Motivated by a question of Baldi-Klingler-Ullmo, we provide a general sufficient criterion for the existence and analytic density of typical Hodge loci associated to a polarizable \(\mathbb {Z}\) -variation of Hodge structures \(\mathbb {V}\) . Our criterion reproves the existing results in the literature on density of Noether-Lefschetz loci. It also applies to understand Hodge loci of subvarieties of \(\mathcal {A}_{g}\) . For instance, we prove that for \(g \geqslant 4\) , if a subvariety S of \(\mathcal {A}_{g}\) has dimension at least g then it has an analytically dense typical Hodge locus. This applies for example to the Torelli locus of \(\mathcal {A}_g\) .
