PMI Score

A PMI Score is a real-number score produced by a pointwise mutual information measure (that ranks the statistical dependence between two random variables).

AKA: Pointwise Mutual Information Value.
Context:
- It can range from being a Negative PMI Score (low co-occurrence likelihood) to being a Non-Positive PMI Score to being a Zero PMI Score (independence) to being a Non-Negative Score to being a Positive PMI Score (high co-occurrence likelihood).
- It can be a Weighted PMI Score.
- It can be a Shifted PMI Score.
- It can be produced by a PMI Calculation System (solving a PMI calculation task).
- It can, if based on [math]\displaystyle{ \log_2 }[/math], be in units of bits.
- It can be a member of a PMI Vector (or a PMI matrix).
Example(s):
- [math]\displaystyle{ 4.0000... \equiv \log_{10}(10,000) \equiv \log_{10} \bigl(8 / \frac{8 \times 8}{80,000}\bigr) }[/math], given contingency table [math]\displaystyle{ \begin{array}{c|cc} & w_2 & \neg w_2 & \\ \hline w_1 & 8 & 0 \\ \neg w_1 & 0 & 79,992 \end{array} }[/math].
- [math]\displaystyle{ 3.5405...\equiv \log(61,556.6...) \equiv \log \bigl(70,008 / \frac{70,100 \times 70,250}{80,000}\bigr) }[/math], given contingency table [math]\displaystyle{ \begin{array}{c|cc} & w_2 & \neg w_2 & \\ \hline w_1 & 69,908 & 92 \\ \neg w_1 & 242 & 9,758 \end{array} }[/math].
- [math]\displaystyle{ 0.000... \equiv \log_{2}(1.00...) \equiv \log_{2} \bigl(6,862 / \frac{23,431 \times 23,431}{80,000}\bigr) }[/math], given contingency table [math]\displaystyle{ \begin{array}{c|cc} & w_2 & \neg w_2 & \\ \hline w_1 & 6,862& 16,569 \\ \neg w_1 & 16,569 & 40,000 \end{array} }[/math].
- [math]\displaystyle{ -0.5051...\equiv \log(0.3125) \equiv \log \bigl(8 / \frac{100 \times 250}{80,000}\bigr) }[/math], given contingency table [math]\displaystyle{ \begin{array}{c|cc} & w_2 & \neg w_2 & \\ \hline w_1 & 8 & 92 \\ \neg w_1 & 242 & 79,658 \end{array} }[/math].
- …
Counter-Example(s):
See: Co-Occurrence Statistic.