# EM algorithm help - Plot of expectation

Can someone plot an expectation of a function and show me how maximizing it = maximizing the lower bound of its likelihood in the EM algorithm ? I don't know how to plot the expectation of a function since the expectation gives me a number. How do i get a plot ?

http://www.nature.com/nbt/journal/v26/n8/extref/nbt1406-S1.pdf

• EM usually traverses the Maximum Likelihood of some random variables. The plot you have there is the log-scaled likelihood of the data given the parameters. Recall that $L(\theta|x)=P(x|\theta)$. – FisherDisinformation May 13 '16 at 17:14
• You are right that the expectation is a constant in terms of the random variables integrated over, but remains a function of the parameters $\theta$. Related: stats.stackexchange.com/questions/138800/… – Andrew M May 13 '16 at 18:42
• Thanks ! After reading through some notes online I found out that the expectation involved in the EM algorithm is actually the conditional expectation $E [ f(x) | \theta ]$. I have gone through the coin toss example and i understand it. I am able to visualize what EM does at every step. What I am left with is again.... the equation of the E step. Is there any link that shows the PLOT of the expectation with varying theta ? – RuiQi May 14 '16 at 13:49
• I know what the M step does, it repositions the mean but I still don't understand the equations involved. But what does it mean to maximize the equation of the expectation ? What does it mean when my expectation is in terms of a variable ? Someone please show me an ACTUAL plot of the expectation with varying theta ! Arrrghhhh !! – RuiQi May 14 '16 at 13:49
• For example, if I have a gaussian distribution, its expectation is only a single value right ? How do I get multiple expectations like the plot you drew in stats.stackexchange.com/questions/138800/… ? – RuiQi May 14 '16 at 13:53