## 4 Exploring Vocabulary-Mismatched Dysarthric Speech Recognition
### Experiment Design
#### 4.2.2 Training Data Selection  
For the very-low-resource setting, we selected training data with limited vocabulary by sorting each source speaker's text transcriptions alphabetically and then using a fraction (10%, 30%, or 90%) of the data for training, reserving the last 10% for validation (**Ordered**). The fewer data we select, the smaller the training vocabulary. However, the models trained with **Ordered** data are influenced by both limited vocabulary and limited data size, complicating our goal of studying the impact of vocabulary alone. To address this, we implemented a second method, **Random**, where a 10%, 30%, or 90% fraction of the data are randomly selected for training, with 10% reserved for validation. With **Random** selection, even a small amount of data may cover the full vocabulary, as utterances from different speakers are randomly selected and contain different vocabulary. With this method, the trained model will suffer more from the limited data size rather than the vocabulary limitation. By comparing models trained on data from both methods, we can better isolate the impact of vocabulary mismatch.  
For the cross-lingual experiments, we use two specific datasets:  
* **C_rich_extgt**: The **C_rich** data with the target language speech excluded, used to train vocabulary-informed base models;
* **D_extgt**: The **D** data with the target language dataset(s) excluded, used as the model training data in the relevant setting.  
In the cross-lingual setting, we do not implement cross-valuation and we train one model for each (target) language. All speakers in **D_extgt** are used as source speakers, while all dysarthric speakers from the target dataset(s) are used for evaluation. A total of 90% of each source speaker's data are randomly selected for training, with the remaining 10% reserved for validation.  
To quantify the extent of vocabulary mismatch between the training and testing data in our experiment design, we calculate the fraction of words and phones in the test data that appear in the training data, referred to as the Overlap. Table 4 presents the Overlap averaged across datasets in the very-low-resource setting and across languages in the cross-lingual setting.  
The table shows that, in the very-low-resource setting, vocabulary mismatch is more pronounced when using a smaller amount of training data, but this mismatch decreases as the amount of training data increases. The phone vocabulary nearly disappears when training data are sufficient (90%). As we expected, the **Random** selection method covers significantly more test words than **Ordered** under the same amount of training data. Compared to the very-low-resource setting, the cross-lingual setting exhibits a much more severe word mismatch, with only 5.1% of test words seen in the training set. The Overlap of phones is even smaller than with minimal training data in the very-low-resource setting,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Averaged Overlap in \% (Word/Phone)**} \\ \hline \multicolumn{4}{c}{**Very-Low-Resource**} \\ \hline \multirow{2}{*}{**Data Selection**} & \multicolumn{2}{c}{**Training Data Amount**} & \multirow{2}{*}{**Cross-Lingual (D\_extgt)**} \\ \cline{2-2} \cline{4-5}  & **10\%** & **30\%** & **90\%** \\ \hline
**Random Ordered** & 74.7 / 96.4 & 86.2 / 99.7 & 90.0 / 99.9 & \\ \cline{1-1} \cline{2-2} \cline{4-5}  & 20.5 / 91.0 & 33.8 / 99.5 & 82.8 / 99.8 & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Overlap between the word/phone vocabulary of training and testing set, averaged over all datasets/languages.  
indicating a more challenging task for the model. Overall, the designed experiments for vocabulary-mismatched settings evaluate the model's performance on both new words and new phones but place greater emphasis on word vocabulary mismatch.