# Speech Recognition for Task Domains with Sparse Matched Training Data
## 2 Related Work
### Disentangled Representation Learning in Speech Processing  
Representation learning is a method that learns representations of input data, with the main aim of yielding abstract and useful representations for tasks such as classification. In the past, research focused on feature engineering to create representations that support machine learning algorithms. However, representations based on deep learning are now being widely studied [28]. Among the many applications of deep representation learning is disentangled representation. This method separates each feature into narrowly defined variables and encodes them into separate dimensions [29]. Assuming that the data is generated from independent factors of variation, disentanglement enables these factors to be captured by different independent variables in the representation, which yields a concise abstract representation of the data [30].  
Several recent works have leveraged variational autoencoders (VAEs) to learn disentangled representations of sequence data such as speech, video, and text. [PERSON] et al. [31] proposed a novel factorized hierarchical VAE, which learns disentangled and interpretable latent representations from speech data by explicitly modeling the multi-scaled information with a factorized hierarchical graphical model. Speech data inherently contains information at multiple scales such as noise, channel, speaker, prosody, and phonetic content. These are independent factors operating at different time scales. For instance, noise, channel, and speaker identity affect the sequence level and tend to have a smaller amount of variation within an utterance compared to the variation between utterances. The sequence level is a time series of speech data that is the object of model training and speech recognition. It can be an utterance or a phrase. However, the phonetic content affects the segmental level and tends to have a similar amount of variation within and between utterances. The segment level is a small unit that comprises a sequence and is composed of frames of a certain length. Factorized hierarchical VAEs consist of an inference model and a generative model that learns a disentangled representation of a latent sequence variable and a latent segment variable, which have properties that change at the utterance and segment level, respectively. Figure 1 is a graphical illustration of factorized hierarchical VAEs [31].  
In Figure 1, \(\left\{x^{(i,n)}\right\}_{n=1}^{N^{(i)}}\) is a sequence of \(N^{(i)}\) observed variables, where \(x^{(i,n)}\) is the n-th segment of the i-th sequence and \(N^{(i)}\) is the number of segments for the i-th sequence. As Figure 1 illustrates, the following generation process is considered. First, an s-vector \(\mu_{2}\) is drawn from a prior distribution \(p_{\theta}\!\left(\mu_{2}^{(i)}\right)\) for each i-th sequence. Second, \(N^{(i)}\) independent and identically distributed \(\left\{z_{2}^{(i,n)}\right\}_{n=1}^{N^{(i)}}\) and \(\left\{z_{1}^{(i,n)}\right\}_{n=1}^{N^{(i)}}\) are drawn from a sequence-dependent prior distribution \(p_{\theta}\!\left(z_{2}^{(i)}\right|\!\mu_{2}^{(i)}\right)\) and sequence-independent distribution, \(p_{\theta}\!\left(z_{1}^{(i)}\right)\), respectively; Finally, \(N^{(i)}\) independent and identically distributed \(\left\{x^{(i,n)}\right\}_{n=1}^{N^{(i)}}\) are drawn from a conditional distribution \(p_{\theta}\!\left(x^{(i)}\right|\!z_{1}^{(i)},z_{2}^{(i)}\right)\).