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What recommenders recommend: an analysis of recommendation biases and possible countermeasures

Abstract

Most real-world recommender systems are deployed in a commercial context or designed to represent a value-adding service, e.g., on shopping or Social Web platforms, and typical success indicators for such systems include conversion rates, customer loyalty or sales numbers. In academic research, in contrast, the evaluation and comparison of different recommendation algorithms is mostly based on offline experimental designs and accuracy or rank measures which are used as proxies to assess an algorithm’s recommendation quality. In this paper, we show that popular recommendation techniques—despite often being similar when compared with the help of accuracy measures—can be quite different with respect to which items they recommend. We report the results of an in-depth analysis in which we compare several recommendations strategies from different perspectives, including accuracy, catalog coverage and their bias to recommend popular items. Our analyses reveal that some recent techniques that perform well with respect to accuracy measures focus their recommendations on a tiny fraction of the item spectrum or recommend mostly top sellers. We analyze the reasons for some of these biases in terms of algorithmic design and parameterization and show how the characteristics of the recommendations can be altered by hyperparameter tuning. Finally, we propose two novel algorithmic schemes to counter these popularity biases.

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Notes

  1. See (Jannach et al. 2012b) for an analysis of the literature on recommender systems, which covers over 300 research papers that were published in the five years after the Netflix Prize.

  2. In contrast to “per-user” diversity measures, this measure rather determines how many different items are recommended to all users.

  3. Table 1 shall be considered as an illustrative example. A systematic comparison of the recommendation lists for all users (Sect. 3.3) shows that the average overlap of the first 10 items for BPR and Funk-SVD is only at about 6 %. The overlap of the two matrix factorization (MF) methods Koren-MF and Funk-SVD is similarly small.

  4. To make our results reproducible, we publish the source code of our evaluation framework, see http://ls13-www.cs.tu-dortmund.de/homepage/recommender101/.

  5. http://www.ismll.uni-hildesheim.de/mymedialite/.

  6. We did not use the officially released MovieLens datasets because we were not able to retrieve content information for all movies. The largest MovieLens dataset we used in our experiments had about 1 million ratings. For this sample, we could, however, not run the simulation experiment using the User-kNN method within reasonable time. To make our research comparable to previous works, we report the other accuracy results for the official MovieLens1M release and a Netflix Prize sample in the Appendix.

  7. The best results are printed in bold face, in case the numbers were significantly different from all other results (p \(<\) 0.05 with Bonferroni correction). Throughout the paper we used paired two-tailed Student’s t-tests with a p \(=\) 0.05 significance level. In most tests, p \(<\) 0.01 holds but we report p \(<\) 0.05 for consistency and because this is the most common significance level in the literature.

  8. http://mymedialite.net/examples/item_recommendation_datasets.html.

  9. In addition, “external” and application-specific measures like sales numbers or box office figures could be used.

  10. Not shown in Fig. 3.

    Fig. 3
    figure 3

    Distribution of recommendations (\(=\) being in the top-10 of a recommendation list) for all items sorted by popularity (number of ratings) and grouped into 8 bins with 120 items each (MovieLens400k dataset)

  11. This concept of system-wide diversity must not be confused with user-perceived diversity or objective measures to determine the diversity of individual recommendation lists as discussed, e.g., by Pu et al. (2011) or Ziegler et al. (2005).

  12. This observation also applies for FM (MCMC).

  13. Compared to the sampling function shown in Fig. 12 for i, a corresponding function for j would have to be flipped horizontally.

  14. Note that even after a 10 % drop with respect to recall (All), BPR would still be the best-performing technique in our comparison in Sect. 3.

  15. Changing the rating prediction by small amounts is usually sufficient to push an item several places up in the recommendation lists.

  16. While the absolute values can vary on each run even when the same data is used, the existence of the biases is not affected by the random initialization.

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Appendix

Appendix

Gini index

The Gini index can be derived from the Lorenz curve, which is a cumulative distribution function as shown in Fig. 17. The diagonal corresponds to an even distribution. The higher the deviation of the Lorenz curve from the diagonal, the stronger is the unevenness of the distribution. The Gini index measures the strength of the inequality of a distribution and can be calculated as twice the difference between the area below the diagonal and the area below the curve (Zhang 2010).

Fig. 17
figure 17

An example of a Lorenz curve. The Gini index is proportional to the area between the diagonal and the curve

In our application setting, we calculate how often each item was included in a top-10 list, sort the items according to their popularity in increasing order and group them into n bins \(x_1, ..., x_n\), each containing 30 items.

For such a discrete distribution, the Gini index G can be computed using the formula

$$\begin{aligned} G = \frac{1}{n} \bigg (\frac{2q_n}{p_n} -1 \bigg ) -1 \end{aligned}$$
(9)

where \(p_n\) is the cumulative sum of the first n bins, i.e.,

$$\begin{aligned} p_n = \sum \limits _{i=1}^{n} x_{i} \end{aligned}$$
(10)

With \(q_n\), we weight each \(x_i\) according to its rank position, i.e.,

$$\begin{aligned} q_n = \sum \limits _{i=1}^{n} i \cdot x_{i} \end{aligned}$$
(11)

To normalize G, we divide it by \(G_{max} = 1-(1/n)\) to finally obtain \(G_{norm}\)

$$\begin{aligned} G_{norm} = \frac{n}{n-1} \cdot G \end{aligned}$$
(12)

Results for other datasets

Table 11 reports statistics for the datasets used in our evaluations. Tables 12, 13, 14, 15, 16, 17 and 18 show the corresponding results for the evaluated metrics (notation: P10T = Precision@10 (TS), R10A = Recall@10 (All), etc.). Furthermore AvgR denotes the average rating and AvgP the average popularity of the top-10 recommended items. Div is the diversity in terms of inverse ILS and NbRec the overall number of different items recommended by the algorithms. In each column, the highest value is highlighted in case the observed difference is statistically significant (p \(<\) 0.05) when compared to the other algorithms. Due to its high computational complexity, we did not test the user-KNN method for the 7 million Netflix and 1 million MovieLens dataset. The content-based algorithm could only be benchmarked on datasets for which content information was available.

