# Expectation Maximisation Algorithm: Understand through numeric example

I am trying to learn machine learning concepts through online materials. I just studied tutorial on Expectation Maximisation algorithm. I thought one numerical example can make better understanding. Here I need your help to solve a problem:

Let, we have data points points: 𝑥1=2, 𝑥2=3, 𝑥3 = 4, 𝑥4=12, 𝑥5=13, 𝑥6=14, 𝑥7=15, 𝑥8=16, and an initial clustering 𝐶1= {𝑥1, 𝑥2, 𝑥3, 𝑥4, 𝑥5} and 𝐶2 = {𝑥6, 𝑥7, 𝑥8}.

We can compute initialization $\Theta$ for EM from sample mean, covariance and relative frequency.

But my question is, how can I compute probability that these points have been generated by the model with parameters $\Theta$, i.e. $𝑝(X|\Theta)$?

• A reference to that tutorial might be helpful. – Juho Kokkala Nov 26 '14 at 14:08
• Defining a model would make your question clearer. As stated it does not directly relate to EM. – Xi'an Nov 26 '14 at 18:03