In many scientific applications, increasingly bigger datasets are being acquired to describe more accurately biological or physical phenomena. While the dimensionality of the resulting measures has increased, the number of samples available is often limited, due to physical or financial
limits. Performing statistical inference in such a high-dimensional setting remains a hard problem that suffers from the curse of dimensionality. In this talk, we will first go through an introduction on conditional (multivariate) inference and the False Discovery Rate (FDR). We then move to some notions of the knockoff filters, a recent advance in multivariate analysis that controls the FDR with limited distribution assumptions. We then present a method for aggregating several samplings to address the knockoff filter's randomness, one of its major limitations. This method comes with non-asymptotic results on FDR control, which relies on usage of concentration inequalities. In the second session, we will work with the Conditional Randomisation Test (CRT), a close cousin of the knockoff filter.