What is the meaning of P[E] in section 3.3 video lecture: "Using Probabilities"

[Sourabh Sinha]

Is it the "joint conditional probabilities of the attributes" i.e. = P[sunny, cool, humid, windy]? Why we can't calculate it?

Thanks

[Fernando DM]

Hi Sourabh, 

Just in case, keep in mind that "sunny" is a category and not a variable, and "windy" is a variable and not a category, E (evidence) is the combination of the values for the new day (Sunny,Cool,High,True), when normalized the Pr (yes) is to get the Pr of YES, without knowing about E (then it is not considered in this point).  

***** ie (A new day) *******

Outlook Temp. Humidity Wind =>Play

Sunny   Cool  High     True =>?

Likelihood of the two classes

For “yes” = 2/9 * 3/9 * 3/9 * 3/9 * 9/14 = 0.0053

For “no” = 3/5 * 1/ * 4/5 * 3/5 * 5/14 = 0.0206

Finally:

Conversion into a probability by normalization:

P(“yes”) = 0.0053 / (0.0053 + 0.0206) = 0.205

P(“no”) = 0.0206 / (0.0053 + 0.0206) = 0.795

Since the probability of play=NO, is greater than the probability of play=YES, this new record (new day) is classified as Play = NO.

However, check out: Lesson 3.3 - page 21 and the "CHAPTER 4 Algorithms: The Basic Methods" from the course book.

For any further information, please let me know.

Best Regards,

Ing. Fernando García

Data Mining Specialist

ar.linkedin.com/in/fernand0garcia/

[Eduard]

Pr[E] is a priori probability of an evidence, in our case this is a probability of a particular combination of attributes. Probably, we can calculate it, but we don't need it, as prof.Witten said (see Lec.3-3, 07:39). Pr[E] is in the denominators of both Pr[yes | E] and Pr[no | E], so one can calculate the likelihoods (numerators) and then normalize them.