Probabilistic latent-variable models are a powerful tool for modelling structured data.
However, traditional expectation-maximization methods of learning such models are both
computationally expensive and prone to local-minima. In contrast to these traditional
methods, recently developed learning algorithms based upon the method of moments are
both computationally efficient and provide strong statistical guarantees. In this work, we
provide a unified presentation and empirical comparison of three general moment-based …

Let A=〈 α0, α∞, T,{Oσ} σ∈ Σ〉 be a HMM with n≤| Σ| states. To prove the consistency of the
algorithm described in Section 3.3, we will show that the when given access to data
computed from f= fA, the algorithm returns a HMM identical to A modulo a permutation on the
states. Suppose that we are given sets of prefixes and suffixes P, S⊂ Σ⋆ like in the
algorithm. We start by defining some notation. Let us write OP∈ RP× n with rows given by
eu OP= α0 Au and S∈ RS× n with rows given by ev S=(Avα∞). For convenience we also …