant attained by the ridge regression procedure can be 4.3
times worse.
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