Computation of segment Likelihood functions using PPT

In (14.2), the PDFs $p({\bf x}_s \vert m_s,k_s)$ are the segment PDFs conditioned on knowing the segment sub-class (the segment sub-classes are assumed to be fixed for each segmentation ${\bf q}$). These are obtained using the PPT (equation 2.2) and a feature transformation specific to sub-class $m_s$ on a segment of length $k_s$ base segments:

$$p({\bf x}_s \vert m_s,k_s) = \frac{p({\bf x}_s\vert H_0)}{p({\bf z}_{k_s,m_s}\vert H_0)} \; p({\bf z}_{k_s,m_s}\vert m_s),$$ (14.4)

where ${\bf z}_{k,m}$ is the feature used for a segment of size $k$ and sub-class $m$, $p({\bf z}_{k,m}\vert m)$ is the PDF of that feature assuming sub-class $m$, and $p({\bf z}_{k,m}\vert H_0)$ is the PDF of that feature under the reference hypothesis. This calculation has been described for a range of different features (See chapters 4 through 11). The MR-HMM requires a large amount of front-end processing to calculate all the necessary features and PDFs for all segments (seen in Figure 14.1 “Available segments") assuming each possible sub-class.