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What are false negatives and false positives and why are they so important?

False negatives positives
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What are false negatives and false positives and why are they so important?

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The statistics about an email filter’s effectiveness are built upon the concept of false positives and false negatives. Since POPFile is not a spam filter, but a general email classifier, the meaning of those terms differs in POPFile’s context from their meaning in the context of spam filters. A normal spam filter that categorizes mail into a spam and a ham category produces a false positive when it puts a ham message into the spam category and a false negative when it places spam into the ham category. But, as you know, POPFile can deal with multiple categories (buckets). It is an email classifier that happens to be very good at filtering spam. But this also means that the definition of a false positive and of a false negative cannot be built around the simple question of spam versus ham. Instead, these terms are defined from the point of view of each single bucket. Suppose POPFile categorizes a message as belonging to bucket A, while it really belongs to bucket B. From the point of v

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