SVEKER.utils.m_coeff

SVEKER.utils.m_coeff(n_i: int, n_d: int, i: int, d: int)

Calculates the multinomial coefficient \(m_\mathrm{coeff}\)

\(m_\mathrm{coeff} = \frac{(N_i+N_d)!(I+D-N_i-N_d-1)!}{(I+D)!}\)

Number of permutations of the coalition \((N_i+N_d)\) multiplied by the number of features not contained in the coalition \((I+D-N_i-N_d-1)\) divided number of all possible coalitions \((I+D)\)

Parameters:

  • n_i (int) – Number of elements in the intersection, \(N_i\)

  • n_d (int) – Number of elemtnes in the symmetric difference, \(N_d\)

  • i (int) – Size of the intersection, \(I\)

  • d (int) – Size of the symmetric difference, \(D\)

Returns:

multinomial coefficient \(m_\mathrm{coeff}\)

Return type:

float