1 / 7

Naive Bayes Collaborative Filtering

Naive Bayes Collaborative Filtering. ICS 77B M ax Welling. We want to compute the probability that: Item 5 will be rated 1, given that Item 1 was rated 1 and Item 2 was rated 3 and Item 3 was rated 3, …. Item 5 will be rated 2 given that Item 1 was rated 1 and Item 2 was rated 3, ….

livia
Télécharger la présentation

Naive Bayes Collaborative Filtering

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Naive Bayes Collaborative Filtering ICS 77B Max Welling

  2. We want to compute the probability that: • Item 5 will be rated 1, given that • Item 1 was rated 1 and • Item 2 was rated 3 and • Item 3 was rated 3, …. • Item 5 will be rated 2 given that • Item 1 was rated 1 and • Item 2 was rated 3, …

  3. To compute these probabilities we first ask: “how frequently did other users rate R1 = 1 & R5 = 1 ? We see that User 2 and User 4 both rated R1 = 1 & R5 = 1. That’s 100% ! Question: What is the probability that R1 = 2 | R5 = 4 ? In the end we will have computed all P(R1=x1|R5=y), P(R2=x2|R5=y), P(R3=x3|R5=y), P(R4=x4|R5=y)

  4. We can also compute: P(R5 = 1), P(R5 = 2), P(R5 = 3), P(R5 = 4), P(R5 = 5). Question: Compute probability that: P(R5 = 1).

  5. In the end we thus have: P(Ri=xi|R5 = y) for i=1,2,3,4 P(R5 = y) How do we combine this: Bayes rule! P(y|x) P(x) = P(x|y) P(y)  P(y|x) = P(x|y) P(y) / P(x)

  6. P(y|x) P(x) = P(x|y) P(y)  P(y|x) = P(x|y) P(y) / P(x) We will also use that we assume the rating for different items to be conditionally independent: P(R1=x1,R2=x2,R3=x3,R4=x4|R5=y) = P(R1=x1|R5=y) P(R2=x2|R5=y) P(R3=x3|R5=y) P(R4=x4|R5=y)

  7. Combining: P(R5=y|R1=1,R2=3,R3=3,R4=2) = P(R1=x1|R5=y) P(R2=x2|R5=y) P(R3=x3|R5=y) P(R4=x4|R5=y) P(R5=y) / constant  Try all values of y and pick the one which has largest probability.

More Related