Informação Mútua (MI) is a statistical measure that quantifies the amount of information obtained about one random variable through another random variable. It is particularly useful in fields like teoria da informação, statistics, and aprendizado de máquina.
Matematicamente, a Informação Mútua entre duas variáveis aleatórias discretas X e Y é definida como:
MI(X; Y) = ∑∑ P(x, y) log( P(x, y) / (P(x) P(y)) )
onde:
- P(x, y) is the distribuição de probabilidade conjunta de X e Y.
- P(x) is the probabilidade marginal distribuição de X.
- P(y) é a distribuição de probabilidade marginal de Y.
A Informação Mútua captura a redução em uncertainty about one variable given knowledge of the other. If X and Y are independent, MI(X; Y) equals zero, indicating no shared information. Conversely, a higher MI value indicates a stronger relationship and greater amount of shared information between the two variables.
In practical applications, MI is widely used in feature selection, where it helps identify the most informative features that contribute to a predictive model. It is also employed in clustering, registro de imagem, and analyzing the dependencies between random variables in complex systems.