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Given the target value of a mixture of expert combinations is 0.8. The predictions of three experts and the probability of picking them are 0.6, 0.4, 0.5 and 0.8, 0.5, 0.7 respectively. Then what is the simple error for training?

Given the target value of a mixture of expert combinations is 0.8. The predictions of three experts and the probability of picking them are 0.6, 0.4, 0.5 and 0.8, 0.5, 0.7 respectively. Then what is the simple error for training? Correct Answer 0.18

We know the simple error for training: E = ∑ipi(d – yi)2 where d is the target value and pi is the probability of picking expert i, and yi is the individual prediction of expert i. Given d = 0.8, y1 = 0.6, y2 = 0.4, y3 = 0.5 and p1 = 0.8, p2 = 0.5, p3 = 0.7 Then E = p1(d – y1)2 + p2(d – y2)2 + p3(d – y3)2 = 0.8(0.8 – 0.6)2 + 0.5(0.8 – 0.4)2 + 0.7(0.8 – 0.5)2 = 0.8(0.2)2 + 0.5(0.4)2 + 0.7(0.3)2 = 0.8 * 0.04 + 0.5 * 0.16 + 0.7 * 0.09 = 0.032 + 0.08 + 0.063 = 0.18

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