Table 11 Statistics of the used datasets
Table 12 Results for the Netflix 7M dataset
Table 13 Results for the official MovieLens 1M dataset
Table 14 Results for the MovieLens 400k dataset
Table 15 Results for the Yahoo!Movies dataset
Table 16 Results for the BookCrossing dataset
Table 17 Results for the HRS dataset
Table 18 Results for the Mobile Games dataset

Artificial popularity on other datasets

Tables 19, 20 and 21 show the results of the artificial popularity bias experiment (see Sect. 4.2) for the three datasets MovieLens400k, MovieLens1M and Yahoo!Movies on the precision and recall strategies All (all items in the test set) and TS (only items with known ratings in the test set). The algorithm only recommends items that were rated by at least p users in the training set.

Table 19 Effects of an artificial popularity bias on Movielens400k
Table 20 Effects of an artificial popularity bias on MovieLens1M
Table 21 Effects of an artificial popularity bias on Yahoo!Movies

Detailed results for the PBA algorithm

Tables 22 and 23 show the detailed results for the PBA method when applied to the output of Koren-MF and FM (ALS) respectively. As before the table headers are shortened (P10T = Precision@10 (TS), etc.). Furthermore AvgP denotes the average popularity of the top-10 recommended items and NbRec the overall number of different recommendations. The column \(\lambda \) shows which value was used for the regularization variable to produce the results in the corresponding row. The first row (with the \(\lambda \) value left blank) contains the raw output of the underlying algorithm unaltered by the PBA method.

Table 22 Results for the PBA strategy when applied to the Koren-MF algorithm on the Movielens400k dataset
Table 23 Results for the PBA strategy when applied to the FM (ALS) algorithm on the Movielens400k dataset

Partial derivatives for the PBA algorithm

To minimize the optimization goal of the PBA algorithm (see Eq. 8) via a gradient descent strategy we have to calculate the partial derivatives of the minimization function to estimate the step width. The derivative for a specific \(x_{ui}\) can be calculated as follows:

$$\begin{aligned}&\frac{\partial }{\partial x_{ui}}\bigg ( \Big ( LB'_{pop}(u, I^{rec}_{u}, \hat{R}_u, \mathbf {x}_u) - UB_{pop}(u, I^{train}_{u}) \Big )^2 + \lambda \cdot \sum _{x_{ui} \in \mathbf {x}_u} \Big ( x_{ui}^2 \Big ) \bigg ) \nonumber \\&\quad = \frac{\partial }{\partial x_{ui}}\bigg ( \Big ( LB'_{pop}(u, I^{rec}_{u}, \hat{R}_u, \mathbf {x}_u) - UB_{pop}(u, I^{train}_{u}) \Big )^2 \bigg )\nonumber \\&\qquad + \frac{\partial }{\partial x_{ui}}\bigg ( \lambda \cdot \sum _{x_{ui} \in \mathbf {x}_u} \Big ( x_{ui}^2 \Big ) \bigg ) \end{aligned}$$
(13)

with the first part being reducible in the following way

$$\begin{aligned}&\frac{\partial }{\partial x_{ui}}\left( \left( LB'_{pop}(u, I^{rec}_{u}, \hat{R}_u, \mathbf {x}_u) - UB_{pop}(u, I^{train}_{u}) \right) ^2 \right) \nonumber \\&\quad =2\cdot \frac{ pop(i) }{ | I^{rec}_{u} | } \cdot \left( \frac{ \sum _{j \in I^{rec}_u} \left( \hat{r}_{uj} \cdot pop(j) \right) }{|I^{rec}_u|} - \frac{ \sum _{j \in I^{train}_u} \left( r_{uj} \cdot pop(j) \right) }{|I^{train}_u|}\right) \end{aligned}$$
(14)

and the latter part being reducible to

$$\begin{aligned} \frac{\partial }{\partial x_{ui}}\bigg ( \lambda \cdot \sum _{x_{ui} \in \mathbf {x}_u} \Big ( x_{ui}^2 \Big ) \bigg ) = 2\lambda x_{ui} \end{aligned}$$
(15)

Thus, the combined derivatives form the following assignment rule for each gradient descent step:

$$\begin{aligned}&x^n_{ui} \leftarrow x^{n-1}_{ui} - \gamma \Bigg ( \frac{ pop(i) }{ | I^{rec}_{u} | } \cdot \Bigg (\frac{ \sum _{j \in I^{rec}_u} \left( \hat{r}_{uj} \cdot pop(j) \right) }{|I^{rec}_u|} \nonumber \\&\quad - \frac{ \sum _{j \in I^{train}_u} \left( r_{uj} \cdot pop(j) \right) }{|I^{train}_u|}\Bigg ) + \lambda x_{ui} \Bigg ) \end{aligned}$$
(16)

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Jannach, D., Lerche, L., Kamehkhosh, I. et al. What recommenders recommend: an analysis of recommendation biases and possible countermeasures. User Model User-Adap Inter 25, 427–491 (2015). https://doi.org/10.1007/s11257-015-9165-3

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Keywords

  • Recommender systems
  • Bias
  • Evaluation