We note that the probability of a label sequence computed using the transformed weights, p (Q|X), is equivalent to taking the nth-root of the CRF probability computed using the unnormalized weights, with a new normalization term Z (X) where, p(Q|X) is as defined in Equation 1.
also observe that the monotonicity of the nth-root function ensures that if the rank order of the n-best phone recognition results are not impacted by this change.