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Equation 5 · Part 1 · AI for Science and Medicine in Practice: An Advanced Technical Guide

Symbol x

EI(x)=E ⁣[max⁡(f(x)−f+, 0)],\mathrm{EI}(x) = \mathbb{E}\!\left[\max(f(x) - f^{+},\ 0)\right],
xx

What this part means

x is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

x is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

…space the initial training data already covered well, and stops finding anything the model did not already believe. The standard fix is an acquisition function such as expected improvement, which for a candidate x with predictive mean μ(x)\mu(x) , predictive standard deviation σ(x)\sigma(x) , and current best observed value f+f^{+} is EI(x)=E ⁣[max⁡(f(x)−f+, 0)]\mathrm{EI}(x) = \mathbb{E}\!\left[\max(f(x) - f^{+},\ 0)\right]. a quantity that rewards both a high predicted mean and high predictive uncertainty. In practice this means the loop deliberately spends some experimental budget on…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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