들어가며
Applications
Automatic Speech Recognition (ASR)
\[\begin{gathered}
y_{1:n}=\text{argmax }P(\text{y}|x;\theta) \\
\text{where }x\text{ is audio signal, and }y_{1:n}\text{ is word sequence, }y_{1:n}=\{y_1,y_2,\cdots,y_n\}.
\end{gathered}\]
\[\begin{aligned}
\hat{y}&={\underset{y\in\mathcal{Y}}{\text{argmax}}}P(y|x) \\
&={\underset{y\in\mathcal{Y}}{\text{argmax}}}\frac{P(x|y)P(y)}{P(x)} \\
&={\underset{y\in\mathcal{Y}}{\text{argmax}}}P(x|y)P(y)
\end{aligned}\]