Learning Parametric-Output HMMs with Two Aliased States
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چکیده
Combining (35) with (34), and the fact that 1nb = 0, we have that P(A,θ,π0) = P(Ã,θ,π0). Since à has identical (n−1)-th and n-th columns, and fθn−1 = fθn we have that P(Ã,θ,π0) = P(Ā,θ̄,π̄0). Thus H ′ = (Ā, θ̄, π̄) is an equivalent (n−1)-state HMM and H is not minimal, proving the claim. We prove (35) by induction on the sequence length k ≥ 2. First note that since δ = 0, by Lemma 1 we have that
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Learning Parametric-Output HMMs with Two Aliased States
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