## Section: New Results

### Miscellaneous

In [25], we devise methods of variance reduction for the Monte Carlo estimation of an expectation of the type $\mathbb{E}\left[\phi \right(X,Y\left)\right]$, when the distribution of $X$ is exactly known. The key general idea is to give each individual of a sample a weight, so that the resulting weighted empirical distribution has a marginal with respect to the variable X as close as possible to its target. We prove several theoretical results on the method, identifying settings where the variance reduction is guaranteed. We perform numerical tests comparing the methods and demonstrating their efficiency.

In [6], we consider the problem of predicting a categorical variable based on groups of inputs. Some methods have already been proposed to elaborate classifi- cation rules based on groups of variables (e.g. group lasso for logistic regression). However, to our knowledge, no tree-based approach has been proposed to tackle this issue. Here, we propose the Tree Penalized Linear Discriminant Analysis algorithm (TPLDA), a new-tree based approach which constructs a classification rule based on groups of variables.