product = exp(ln(product)) = exp(ln(sum of ln(pn))
If you are multiplying values together, they look like this:
product = 1*p1*....*pn
If you take the natural log of both sides it looks like this:
ln(product) = ln(1) + ln(p1) + .... + ln(pn)
But ln(1) = 0, so that's how you initialize the sum of logarithms. Set it to zero.
Remember what you're summing here: the log of each probability adds into the log of the total probability. Once you complete the sum, you can get the product like this:
product = exp(ln(product)) = exp(ln(sum of ln(pn))
The antilog of zero is one, not negative infinity. That means that starting adding with zero for the logarithm is the same as starting multiplying with one for the probabilities themselves.
If you are calculating the intersection of events. Just multiply them. No need to take into logarithmic space. If it gets really really small then is zero probability for the intersection of events.
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如果您将值相乘，它们看起来像这样：
如果您取两边的自然对数，它看起来像这样：
但是
ln(1) = 0，这就是初始化对数总和的方式。将其设置为零。记住你在这里总结的内容：每个概率的对数加到总概率的对数中。完成总和后，您可以获得如下产品：
If you are multiplying values together, they look like this:
If you take the natural log of both sides it looks like this:
But
ln(1) = 0, so that's how you initialize the sum of logarithms. Set it to zero.Remember what you're summing here: the log of each probability adds into the log of the total probability. Once you complete the sum, you can get the product like this:
零的反对数是一，而不是负无穷大。这意味着从零开始加对数与从一开始乘以概率本身相同。
The antilog of zero is one, not negative infinity. That means that starting adding with zero for the logarithm is the same as starting multiplying with one for the probabilities themselves.
如果您正在计算事件的交集。只需将它们相乘即可。无需考虑对数空间。如果它变得非常非常小，那么事件交叉的概率为零。
If you are calculating the intersection of events. Just multiply them. No need to take into logarithmic space. If it gets really really small then is zero probability for the intersection of events.