However, if we take the Hierarchical Softmax Tree form as shown in Equation 4to model P(w m |h m = i, w), and perform only one step gradient ascent in M-Step, the aforementioned two expensive operations in M-Step will be avoided by leveraging the pre-computed results in the E-Step.
since the gradient of the function f (x) = log ς (x) is given by f (x) = 1 − ς (x), the sigmoid values computed in the E-Step to obtain P(w m |h m = i, w) (i.e.