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weights for which the partition (C+, C-) approximates the partition (C1, C0), so that C+@ C1 and C-@ C0. (This device, as noted earlier, is quite limited; there are many partitions (C1, C0) that can only be poorly approximated by (C+, C-), no matter what set of weights is chosen.) Now, let W = {v1, v2,. . . , vk} be the set of possible values for the weights wi; that is, each . Thus, with a fixed threshold K, the set of attainable structures  is the set of all ab-tuples, Wab. |
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The natural performance measure,µE, relative to any particular partition  is the proportion of all configurations correctly assigned (to C1 and C0). That is, µE maps each ab-tuple into the fraction of correct recognitions achieved thereby, a number in the interval [0, 1], µE: Wab® [0, 1]. (In this example the outcome of each test"configuration correctly classified" or "configuration incorrectly classified"will be treated as the plan's input. The same ab-tuple may have to be tested repeatedly to establish an estimate of its performance.) |
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A simple plan t0 for discovering the best set of weights in Wab is to try various ab-tuples, either in some predetermined order or at random, estimating the performance of each in its turn; the best ab-tuple encountered up to a given point in time is saved for comparison with later trialsthis "best-to-date" ab-tuple being replaced immediately by any better ab-tuple encountered in a later trial. It should be clear that this procedure must eventually uncover the "best" ab-tuple in Wab. But note that even for k = 10 and a = b = 10, Wab has 10100 elements. This is a poor augury for any plan which must exhaustively search Wab. And that is exactly what the plan just described must undertake, since the outcome of earlier tests in no way affects the ordering of later tests. |
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Let's look at a (fairly standard) plan t00 which does use the outcome of each test to help determine the next structure for testing. The basic idea of this plan is to change the weights whenever a presentation is misassigned so as to decrease the likelihood of similar misassignments in the future. In detail: Let the values in W be ordered in increasing magnitude so that vj+1 > vj, j = 1, 2,. . ., k - 1 (for instance, the weights might be located at uniform intervals so that vj+1 = vj + D). Then the algorithm proceeds according to the following prescription: |
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1. If the presentation at time t is assigned to C0 when it should have been assigned to C1then, for each i such that di(t) = 1, replace the corresponding weight by the next highest weight (in the case of uniform intervals the new weight would be the old weight wi increased by D, wi + D). Leave the other weights unchanged. |
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