Competence Center Information Retrieval & Machine Learning
@alansaid, @saschanarr, @matip
Users and Noise: The Magic Barrier of Recommender Systems
Alan Said, Brijnesh J. Jain, Sascha Narr, Till Plumbaum
Outline
►The Magic Barrier
►Empirical Risk Minimization
►Deriving the Magic Barrier
►User Study
►Conclusion
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The Magic Barrier
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The Magic Barrier
►No magic involved....
►Coined by Herlocker et al. in 2004
“...an algorithm cannot be more accurate than the variance in a user’s ratings for the same item.”
The maximum level of prediction that a recommender algorithm can attain.
►What does this mean?
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The Magic Barrier
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The Magic Barrier
►Even a “perfect” recommender should not reach RMSE = 0 or Precision @ N = 1
►Why?
People are inconsistent and noisy in their ratings
“perfect” accuracy is not perfect
►So?
Knowing the highest possible level of accuracy, we can stop optimizing our algorithms at “perfect” (before overfitting)
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The Magic Barrier
So – how do we find the magic barrier?
We employ the Empirical Risk Minimization principle and a statistical model for user inconsistencies
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The Magic Barrier – User Inconsistencies
Assumption:
If a user were to re-rate all previously rated items, keeping in mind the inconsistency, the ratings would differ, i.e.
𝑟𝑢𝑖 = 𝜇𝑢𝑖 + 𝜀𝑢𝑖
where 𝜇𝑢𝑖 is the expected rating, and
𝜀𝑢𝑖 the rating error (has zero mean)
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Empirical Risk Minimization
►… is a principle in statistical learning theory which defines a family of learning algorithms and is used to give theoretical bounds on the performance of learning algorithms.[Wikipedia]
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Empirical Risk Minimization
►We formulate our risk function as
𝑅 𝑓 = 𝑝 𝑢, 𝑖, 𝑟𝑢,𝑖,𝑟 𝑓 𝑢, 𝑖 − 𝑟2
►Keeping the assumption in mind, we formulate the risk for a true, unknown, rating function as the sum of the noise variance, i.e.
𝑅 𝑓∗ = 𝑝 𝑢, 𝑖𝑢,𝑖 𝕍 𝜀𝑢𝑖
where 𝕍 𝜀𝑢𝑖 is the noise variance
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The probability of user u rating item i with score r
The prediction error
Deriving the Magic Barrier
►We want to express the risk function in terms of a magic barrier for RMSE – we take the root of the risk function
ℬ𝒰×ℐ = 𝑝 𝑢, 𝑖 𝕍 𝜀𝑢𝑖𝑢,𝑖
RMSE=0 iff 𝜀𝑢𝑖 = 0 over all ratings users and items
► In terms of RMSE we can express this as
𝐸𝑅𝑀𝑆𝐸 𝑓 = ℬ𝒰×ℐ + 𝐸𝑓 > ℬ𝒰×ℐ
where 𝐸𝑓 is the error
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Estimating the Magic Barrier
1. For each user-item pair in our population
a) Sample ratings on a regular basis, i.e. re-ratings
b) Estimate the expected value of ratings
𝜇 𝑢𝑖 =1
𝑚 𝑟𝑡𝑢𝑖
𝑚
𝑡=1
c. Estimate the rating variance
𝜀 𝑢𝑖2 =
1
𝑚 𝜇 𝑢𝑖 − 𝑟𝑡𝑢𝑖
2𝑚
𝑡=1
2. Estimate the magic barrier by taking the average
ℬ =1
𝒳 𝜀 𝑢𝑖
2
𝑢𝑖 ∈𝒳
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A real-world user study
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A User Study
►We teamed up with moviepilot.de
Germany’s largest online movie recommendation community
Ratings scale 1-10 stars (Netflix: 1-5 stars)
►Created a re-rating UI
Users were asked to re-rate at least 20 movies
1 new rating (so-called opinions) per movie
Collected data:
306 users
6,299 new opinions
2,329 movies
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A User Study
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User study moviepilot
A User Study
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Predictions vs Ratings
Overall Magic Barrier
Ratings above user’s average
Opinions above user’s average
Ratings below user’s average
Opinions below user’s average
~4 ratings steps
~1 rating steps
Room for improvement
Conclusion
►We created a mathematical characterization of the magic barrier
►We performed a user study on a commercial movie recommendation website and estimated its magic barrier
►We concluded the commercial recommender engine still has room for improvement
►No magic
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More?
► Estimating the Magic Barrier of Recommender Systems: A User Study
SIGIR 2012
► Magic Barrier explained
http://irml.dailab.de
► Movie rating and explanation user study
http://j.mp/ratingexplain
► Recommender Systems Wiki
www.recsyswiki.com
► Recommender Systems Challenge
www.recsyschallenge.com
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Questions?
►Thank You for Listening!
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