55 citations · 565 across the 70 of their papers we have counts for
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Influence and interaction indexes for pseudo-Boolean functions: a unified least squares approach
Jean-Luc Marichal, Pierre Mathonet
The Banzhaf power and interaction indexes for a pseudo-Boolean function (or a cooperative game) appear naturally as leading coefficients in the standard least squares approximation…
Symmetric approximations of pseudo-Boolean functions with applications to influence indexes
Jean-Luc Marichal, Pierre Mathonet
We introduce an index for measuring the influence of the k-th smallest variable on a pseudo-Boolean function. This index is defined from a weighted least squares approximation of t…
Measuring the influence of the k-th largest variable on functions over the unit hypercube
Jean-Luc Marichal, Pierre Mathonet
By considering a least squares approximation of a given square integrable function f:[0,1]^n --> R by a shifted L-statistic function (a shifted linear combination of order statisti…
Weighted Banzhaf power and interaction indexes through weighted approximations of games
Jean-Luc Marichal, Pierre Mathonet
The Banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game. The Banzhaf interaction index was then proposed to measure the int…
Measuring the interactions among variables of functions over the unit hypercube
Jean-Luc Marichal, Pierre Mathonet
By considering a least squares approximation of a given square integrable function by a multilinear polynomial of a specified degree, we define an index which…