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. 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. Outline βΊ The Magic Barrier βΊ Empirical Risk Minimization βΊ Deriving the Magic Barrier βΊ User Study βΊ Conclusion 20 July 2012 The Magic Barrier 2
- 3. The Magic Barrier 20 July 2012 The Magic Barrier 3
- 4. The Magic Barrier βΊ No magic involved.... βΊ Coined by Herlocker et al. in 2004 ο§ β...an algorithm cannot be more accurate than the variance in a userβs ratings for the same item.β ο§ The maximum level of prediction that a recommender algorithm can attain. βΊ What does this mean? 20 July 2012 The Magic Barrier 4
- 5. The Magic Barrier 20 July 2012 The Magic Barrier 5
- 6. The Magic Barrier βΊ Even a βperfectβ recommender should not reach RMSE = 0 or Precision @ N = 1 βΊ Why? ο§ People are inconsistent and noisy in their ratings ο§ βperfectβ accuracy is not perfect βΊ So? ο§ Knowing the highest possible level of accuracy, we can stop optimizing our algorithms at βperfectβ (before overfitting) 20 July 2012 The Magic Barrier 6
- 7. The Magic Barrier So β 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. The Magic Barrier β User Inconsistencies Assumption: ο§ If a user were to re-rate all previously rated items, keeping in mind the inconsistency, the ratings would differ, i.e. π π’π = π π’π + π π’π ο§ where ο π π’π is the expected rating, and ο π π’π the rating error (has zero mean) 20 July 2012 The Magic Barrier 8
- 9. Empirical Risk Minimization βΊ β¦ 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. Empirical Risk Minimization βΊ We formulate our risk function as ο§ π π = π’,π,π π π’, π, π π π’, π β π 2 The prediction error The probability of user u rating item i with score r βΊ Keeping the assumption in mind, we formulate the risk for a true, unknown, rating function as the sum of the noise variance, i.e. ο§ π πβ = π’,π π π’, π π π π’π ο§ where π π π’π is the noise variance 20 July 2012 The Magic Barrier 10
- 11. Deriving the Magic Barrier βΊ We want to express the risk function in terms of a magic barrier for RMSE β we take the root of the risk function ο§ β¬ π°Γβ = π’,π π π’, π π π π’π ο§ RMSE=0 iff π π’π = 0 over all ratings users and items βΊ In terms of RMSE we can express this as ο§ πΈ π πππΈ π = β¬ π°Γβ + πΈ π > β¬ π°Γβ ο§ where πΈ π is the error 20 July 2012 The Magic Barrier 11
- 12. 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 π 1 π π’π = π π‘ π’π π π‘=1 c. Estimate the rating variance π 1 2 π π’π 2 = π π π’π β ππ‘ π’π π‘=1 2. Estimate the magic barrier by taking the average 1 β¬= π π’π 2 π³ π’π βπ³ 20 July 2012 The Magic Barrier 12
- 13. A real-world user study 20 July 2012 The Magic Barrier 13
- 14. A User Study βΊ We teamed up with moviepilot.de ο§ Germanyβs largest online movie recommendation community ο§ Ratings scale 1-10 stars (Netflix: 1-5 stars) βΊ Created a re-rating UI ο§ Users were asked to re-rate at least 20 movies ο§ 1 new rating (so-called opinions) per movie ο§ Collected data: ο§ 306 users ο§ 6,299 new opinions ο§ 2,329 movies 20 July 2012 The Magic Barrier 14
- 15. A User Study User study moviepilot 20 July 2012 The Magic Barrier 15
- 16. A User Study ~4 ratings steps Room for improvement ~1 rating steps Predictions vs Ratings above Ratings below Ratings userβs average userβs average Overall Opinions above Opinions below Magic Barrier userβs average userβs average 20 July 2012 The Magic Barrier 16
- 17. Conclusion βΊ We created a mathematical characterization of the magic barrier βΊ We performed a user study on a commercial movie recommendation website and estimated its magic barrier βΊ We concluded the commercial recommender engine still has room for improvement βΊ No magic 20 July 2012 The Magic Barrier 17
- 18. More? βΊ Estimating the Magic Barrier of Recommender Systems: A User Study ο§ SIGIR 2012 βΊ Magic Barrier explained ο§ http://irml.dailab.de βΊ Movie rating and explanation user study ο§ http://j.mp/ratingexplain βΊ Recommender Systems Wiki ο§ www.recsyswiki.com βΊ Recommender Systems Challenge ο§ www.recsyschallenge.com 20 July 2012 The Magic Barrier 18
- 19. Questions? βΊ Thank You for Listening! 20 July 2012 The Magic Barrier 19