Mean

The mean aggregation function calculates the average value for each condition. It is thus suitable for problems where the objective should be optimized overall. CurryBO uses this method as a default.

Definition

The mean aggregation function is described as

\phi\left(f(\mathbf{x};\mathbf{w}), \mathcal{W}\right) = \frac{1}{|\mathcal{W}|} \sum_{\mathbf{w} \in \mathcal{W}} f(\mathbf{x}; \mathbf{w}) = \frac{1}{n} \sum^n_{i = 1}f(\mathbf{x};\mathbf{w}_i)

where $\phi$ denotes the aggregation function, $f$ describes the sample points, $\mathbf{x}$ are the sampled conditions, $\mathbf{w}$ are the sampled substrates, $\mathcal{W}$ is the set of all possible substrates and $n$ is the number of possible substrates.

The mean aggregation functions adds up all the condition functions for a substrate $\mathbf{w}_i$ and then divides by the number of substrates in order to get the generality.