Naïve Bayes Classifier TUTORIAL 5

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A.Calculating Probabilities B. Laplace Estimator C. C. Creating prediction rules

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A. Calculating Probabilities

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1. Count calculations for all attributes

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2. Convert Counts into ratio

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3.1 Calculate the likelihood of playing product of all the associated ratios

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3.2 Calculate the likelihood of NOT playing product of all the associated ratios

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4. Convert these likelihoods into probabilities for playing and not playing

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B. Laplace Estimator

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Laplace Estimator (0.44) (0.33) (0.33) (0.33) Yes (0.64)

0.44

ₓ 0.33 ₓ 0.33 ₓ 0.33 ₓ 0.64 =

0.010119

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Laplace Estimator

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Laplace Estimator

100% chance of playing

0.00 0 0.000 + 0.010119

0%

0.010119 0 0.000 + 0.010119

100 %

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Laplace Estimator Is it true that the Team always performs the play when the outlook is overcast? Or

is it that we just didn’t have enough samples in our dataset to have an instance where the play was not performed when the outlook was overcast. To solve this problem, statisticians have invented the so-called Laplace estimator, which amounts to simply adding a value of 1 to each attribute values as shown

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1. Adding a value of 1 to each attribute values

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2. Re-convert the increment counts to ratios

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3. Re-calculate probabilities

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4. Re-calculate probabilities So, instead of a 100% chance of playing whenever Outlook=overcast, we now calculated the probability as 72% for this combination of weather conditions which includes Outlook=overcast.

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So the Laplace estimator solved the problem of attribute with zero occurrences with minimal impact on the overall.

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C. Creating prediction rules

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C. Creating prediction rules Our next step, we need to repeat this calculation for all possible combination of weather condition. Then, the goal in all cases will be to choose the rule for each combination with higher probability, and then use that rule to predict the outcome for the associated weather condition.

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C. Creating prediction rules Now we have

3 values for Outlook, 3 for Temperature, 2 for Humidity, and 2 for Windy,

Having a total 36 pairs of combination,

with each pair having a Play=yes and a Play=no possible outcome.

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