Thus, P (y, X y = 1) = P (y, X y = 1) + P (y, X y = 0) = P (y) One iteration of EM to calculate this probability is equivalent to the distillation method of DLD09.
the numerator of (17), which we just showed to be equal to the estimate of P (Y ) given by (16), is exactly the sum of the responsibilities for a particular y, and is proportional to the summation in (8) modulo normalization, because P ( X|y) is constant for all y in the context.