Contents
What happens to entropy when there is no uncertainty?
Then there is no uncertainty. The entropy is zero: each toss of the coin delivers no new information as the outcome of each coin toss is always certain. Entropy can be normalized by dividing it by information length. This ratio is called metric entropy and is a measure of the randomness of the information.
Entropy (information theory) Conversely, rarer events provide more information when observed. Since observation of less probable events occurs more rarely, the net effect is that the entropy (thought of as average information) received from non-uniformly distributed data is always less than or equal to log2 (n).
Is the logarithm of the probability distribution a measure of entropy?
The logarithm of the probability distribution is useful as a measure of entropy because it is additive for independent sources. For instance, the entropy of a fair coin toss is 1 bit, and the entropy of m tosses is m bits.
How is entropy related to the base of the algorithm?
We also say that H(X) is approximately equal to how much information we learn on average from one instance of the random variable X. Note that the base of the algorithm is not important since changing the base only changes the value of the entropy by a multiplicative constant.
How is entropy a cornerstone of information theory?
A cornerstone of information theory is the idea of quantifying how much information there is in a message. More generally, this can be used to quantify the information in an event and a random variable, called entropy, and is calculated using probability.
Do you need an intuition for information entropy?
As such, a machine learning practitioner requires a strong understanding and intuition for information and entropy. In this post, you will discover a gentle introduction to information entropy. After reading this post, you will know:
How is entropy expressed in the base 2?
In this Chapter we use the logarithm to the base 2, which is well adapted to digital communication, and the entropy is then expressed in bits. In other contexts one rather uses the natural logarithm (to base e≈ 2.7182818). It is sometimes said that, in this case, entropy is measured in nats.