Timeline for Question on how to use EM to estimate parameters of this model
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 21, 2015 at 11:27 | vote | accept | Luca | ||
| Jan 20, 2015 at 17:17 | history | tweeted | twitter.com/#!/StackStats/status/557587810728042498 | ||
| Jan 20, 2015 at 16:56 | answer | added | Xi'an | timeline score: 3 | |
| Jan 20, 2015 at 16:34 | comment | added | Luca | I am quite confused now as to why $\beta$ (regression parameters) cannot be treated as latent variables. We are modelling $\beta$ as a normal distribution and interested in estimating the mean and its covariance. Since $\beta$ is not observed, is it not a latent random variable in this setup? Should I make a new question about this? | |
| Jan 20, 2015 at 15:57 | comment | added | Luca | I did look at a few books and references but it has not sunk in yet to be honest. | |
| Jan 20, 2015 at 15:50 | comment | added | Xi'an | How much do you already know about the EM algorithm? Which book or paper have you studied about it? Starting from scratch on a forum like this sounds like a bad idea. | |
| Jan 20, 2015 at 15:45 | comment | added | Luca | Thanks for your comment. If I may try and clarify, the paper does mention that we are interested in maximizing the incomplete log likelihood $\log p(Y|X)$ but we work with the complete data likelihood given by: $\log P(y, w, \beta|X)$, which to me looked like the posterior distribution in this setup. So, I assumed $\beta$ is being treated as a hidden bvariable in this setup. | |
| Jan 20, 2015 at 15:21 | comment | added | Xi'an | The latent variables cannot be $\beta$ and the $w_i$'s. If you are interested in $\beta$, the latent variables are presumably the $w_i$'s. In which case you have to find the expected complete log-likelihood $Q(\beta|\beta_0)$ function of the E-step and optimise it in $\beta$ in the M-step. | |
| Jan 20, 2015 at 15:17 | comment | added | Luca | I think so. I am trying to understand a paper and they use EM for solving this weighted bayesian linear regression problem. | |
| Jan 20, 2015 at 15:17 | comment | added | Xi'an | are you sure EM as in Expectation-Maximisation applies to your problem? | |
| Jan 20, 2015 at 14:34 | history | asked | Luca | CC BY-SA 3.0 |