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I am referring to paper: Show, Attend and Tell: Neural Image Caption Generation with Visual Attention (page 4). I wished to know, why we look to maximize the lower bound of the log likelihood probability $log p(y|a)$ and not itself. I agree that we sample images for the $t_{th}$ word stochastically, but I don't get the complete reasoning as to why we do this...

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Because $\log p(y|a) = \log \sum_s p(s|a)p(y|s,a)$ is computationally infeasible to compute. The hard attention attention $s$ is a discrete random variable which can take on $T^L$ values, where $T$ is the number of words and $L$ is the number possible of attention locations. Therefore the sum cannot be realistically computed, and variational lower bound is used instead.

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  • $\begingroup$ Thanks for the reply! One more question: Then why do we maximize log p(y|a) for soft attention (in the paper, the authors didn't write that they use the same lower bound technique for soft attention case and have instead showed only the log p(y|a) likelihood to be optimized.) $\endgroup$ – kg__ Jan 16 at 21:12
  • $\begingroup$ @kg__ in the soft attention case the $s$ are a deterministic function of $a$, and not a random variable conditioned on $a$, so there is no need to marginalize it out, so there is no intractable sum. $\endgroup$ – shimao Jan 16 at 21:19

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