TABLE 1:

$\mathcal{L}\left(y_i,F\left({\text{x}}_i\right)\right)$ choices for weighting samples-$\mathcal{L}$ is a decreasing function with respect to y_i × F(x_i). Hard functions depend on the sign of y_i F(x_i) that makes MP-Boost less sensitive to outlier samples.

	Exponential	Logistic
Soft	exp(−yi F(xi))	$\frac{1}{1+\exp \left(y_{i}F\left({\text{x}}_i\right)\right)}$
Hard	exp(−yi sgn(F(xi)))	$\frac{1}{1+\exp \left(y_i\mathrm{sgn}\left(F\left({\text{x}}_i\right)\right)\right)}$