users and noise: the magic barrier of recommender systems
DESCRIPTION
Recommender systems are crucial components of most commercial websites to keep users satisfied and to increase revenue. Thus, a lot of effort is made to improve recommendation accuracy. But when is the best possible performance of the recommender reached? The magic barrier, refers to some unknown level of prediction accuracy a recommender system can attain. The magic barrier reveals whether there is still room for improving prediction accuracy or indicates that further improvement is meaningless. In this work, we present a mathematical characterization of the magic barrier based on the assumption that user ratings are afflicted with inconsistencies - noise. In a case study with a commercial movie recommender, we investigate the inconsistencies of the user ratings and estimate the magic barrier in order to assess the actual quality of the recommender system.TRANSCRIPT
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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