# Semantic Features Based N-Best Rescoring Methods for Automatic Speech Recognition
## 5 Experiments
### LDA-Based Rescoring  
In this section, we use LDA-based scores to re-rank hypotheses. The average scores of hypotheses at different ranks are in Figure 4. The upper sub-figures show the average logarithms of sentence probability and the ones at the bottom are the averages of topic similarity. \"LDAprob\" refer to the LDA sentence probability score, and \"LDAtopsim\" refer to the topic similarity score in this table. The tendency of the curves shows that the hypotheses ranked at the front are of higher scores than those ranked at the back for all sub-figures. Given the assumption that generally hypotheses ranked in front are of better quality, the curves could reflect this to some extent. The average scores with fallibility are in the right two sub-figures. We aligned all the hypotheses in both testsets with references and tag words in hypotheses with 'correct','substitute' and 'insert' by the aligning algorithm described in Section 3.2. Deletion error cannot be reported in hypotheses, so we do not have a 'delete' tag. Figure 5 shows the distribution of the two word scores for words with 'correct','substitute' and 'insert' tags respectively. The sub-figures on the top are those of word probability score, and the bottom ones are of topic similarity score. The statistic of the averaged score for words with 'correct''substitute' and 'insert' tags is listed in Table 1. As shown in the table, for both score-types, the average score of the 'correct' tags are the highest and the average of 'insert' words are much lower than 'correct' and'substitute'. This shows that the two scores can discriminate the wrong words in the hypotheses to a certain extent. Figure 4: The average score of Latent Dirichlet allocation (LDA)-based methods for hypotheses. The horizontal axis, ranging from 1 to 100, represents the rank of hypotheses by the 1-pass decoding process. The vertical axis represents the average score of the hypotheses at the corresponding rank. Figure 5: Distribution function of LDA based scores for words with “c”, “s” and “i” tags. The word error rate (WER) of the new best hypothesis sentences rescored by LDA-based scores are listed in Table 2. \"Baseline\" here means the WER of the original recognition system, where corresponds to Equation (18). As mentioned before, the word-pair probability score can be regarded as the smoothed 2-gram language model. So we list the result of the 2-gram language model, which is trained by SriLM on the large text corpus. \"smallRNN\" here refer to a 2-layer RNN with 100 hidden units each layer. In this experiment, \(\alpha\) described in Equation (19) is around 0.95 and k is 1 for LDAprob without fallibility weight and 0.03 with fallibility. And \(\alpha\) is 25 and 1.5 for LDAtopsim without fallibility and with fallibility respectively. The best result of LDAprob without fallibility weight for Dev93 and Eval92 testset are 9.38% and 6.59% respectively, and are comparable to a small scale RNN. The best result of LDAtopsim for Dev93 and Eval92 testset without fallibility are 9.45% and 6.70% respectively, both of which are higher than the LDAprob score. From the table, we notice that the number of topics, which is a hyperparameter in the topic model, has a strong effect on WER. For LDAprob score, 20 and 30 is a better choice for Dev93, while a topic model with only 10 topics leads to the best result for Eval92. With respect to LDAtopsim, the best choices for the both testsets are 10. We have conducted experiments on topic models of larger number of topics, and find that when \(n\) is more than 30, the result is worse as \(n\) increases. That is probably because that when \(n\) is large, the difference between topics is small. Moreover, for actual speech, if topics are similar, it is easy to transfer between topics. Thus, the larger topic model may reduce the score of correct words together with the incorrect words, and decrease the difference between correct and incorrect words. The fallibility weight reduces WER for all the features.