Let Φ a , Ψ a , Ξ a , Υ a be the projection matrices from proposition 5.1.
input: samples of (X, A1, A2, F1, F2, P, R, D, B); feature functions φ, ψ, ξ, and υ; number of hidden states m Output: estimates Ĉ b|a ,Ĉ * |a ,ĉ 1 a ,ĉ a x of the operators used in algorithm 2 [Singular Value Decomposition] • For each label a ∈ [l], compute empirical estimates of and obtain their singular vectors via an SVD.