where ν x (γ), defined in the supplementary, is a function of the underlying distribution over the tag sequences x and the kernel bandwidth γ.
the sample complexity of our approach depends on the dimensionality of the latent and observed states (m and p), the underlying singular values of the cross-covariance matrices (σ * (x)) and the difference in the cost of the true tree compared to the cost of the incorrect trees ( (x)).