# Friedman H'statistic for interaction

I'm interested in interaction effects in Random Forest. I try to implement Friedman H'statistic basically developped for Gradient boosting Friendman, 2001. But I have no idea how calculate (44) on the real data.

If anybody has some examples or explanations?

In your article $$\hat F$$ is defined by Eq. (39). Although it's a bit abstract, it says that the partial dependency function $$\hat F_j$$ is obtained by averaging over all variables but a subset $$s$$.
As an example, the one-variable dependency function for the variable $$1$$ is given by $$\hat F_1(x_1) = \frac{1}{n}\sum_{i=1}^n \hat f \left (x_{1}, x_{i2}, \dots, x_{im} \right ) ,$$ where $$\hat f$$ is your model prediction function (Random Forest in your case), $$n$$ is the number of samples, $$m$$ is the number of features (I've included $$\hat f$$ instead of $$\hat F$$ for the predictor to avoid confusion). Here $$x_1$$ is a variable, and the $$x_{i2}, \dots, x_{im}$$ values are taken from your samples.
For example, if you have two variables and two samples $$(x_1=0,x_2=0)$$ and $$(x_1=1, x_2=1$$) in your dataset (this is a very dummy, pedagogical example), the partial dependence function for the first variable reads: $$\hat F_1 (x_1) = \frac{1}{2}\left [ \hat f(x_1, x_2=0) + \hat f(x_1, x_2=1) \right ].$$
Similarly, you can compute the two-variables partial dependence function as $$\hat F_{12}(x_1, x_2) = \frac{1}{n}\sum_{i=1}^n \hat f \left (x_{1}, x_{2}, \dots, x_{im} \right )$$ (same as before, but note that the $$i$$ index is not under $$x_2$$ anymore).
The two equation I've just made explicit are the only two terms that appear in the equation (44), thus you should be able to compute the $$H$$-statistic with them.
Let me know if it is still unclear, and check out this for more exegesis on the $$H$$-statistic.