Notation for valuation

The following notation is used throughout the documentation:

Let \(D = \{x_1, \ldots, x_n\}\) be a training set of \(n\) samples.

The utility function \(u:\mathcal{D} \rightarrow \mathbb{R}\) maps subsets of \(D\) to real numbers.

The value \(v\) of the \(i\)-th sample in dataset \(D\) wrt. utility \(u\) is denoted as \(v_u(x_i)\) or simply \(v(i)\).

For any \(S \subseteq D\), we donote by \(S_{-i}\) the set of samples in \(D\) excluding \(x_i\), and \(S_{+i}\) denotes the set \(S\) with \(x_i\) added.

The marginal utility of adding sample \(x_i\) to a subset \(S\) is denoted as \(\delta(i) := u(S_{+i}) - u(S)\).

The set \(D_{-i}^{(k)}\) contains all subsets of \(D\) of size \(k\) that do not include sample \(x_i\).

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Last update: 2023-08-26
Created: 2023-08-26