Things to include

• Rev
• How to handle interspersed results
• Utterance segmentation
• Why --prealigned and the overall performance of MFA
• Beginning/End Bullet and why we throw away Rev’s output
• fixbullets and manual utterance segmentation
• &*INV= interspersed comments

For some Baysian Network situation, you will note that there’s some bodge of values below:

\begin{equation} P(A|M) = \frac{P(M|A)P(A)}{P(M)} \end{equation}

if we are only interested in a function in terms of different values of \(a\), \(P(M)\) is not that interesting. Therefore, we can just calculate \(A\) for all \(a\), and then normalize it to sum to 1:

\begin{equation} P(A|M) \propto P(M|A)P(A) \end{equation}

and then, after calculating each \(P(M|A)P(A)\) , we just ensure that each thing sums to one.

\begin{align} p(x\mid y) = \frac{p(y \mid x) p(x)}{p(y)} \end{align}

this is a direct result of the probability chain rule.

Typically, we name \(p(y|x)\) the “likelihood”, \(p(x)\) the “prior”.

Better normalization

What if you don’t fully know \(p(y)\), say it was parameterized over \(x\)?

\begin{align} p(x|y) &= \frac{p(y|x) \cdot p(x)}{p(y)} \\ &= \frac{p(y|x) \cdot p(x)}{\sum_{X_{i}} p(y|X_{i})} \end{align}

just apply law of total probability! taad

\begin{equation} P(B=b | D=d) = P(D=d|B=b) P(B=b) k \end{equation}

where, \(P(B=b | D=d)\) is your “posterior”; \(P(D=d|B=b)\) is your likelyhood; and \(P(B=b)\) is your prior.

A Baysian Network is composed of:

1. a directed, acyclic graph
2. a set of conditional probabilities acting as factors.

You generally want arrows to go in the direction of causality.

Via the chain rule of Bayes nets, we can write this equivalently as:

\begin{equation} (P(B) \cdot P(S)) \cdot P(E \mid B,S) \cdot P(D \mid E) \cdot P(C \mid E) \end{equation}

generally, for \(n\) different variables,

\begin{equation} \prod_{i=1}^{n} p(X_{i} \mid pa(x_{i})) \end{equation}

where, \(pa(x_{i})\) are the parent values of \(x_{i}\).