## 4 The Evaluation Results and Discussions
### Experimental Results and Discussions for the Proposed Method
#### 4.3.1 Multi-Condition Training Mode  
Tables 4-6 list the WER (%) for our method, MSPP, and FMSE, together with the two SE methods (MMSE and IRM) in the preceding sub-section **using the acoustic models learned from the multi-condition training set**. The used acoustic models are common to the four comparative methods. Since the presented MSPP is directly related to state posteriors in the acoustic models, here we also list the state error rates with the various methods for the test utterances. From these three tables, we have the following observations:  
1. On average, Table 6 shows that the WERs achieved by various methods in the jackhammer noise environment are significantly lower than those in the white and engine noise environments as in Tables 4 and 5, indicating that jackhammer noise brings less distortion to speech signals compared with the white and engine noises. However, we find that all of the used methods here fail to outperform the baseline results for the jackhammer noise case, indicating that the speech enhancement/noise-robust feature methods might introduce further observable distortion to less contaminated utterances. 2. As for the white and engine noise situations as in Tables 4 and 5, the newly proposed MSPP can achieve lower WERs in most SNR cases and outperform the other methods in comparison, which clearly validates the main thought of MSPP that increasing the state posteriors helps to improve the noise robustness and promote recognition accuracy. For example, observing the the lower part of Tables 4 and 5, MSPP achieves 54.9% and 54.6% WER at 0 dB SNR for white and engine noise cases, better than the baseline results 57.0% and 55.1%. In particular, the denoising framework in the presented MSPP is created upon the noisy dataset in which noise types are neither white nor engine. Thus, MSPP is shown to have a generalization capability to conquer unseen noise. 3. When observing the state error rates achieved by the various methods as shown in the upper parts of Tables 4-6, we do not see they strongly correlate with the obtained WERs. For example, the presented MSPP does not always have a lower state error rate, while the method IRM, which has the lowest state error rate in some SNR cases, results in higher WERs. One possible explanation is that the state error rate is quite sensitive to distortion, making it not feasible to be a good evaluation metric. In addition, the presented MSPP attempts to choose the best possible state sequence and is a decision process, which does not necessarily coincide with the minimization of the state error, an estimation process. 4. The method FMSE, which is developed to minimize the mean squared error (MSE) between the clean-noisy FBANK pairs, behaves worse than the baseline in almost all noise situations. For example, in Tables 4 and 5, FMSE achieves 57.2% and 56.2% WER at 0 dB SNR for white and engine noise cases, worse than the baseline results 57.0% and 55.1%. These results seem to agree with our earlier discussions in Section 1, i.e., the mismatch in evaluation (optimization) metrics makes the MMSE-wise transformed speech features give rise to worse recognition accuracy. Another reason is that the learned DNN in FMSE overfits the training data and thus fails to enhance the test data well. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Signal-To-Noise Ratio (SNR)**} \\ \hline \hline  & \(-\)**6 dB** & \(-\)**3 dB** & **0 dB** & **3 dB** & **6 dB** & **12 dB** \\ \hline \multirow{6}{*}{state error rate} & baseline & 0.693 & 0.656 & 0.622 & 0.600 & 0.585 & 0.568 \\ \cline{2-7}  & MSPP & 0.704 * & 0.667 * & 0.638 * & 0.614 * & 0.598 * & 0.579 * \\ \cline{2-7}  & FMSE & 0.725 * & 0.692 * & 0.663 * & 0.644 * & 0.630 * & 0.618 * \\ \cline{2-7}  & MMSE & 0.712 * & 0.678 * & 0.647 * & 0.625 * & 0.610 * & 0.591 * \\ \cline{2-7}  & IRM & 0.707 * & 0.675 * & 0.645 * & 0.618 * & 0.604 * & 0.585 * \\ \hline \hline \end{tabular}
\end{table}