1. Mutual Information Brian Dils I590 – ALife/AI 02.28.05

2. Mutual Information Brian Dils I590 – ALife/AI 02.28.05

3. Mutual Information Brian Dils I590 – ALife/AI 02.28.05 What is Mutual Information? Essential to Probability and Information Theory MI is concerned with quantifying the independence of two variables

4. Mutual Information Brian Dils I590 – ALife/AI 02.28.05 What is Mutual Information? MI measures the amount of information in variable x that is shared by variable y MI quantifies the distance between the joint distribution of x and y

5. Mutual Information Brian Dils I590 – ALife/AI 02.28.05 When is MI important? Suppose we know y. If x contains no shared information with y, then the variables are totally independent –Mutual Information: 0 – Entropy of x is very high –However x is not important since it’s not informative about y

6. Mutual Information Brian Dils I590 – ALife/AI 02.28.05 When is MI important? Again we know y, but this time all the information conveyed in x is also conveyed in y –Mutual Information: 100 –Nothing surprising about x, so entropy is very low –x not important because we could simply study y

7. Mutual Information Brian Dils I590 – ALife/AI 02.28.05 When is MI important? MI is important (and powerful) when two variables are not independent and are not identical in the information they convey

8. Mutual Information Brian Dils I590 – ALife/AI 02.28.05

9. Mutual Information Brian Dils I590 – ALife/AI 02.28.05 Why Apply MI? If mutual information is maximized (dependencies increased), conditional entropy can be minimized Reducing conditional entropy makes the behavior of random variables more predictable because their values are more dependent on one another

10. Mutual Information Brian Dils I590 – ALife/AI 02.28.05 MI Applications Discriminative training procedures for hidden Markov models have been proposed based on the maximum mutual information (MMI) criterion. –Hidden parameters predicted from known –Applicable to speech recognition, character recognition, natural language processing

11. Mutual Information Brian Dils I590 – ALife/AI 02.28.05 MI Applications Mutual information is often used as a significance function for the computation of collocations in corpus linguistics. –Essential to coherent speak –Easy for humans, hard to artificial systems –MI has been shown improve connections in AI systems

12. Mutual Information Brian Dils I590 – ALife/AI 02.28.05 MI Applications Mutual information is used in medical imaging for image registration. –Given a reference image (for example, a brain scan), and a second image which needs to be put the same coordinate system as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.

13. Mutual Information Brian Dils I590 – ALife/AI 02.28.05 MI Applications Mutual information has been used as a criterion for feature selection and feature transformations in machine learning and agent-based learning. –Using MI criteria, it was found that the more input variables available, the lower the conditional entropy become –MI-based criteria could effectively select features AND roughly estimate optimal feature subsets, classic problems in feature selection

14. Mutual Information Brian Dils I590 – ALife/AI 02.28.05 References Huang, D., & Chow, T.W.S. (2003). Searching optimal feature subset using mutual information. Proceedings of the 2003 International Symposium on Artificial Neural Networks (pp. 161-166). Bruges, Belgium. Battiti, R. (1994) Using mutual information for selecting features in supervised neural net learning. Neural Networks, 5, 537-550 Bonnlander, B., & Weigend, A.S. (1994). Selecting input variables using mutual information and nonparametric density estimations. Proceedings of the 1994 International Symposium on Artificial Neural Networks (pp. 42-50). Tainan, Taiwan. Wikipedia entries on “Mutual Information”, “Probability Theory”, and “Information Theory”