Contents
What is pointwise mutual information in NLP?
Pointwise mutual information (PMI), or point mutual information, is a measure of association used in information theory and statistics. In contrast to mutual information (MI) which builds upon PMI, it refers to single events, whereas MI refers to the average of all possible events.
What is pointwise mutual information used for?
The pointwise mutual information represents a quantified measure for how much more- or less likely we are to see the two events co-occur, given their individual probabilities, and relative to the case where the two are completely independent.
How do you calculate positive Pointwise mutual information?
The general formula for pointwise mutual information is given below; it is the binary logarithm of the joint probability of X = a and Y = b, divided by the product of the individual probabilities that X = a and Y = b.
What does negative PMI mean?
A PMI(x,y) = 0 means that the particular values of x and y are statistically independent; positive PMI means they co-occur more frequently than would be expected under an independence assumption, and negative PMI means they cooccur less frequently than would be expected.
What is the difference between mi and pointwise mutual information?
Pointwise mutual information ( PMI ), or point mutual information, is a measure of association used in information theory and statistics. In contrast to mutual information (MI) which builds upon PMI, it refers to single events, whereas MI refers to the average of all possible events.
How to normalize pointwise mutual information for independence?
Pointwise mutual information can be normalized between [-1,+1] resulting in -1 (in the limit) for never occurring together, 0 for independence, and +1 for complete co-occurrence. npmi ( x ; y ) = pmi ( x ; y ) h ( x , y ) {displaystyle operatorname {npmi} (x;y)={frac {operatorname {pmi} (x;y)}{h(x,y)}}}.
How is pointwise mutual information related to conditional probability?
The pointwise mutual information can be understood as a scaled conditional probability. The pointwise mutual information represents a quantified measure for how much more- or less likely we are to see the two events co-occur, given their individual probabilities, and relative to the case where the two are completely independent.
Which is a negative number in pointwise mutual information?
Pointwise mutual information measure is not confined to the [0,1] range. So here we explain how to interpret a zero, a positive or, as it is in our case, a negative number. The case where PMI=0 is trivial. It occurs for log (1) =0 and it means that which tells us that x and y are independents.