Users and Noise: The Magic Barrier of Recommender Systems Alan Said, Brijnesh J. Jain, Sascha Narr, Till Plumbaum  Compete...
Outline► The Magic Barrier► Empirical Risk Minimization► Deriving the Magic Barrier► User Study► Conclusion           20 J...
The Magic Barrier         20 July 2012   The Magic Barrier   3
The Magic Barrier► No magic involved....► Coined by Herlocker et al. in 2004      “...an algorithm cannot be more accurat...
The Magic Barrier         20 July 2012   The Magic Barrier   5
The Magic Barrier►   Even a “perfect” recommender should not reach RMSE = 0 or    Precision @ N = 1►   Why?       People ...
The Magic BarrierSo – how do we find the magic barrier?We employ the Empirical Risk Minimization principle and a statistic...
The Magic Barrier – User InconsistenciesAssumption:    If a user were to re-rate all previously rated items, keeping in  ...
Empirical Risk Minimization►   … is a principle in statistical learning theory which defines a    family of learning algor...
Empirical Risk Minimization►   We formulate our risk function as       𝑅 𝑓 = 𝑢,𝑖,𝑟 𝑝 𝑢, 𝑖, 𝑟 𝑓 𝑢, 𝑖 − 𝑟 2                ...
Deriving the Magic Barrier►   We want to express the risk function in terms of a magic barrier    for RMSE – we take the r...
Estimating the Magic Barrier1.   For each user-item pair in our population      a) Sample ratings on a regular basis, i.e....
A real-world user study     20 July 2012   The Magic Barrier   13
A User Study► We teamed up with moviepilot.de      Germany’s largest online movie recommendation community      Ratings ...
A User Study      User study                             moviepilot          20 July 2012   The Magic Barrier             ...
A User Study                    ~4 ratings steps          Room for improvement                                        ~1 r...
Conclusion► We created a mathematical characterization of the magic  barrier► We performed a user study on a commercial mo...
More?►   Estimating the Magic Barrier of Recommender Systems: A User Study         SIGIR 2012►   Magic Barrier explained ...
Questions?►   Thank You for Listening!              20 July 2012     The Magic Barrier   19
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Users and Noise: The Magic Barrier of Recommender Systems

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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.

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Users and Noise: The Magic Barrier of Recommender Systems

  1. 1. Users and Noise: The Magic Barrier of Recommender Systems Alan Said, Brijnesh J. Jain, Sascha Narr, Till Plumbaum Competence Center Information Retrieval & Machine Learning @alansaid, @saschanarr, @matip
  2. 2. Outline► The Magic Barrier► Empirical Risk Minimization► Deriving the Magic Barrier► User Study► Conclusion 20 July 2012 The Magic Barrier 2
  3. 3. The Magic Barrier 20 July 2012 The Magic Barrier 3
  4. 4. 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? 20 July 2012 The Magic Barrier 4
  5. 5. The Magic Barrier 20 July 2012 The Magic Barrier 5
  6. 6. 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) 20 July 2012 The Magic Barrier 6
  7. 7. The Magic BarrierSo – how do we find the magic barrier?We employ the Empirical Risk Minimization principle and a statistical model for user inconsistencies 20 July 2012 The Magic Barrier 7
  8. 8. The Magic Barrier – User InconsistenciesAssumption:  If a user were to re-rate all previously rated items, keeping in mind the inconsistency, the ratings would differ, i.e. 𝑟 𝑢𝑖 = 𝜇 𝑢𝑖 + 𝜀 𝑢𝑖  where  𝜇 𝑢𝑖 is the expected rating, and  𝜀 𝑢𝑖 the rating error (has zero mean) 20 July 2012 The Magic Barrier 8
  9. 9. 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] 20 July 2012 The Magic Barrier 9
  10. 10. Empirical Risk Minimization► We formulate our risk function as  𝑅 𝑓 = 𝑢,𝑖,𝑟 𝑝 𝑢, 𝑖, 𝑟 𝑓 𝑢, 𝑖 − 𝑟 2 The prediction error The probability of user u rating item i with score r► 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∗ = 𝑢,𝑖 𝑝 𝑢, 𝑖 𝕍 𝜀 𝑢𝑖  where 𝕍 𝜀 𝑢𝑖 is the noise variance 20 July 2012 The Magic Barrier 10
  11. 11. 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  ℬ 𝒰×ℐ = 𝑢,𝑖 𝑝 𝑢, 𝑖 𝕍 𝜀 𝑢𝑖  RMSE=0 iff 𝜀 𝑢𝑖 = 0 over all ratings users and items► In terms of RMSE we can express this as  𝐸 𝑅𝑀𝑆𝐸 𝑓 = ℬ 𝒰×ℐ + 𝐸 𝑓 > ℬ 𝒰×ℐ  where 𝐸 𝑓 is the error 20 July 2012 The Magic Barrier 11
  12. 12. Estimating the Magic Barrier1. 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 𝑚 1 𝜇 𝑢𝑖 = 𝑟 𝑡 𝑢𝑖 𝑚 𝑡=1 c. Estimate the rating variance 𝑚 1 2 𝜀 𝑢𝑖 2 = 𝑚 𝜇 𝑢𝑖 − 𝑟𝑡 𝑢𝑖 𝑡=12. Estimate the magic barrier by taking the average 1 ℬ= 𝜀 𝑢𝑖 2 𝒳 𝑢𝑖 ∈𝒳 20 July 2012 The Magic Barrier 12
  13. 13. A real-world user study 20 July 2012 The Magic Barrier 13
  14. 14. 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 20 July 2012 The Magic Barrier 14
  15. 15. A User Study User study moviepilot 20 July 2012 The Magic Barrier 15
  16. 16. A User Study ~4 ratings steps Room for improvement ~1 rating steps Predictions vs Ratings above Ratings below Ratings user’s average user’s average Overall Opinions above Opinions below Magic Barrier user’s average user’s average 20 July 2012 The Magic Barrier 16
  17. 17. 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 20 July 2012 The Magic Barrier 17
  18. 18. 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 20 July 2012 The Magic Barrier 18
  19. 19. Questions?► Thank You for Listening! 20 July 2012 The Magic Barrier 19
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