1. Statistics 202: Statistical Aspects of Data Mining
Professor Rajan Patel
Lecture 6 = Collaborative Filtering
Agenda:
1) Homework #2 due Monday
2) Reminder: Midterm is on Monday, July 14th
3) Collaborative Filtering
3) Simpson's Paradox
3) Review for the Midterm *

2. Announcement – Midterm Exam:
The midterm exam will be Monday, July 14
Stanford and SCPD students should try to take it in class (4:15 PM)
Remote students who can’t come to class should take it with a proctor and return it via Scoryst by July 15 at 11:59 PM.
You are allowed one 8.5 x 11 inch sheet (front and back) containing notes
No books or computers are allowed, but please bring a hand held calculator
The exam will cover the material that we covered in class from Chapters 1,2,3 and 6 * *

3. The Netflix Prize
• 100M ratings of movies
• 18k movies and 48k users
• On average ~ 5600 ratings / movie
• On average ~ 208 ratings / user
• Data collected over several years
• Ratings are integers from 1 to 5

4. Objective
• Reduce RMSE on new data by 10%
• Current is 0.951, so reduce to
• New data may not have the same
distributions as older data (Netflix is
growing, more users and movies, fewer
movies rated per user and per movie)

5. A baseline model
• bui = μ + bu + bi
• Where μ is the item rating
• bi is the mean rating for that item
• bu is the mean rating for that user
• Models how “critical” a user is and how good a movie is, on average.

6. Collaborative Filtering
• CF produces recommendations of items based on patterns of ratings or usage (e.g. purchases) without the need for exogenous information about the item or user
• Relates two fundamentally different
entities: items and users

7. Collaborative Filtering
• Two main techniques
– Neighborhood approach
– Latent factor models
• Neighborhood methods focus on
relationships between items (or users),
modeling the preference of a user to an
item based on ratings of similar items by
that user.

8. Neighborhood approaches
• Two items are more similar if a user rated both items similarly.
• Cluster items based on similarity
• Or build a kNN based predictive model

9. Latent factor models
• Transform items and users to the same latent factor space.
• Explains ratings by characterizing products and users on factors inferred from user feedback.
• This new space might identify factors relating to “comedy”, “romance”, or a particular actor, etc.
• The model provides weights for each user and item in this space

12. Latent factor models
• Map items and users into a latent factor space of dimensionality, f

13. Latent factor models • Estimate the parameters with the least
squared error with some regularization
• λ is a regularization parameter to bias
parameters towards 0.
• Estimate with gradient ascent

14. Latent factor models • Bonus - include information about whether a
result was rated at all
• Each item associated with a new factor vector
y which is then used to modify our user features based on which items they rated

16. Simpson's Paradox

17. Simpson’s “Paradox” (page 384)
Occurs when the relationship between a pair of variables across different groups changes when the groups are combined
Baseball Example: Batting averages of David Justice and Derek Jeter in 1995 and 1996
Justice has a better batting average in 1995 and 1996, but overall for the two seasons, he has a lower average
1995
1996
Combined
Derek Jeter
12/48
.250
183/582
.314
195/630
.310
David Justice
104/411
.253
45/140
.321
149/551
.270 *

18. Another example of Simpson’s “Paradox”
Real example from a medical study comparing the effectiveness of a treatment on kidney stones
Overall success rate
Above table seems to suggest that Treatment B is more effective, but if we break down the data by kidney stone size, we see that the opposite may be true
Treatment A
Treatment B
78% (273/350)
83% (289/350)
Treatment A
Treatment B
Small Stones
93% (81/87)
87% (234/270)
Large Stones
73% (192/263)
69% (55/80)
Both
78% (273/350)
83% (289/350) *

19. Sample Midterm Question #1:
What is the definition of data mining used in your textbook?
A) the process of automatically discovering useful information in large data repositories
B) the computer-assisted process of digging through and analyzing enormous sets of data and then extracting the meaning of the data
C) an analytic process designed to explore data in search of consistent patterns and/or systematic relationships between variables, and then to validate the findings by applying the detected patterns to new subsets of data *

20. Sample Midterm Question #2:
If height is measured as short, medium or tall then it is what kind of attribute?
A) Nominal
B) Ordinal
C) Interval
D) Ratio *

21. Sample Midterm Question #3:
If my data frame in R is called “data”, which of the following will give me the third column?
A) data[2,]
B) data[3,]
C) data[,2]
D) data[,3]
E) data(2,)
F) data(3,)
G) data(,2)
H) data(,3) *

22. Sample Midterm Question #4:
Compute the confidence for the association rule
{b, d} → {a} by treating each row as a market basket. Also, state what this value means in plain English. *

23. Sample Midterm Question #5:
Compute the standard deviation for the numbers 23, 25, Show your work below. *