I am trying to follow this lecture on variational autoencoders. When talking about random observed data $o$ with missing components $m$ (min 14:10) he states that to calculate the log-likelihood of your data $X$ you need to marginalize out the missing components $P(X) = P(o,m)$. However, I can't quite visualize how you can build a joint pdf with vectors that are not constant in size?
For example, let's say the probability of an observed vetor $o_1 = (1, 2, -)$ with missing component $m_3 = 3$ is 0.3. How would the entry of the joint pdf table $P(o,m)$ would look like? Is this correct? I think Im just getting stupidly confuse with the unimportant fact whether if the data is 1 or N-dimensional
| $o_1$ | $o_2$ | |
|---|---|---|
| $m_1$ | ||
| $m_2$ | ||
| $m_3$ | 0.3 |
