使用正常数据直方图与直接公式(matlab)进行熵估计 [英] entropy estimation using histogram of normal data vs direct formula (matlab)

问题描述

假设我们已经绘制了标准正态分布的n=10000个样本.

Let's assume we have drawn n=10000 samples of the standard normal distribution.

现在我想使用直方图来计算其熵来计算概率.

Now I want to calculate its entropy using histograms to calculate the probabilities.

1)计算概率(例如，使用matlab)

1) calculate probabilities (for example using matlab)

[p,x] = hist(samples,binnumbers);
area = (x(2)-x(1))*sum(p);
p = p/area;

(binnumbers是根据某些规则确定的)

(binnumbers is determined due to some rule)

2)估计熵

H = -sum(p.*log2(p))

给出58.6488

现在，当我使用直接公式计算正常数据的熵时

Now when i use the direct formula to calculate the entropy of normal data

H = 0.5*log2(2*pi*exp(1)) = 2.0471

使用直方图+熵公式时，我该怎么做? 非常感谢您的帮助！

What do i do wrong when using the histograms + entropy formula? Thank you very much for any help!!

推荐答案

您缺少总和中的dp项

dp = (x(2)-x(1));
area = sum(p)*dp;
H = -sum( (p*dp) * log2(p) );

这应该使您足够接近...

This should bring you close enough...

PS，
拿log2(p)时要小心，因为有时您可能有空的垃圾箱.您可能会发现 nansum 有用.

PS,
be careful when you take log2(p) for sometimes you might have empty bins. You might find nansum useful.

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