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Inequality Experimentalist

The inequality experimentalist is a method used to compare experimental conditions and select new conditions based on a pairwise distance metric. Here's how it works:

Given: - Existing experimental conditions represented by \(\vec{x}\) in the set \(X\). - Candidate experimental conditions represented by \(\vec{x}'\) in the set \(X'\). - A pairwise distance metric \(d(\vec{x}, \vec{x}')\) that calculates the distance between \(\vec{x}\) and \(\vec{x}'\). - A threshold value (default = 0) that determines the maximum allowable distance for two conditions to be considered equal. - A number \(n\) of conditions to sample.

The inequality experimentalist operates as follows:

  1. For each candidate condition \(\vec{x}'\) in \(X'\) calculate an \(inequality\) \(score\):
  2. Calculate the distances \(d(\vec{x}, \vec{x}')\) between \(\vec{x}\) and \(\vec{x}'\) using the pairwise distance metric for all \(\vec{x}\) in \(X\).
  3. If \(d(\vec{x}, \vec{x}')\) is greater than the threshold:
    • Consider \(\vec{x}'\) as different from the existing condition \(\vec{x}\).
    • add 1 to the \(inequality\) \(score\) for \(\vec{x'}\)
  4. If \(d(\vec{x}, \vec{x}')\) is less than the threshold:
    • Consider \(\vec{x}'\) as equal to the existing condition \(\vec{x}\).
    • Do not add 1 to the score for \(\vec{x'}\)

The \(n\) \(\vec{x'}\) with the highest \(inequality\) \(scores\) are chosen as new conditions.