Predicting Movie Plans Example

You want to predict whether you'll end up watching a movie based on whether you've finished your homework, the weather, and if your friends are available. Here's data from your past decisions:

HW Completed	Weather	Friend Available	Watched Movie?
Yes	Sunny	TRUE	yes
No	Rainy	FALSE	yes
Yes	Rainy	TRUE	yes
Yes	Sunny	TRUE	yes
No	Sunny	TRUE	no
On it	Sunny	TRUE	no
Yes	Rainy	FALSE	yes
No	Sunny	FALSE	no
On it	Rainy	FALSE	yes
On it	Sunny	TRUE	no
On it	Rainy	FALSE	yes
Yes	Rainy	FALSE	no
Yes	Rainy	TRUE	yes
No	Sunny	FALSE	no

The Naive Bayes algorithm will:

1. Calculate the base probability of going to movies
2. Compute the probability of each feature given "yes" and "no" movie outcomes
3. Multiply these probabilities together
4. Determine which outcome has the highest probability

From this table, we can calculate:

• Prior probability of watching a movie: $P(Watch=yes) = \frac{8}{14}$ (watched movies 8 times out of 14 total occasions)
• Prior probability of watching a movie: $P(Watch=no) = \frac{6}{14}$ (didn't watch movies 6 times out of 14 total occasions)
• For completed homework when watching movies: $P(HW=Yes|Watch=yes) = \frac{4}{8}$
• For rainy weather when watching movies: $P(Rainy|Watch=yes) = \frac{5}{8}$
• For friend availability when watching movies: $P(Friend=TRUE|Watch=yes) = \frac{4}{8}$
• etc.

Let's predict if you'll watch a movie when:

• Homework is completed (Yes)
• It's rainy outside
• Your friend is available (TRUE)

For Watch=yes:

• $P(Watch=yes) = \frac{8}{14}$
• $P(HW=Yes|Watch=yes) = \frac{4}{8}$
• $P(Rainy|Watch=yes) = \frac{5}{8}$
• $P(Friend=TRUE|Watch=yes) = \frac{4}{8}$

$P(Watch=yes|Scenario) \propto \frac{8}{14} \times \frac{4}{8} \times \frac{5}{8} \times \frac{4}{8} = 0.089$

For Watch=no:

• $P(Watch=no) = \frac{6}{14}$
• $P(HW=Yes|Watch=no) = \frac{1}{6}$
• $P(Rainy|Watch=no) = \frac{1}{6}$
• $P(Friend=TRUE|Watch=no) = \frac{2}{6}$

$P(Watch=no|Scenario) \propto \frac{6}{14} \times \frac{1}{6} \times \frac{1}{6} \times \frac{2}{6} = 0.002$

Since 0.089 > 0.002, we predict you'll watch a movie!