The notion of IRS (invariant random subgroup) is well-studied in dynamics on groups. We extend this notion to group von Neumann algebras LG, where G is a discrete countable group. We call this concept IRA (invariant random sub-algebra). In particular, we study the case of amenable IRAs, i.e. almost every sub-von Neumann algebra of LG is amenable. This generalizes a result of Bader-Duchesne-Lécureux about amenable IRSs. This is joint work with Tattwamasi Amrutam and Yair Hartman. No prior knowledge about von Neumann algebras is assumed.