Modeling Uncertainty Driven Curiosity for Social Recommendation

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1 Modeling Uncertainty Driven Curiosity for Social Recommendation Qiong Wu, Siyuan Liu and Chunyan Miao Joint NTU-UBC Research Centre of Excellence in Active Living for the Elderly Nanyang Technological University Singapore ABSTRACT Most of the current recommender systems focus on estimating user preferences. However, a person s interest in an item is not determined by his/her preference alone. Psychological research has shown that curiosity is a critical motivation relating to a person s interests and driving explorative behaviours. Motivated as above, we aim to model user curiosity in social recommendation context. In this work, we model uncertainty driven curiosity, wherein uncertainty is a well acknowledged factor that stimulates human curiosity. We model user uncertainty based on two well-known theories of uncertainty, i.e., Shannon entropy and Damster-Shafter theory. Then, we rank items by consolidating both user preference and user uncertainty using weighted Borda count. The proposed model is evaluated with two large-scale real world datasets, Douban and Flixster. The experimental results highlight that uncertainty driven curiosity has a positive impact on personalized ranking, by remarkably improving recommendation precision and diversity. KEYWORDS Uncertainty, Curiosity, Social recommendation, Precision, Diversity, 1 motivation in human beings that is closely related to interests and exploratory behaviours [26]. Instead of focusing on what a person generally prefers, curiosity seeks after novelty and pushes one s knowledge edge forward. Hence, we believe modeling user curiosity may bring interesting new insights into recommender systems. In order to model user curiosity, we adopt a psychologically inspired approach. Psychological research has pointed out that curiosity is often stimulated externally by stimuli exhibiting certain properties [4], including surprise, uncertainty, conflict, etc. In our previous work [25], we have modeled surprise driven curiosity in social recommendation, wherein a person s curiosity is elicited by his/her friends rating behaviours that are unexpected. Empirical studies in [25] have shown that by giving priority to those items that have a surprising effect in personalized ranking greatly enhances several aspects of the recommendation results, including precision, coverage and diversity. In this work, we continue with this line of research and focus on modeling uncertainty driven curiosity. In social recommendation context, user uncertainty is often aroused when friends offer greatly varied opinions about an item. An example is illustrated in Figure 1. Suppose Iron man and Deadpool are both superhero movies that Al- INTRODUCTION The constant flux of information in the online world has led to an age of information overload. Recommender systems have emerged as a useful tool for filtering through the vast amount of online information and detecting potentially interesting contents for their users. A general consensus among the current recommender systems is that user preferences reflect their interests. Accordingly, various Collaborative Filtering (CF) techniques have been proposed to discover items that best match users preferences through predicting ratings for items accurately [15, 24]. However, a person s impulse to watch a movie or purchase a product is not determined by his/her preference alone. For example, our curiosity may be very well stimulated when all our friends are talking about the same movie in a party, especially when they are holding varied opinions. Curiosity is a key intrinsic Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. WI 17, Leipzig, Germany 217 Copyright held by the owner/author(s). Publication rights licensed to ACM /17/8... $15. DOI: / Figure 1: A real world example of uncertainty driven curiosity ice holds similar preferences to. As such, traditional user preference centered recommendation techniques tend to rank the two movies at a similar position in the recommendation list for Alice. However,

2 WI 17, August 23-26, 217, Leipzig, Germany Wu et al. when we look at the opinions of Alice s friends, all her friends gave similar (i.e., mediocre) ratings to Iron man whereas they hold very diverse views for Deadpool (i.e., some give extremely high ratings while some give extremely low ratings). In this scenario, out of the two movies that Alice shows similar preferences, Deadpool tends to be more curiosity-stimulating as it induces a feeling of uncertainty due to the high disputation among her friends. Ideally, Deadpool should be ranked higher than Iron man in the recommendation list for Alice. Motivated as above, we aim to explore the impact of uncertainty driven curiosity on social recommendation. To model user uncertainty, we adopt two well-known theories of uncertainty, including Shannon entropy [3] and Damster-Shafer theory [11]. After that, we adopt weighted Borda count [23] to consolidate both user preference and user uncertainty to produce personalized ranking. The impact of considering user uncertainty for social recommendation is evaluated using two large-scale real world datasets, i.e., Douban [19] and Flixster [1], on personalized ranking. The experimental results highlight that user uncertainty has a strong positive impact on improving recommendation precision and diversity. The rest of this paper is organized as follows. Section 2 reviews the related works to this research, including user preference centered recommendation techniques, personalized ranking and computational curiosity. Section 3 elaborates on the proposed uncertainty driven curiosity method for recommendation. Section 4 presents the experimental results over two large scale real world datasets. Conclusion and future work are outlined in Section 5. 2 RELATED WORKS In this section, we discuss the background and related works for this research. 2.1 User Preference Centered Recommendation Most of the current recommender systems focus on estimating users preferences based on the existing user-item rating information [15, 24]. A user s preference for an item is usually estimated by its predicted rating. Popular techniques for rating prediction include neighborhood-based Collaborative Filtering (CF) [8] and Matrix Factorization (MF) [13, 18]. A neighborhood-based CF technique can be user-based [8] or item-based [16], depending on whether the similarity is calculated between users or items. MF has recently gained popularity due to its high recommendation accuracy and efficiency in dealing with large-scale user-item rating matrices. In this work, we adopt MF for estimating users preferences. The basic MF model maps both users and items to a joint latent factor space of dimensionality d, such that user-item interactions are modeled as inner products in that space. Accordingly, each user u is associated with a vector p u R d, where the elements in p u measure the user s preferences with respect to d latent factors. Each item i is associated with a vector q i R d, where the elements in q i measure the item s importance weights for the d latent factors. The preference of target user u towards an unexperienced item i is measured by the predicted rating ˆR(u, i), which is obtained by: ˆR(u, i) = p T u q i. (1) The values in p u and q i are initially assigned arbitrarily and then iteratively updated by a simple gradient descent technique. For each observed rating R(u, i), the latent variable vectors p u and q i are updated as follows: where p u p u + γ( ui q i λ p u), (2) q i q i + γ( ui p u λ q i), (3) ui = R(u, i) p T u q i. (4) Here, γ is the learning rate and λ is a regularization parameter to minimize overfitting. The algorithm iterates until an accuracy threshold is reached. 2.2 Personalized Ranking Traditional recommender systems focus on optimizing towards predicting user preferences over individual items. The typical metrics adopted by user preference centered techniques are accuracy measures for rating prediction, such as Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) [17]. However, in recent years, it has been shown that it is more meaningful to evaluate user s interests over a list of items. Therefore, a growing interest has been shown in studying different aspects of personalized ranking, such as precision, coverage and diversity. Zhao et al. [31] argue that a historical rating for an item can be treated as evidence showing that the user indeed got interested to explore the item. Therefore, precision is often used to evaluate how effective a recommender system can detect items that users will explore, which is defined as the percentage of items in the recommendation lists that have observed ratings in the testing set. Herlocker et al. [9] point out that algorithms striving for high accuracy often provide recommendations with high quality, but only for a small portion of items. To address this issue, techniques are proposed to improve recommendation coverage, which refers to the percentage of items for which a recommender system is able to generate recommendations [7, 14]. In [2], it is pointed out that recommender systems should provide users with highly idiosyncratic and personalized items. