说道Redundancy,怎么定义正式呢?
The redundancy of a random event depends on how uncertain its outcome is, compared to how uncertain a variable on the same probability space could be.
注意,这里有个potential outcome思考:
The latter is defifined by the maximum entropy distribution Hmax(X) on the set of possible outcomes X.
....maximum entropy is equal to the log number of possible states.
还是看截图吧:
![](https://img.haomeiwen.com/i11508273/0541eb2b0ec2505a.png)
为什么呢?因为这种情况下,是假设均匀分布,大家都等可能,每个发生的概率是1/|X|,得到以上公式。
因此:
The redundancy W is the difffference between this maximum entropy and the actual entropy of the random variable:
![](https://img.haomeiwen.com/i11508273/cfebf0db34121d2d.png)
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