What is the difference between mutual information and information gain?

Information gain is the reduction in entropy or surprise by transforming a dataset and is often used in training decision trees. Mutual information calculates the statistical dependence between two variables and is the name given to information gain when applied to variable selection.

How is pointwise mutual information calculated?

The general formula for all versions of 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 is the difference between mutual information and correlation?

Mutual information is a distance between two probability distributions. Correlation is a linear distance between two random variables.

Is pointwise mutual information symmetric?

The mutual information (MI) of the random variables [math]X[/math] and [math]Y[/math] is the expected value of the PMI over all possible outcomes. The measure is symmetric ([math]SI(x,y)=SI(y,x)[/math]).

What does Pointwise mutual information between two words measure?

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.

What is Pointwise mutual information used for?

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.

Is mutual information linear?

The Mutual Information between two random variables measures non-linear relations between them. This is because it can also be known as the reduction of uncertainty of a random variable if another is known.

Is cross entropy the same as mutual information?

The standard cross-entropy loss for classification has been largely overlooked in DML. Second, we show that, more generally, minimizing the cross-entropy is actually equivalent to maximizing the mutual information, to which we connect several well-known pairwise losses.

What is meant by mutual information?

Mutual information is a quantity that measures a relationship between two random variables that are sampled simultaneously. In particular, it measures how much information is communicated, on average, in one random variable about another. That is, these variables share mutual information.

What is mutual information in communication?

3 Mutual Information. Mutual information is a quantity that measures a relationship between two random variables that are sampled simultaneously. In particular, it measures how much information is communicated, on average, in one random variable about another.