Question about 4.1 - Classification boundaries

[yanyu liang]

Why "checkerboard pattern" comes from "variables are treated independently" in Naive Bayes?

[Ian Witten]

Suppose in a simple 2-class case there are two numeric attributes, x and y, both ranging from 0 to 1.

The information that attribute x contains about the class can be visualised as a probability distribution along the x-axis. Suppose that there are some regions on the x-axis where a certain outcome has probability 1, and others where it has probability 0. Choose some regions and draw a picture.

The information that attribute y contains about the class can be visualised as a probability distribution along the y-axis. Suppose that there are some regions on the y-axis where a certain outcome has probability 1, and others where it has probability 0. Add this to your picture.

Naive Bayes multiples the two probability distributions to get the final distribution used to determine the outcome. Do this on your picture. Some regions will have probability 1 (1 times 1) and others will have probability 0 (0 times 0, 0 times 1, 1 times 0). It will have a checkerboard pattern.

This interpretation is simplistic because Naive Bayes has been defined in the class as applying to nominal attributes, not numeric ones. What picture you get from Weka will depend on the how the Naive Bayes implementation deals with numeric attributes. But the principle remains true.

cheers

ian

On 20/09/2015, at 7:26 am, yanyu liang <yany...@gmail.com> wrote:

Why "checkerboard pattern" comes from "variables are treated independently" in Naive Bayes?

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[yanyu liang]

Hi, Ian

Thanks for your reply. What if the attributes are not treated independently? I think it will also lead to "checkerboard" pattern disappears. Is that right?

Thanks,

Yanyu

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