# Rate of convergence of EM algorithm?

What can be said in general about the rate of convergence of EM algorithm?

For example, if I let the parameters to be $\theta$, starting point to be $\theta^0$, and the optimal solution is $\theta^*$, so that $||\theta^t-\theta^*||<\alpha||\theta^0-\theta^*||$, what can be said about $\alpha$ in general?

Also, how can we prove that it is slower than the other methods (Like Newton-Rapson, Expected Conjugate Gradient)?

• I think this paper is relevant to your question. – Digio Sep 16 '17 at 20:25

$$|\theta^{k+1} - \theta^*| \leq \gamma |\theta^{k}-\theta^*|.$$
If $$\gamma=1$$ then convergence is linear and if $$1<\gamma<2$$ then the algorithm is said to have super-linear convergence and if $$\gamma=2$$ is quadratic convergence. The convergence rate really depends on the specifics of the problem. Many examples and an a pedagogic introduction to convergence rates of the EM algorithm are given in the book by McLachlin and Krishnan if you want more details.