Improvement on Simple Greedy Inference Algorihtm One draw back of this greedy inference algorithm is that, for example, given $X$, let there be 3 most probable alignment “a_b”, “b_b”, “b_bb”, and let their probability be 0.4, 0.3, 0.3. The greedy algorithm would choose “a_b” and this led to output “ab”. However, both “b_b” and “b_bb” lead to “bb”, and “bb” has a total probability of 0.6, which is more likely than “ab”.

For this reason, we can improve simple greedy inference algorithm by choose the output $Y$ that has maximum conditional probability, instead of maximizing a single alignment.

Mathematically, $P_{CTC}(Y|X)=\sum_\text{all A that produce Y }p(A|X)$, and $\hat{Y}=\text{argmax}_\text{all possible Y} P_{CTC}(Y|X)$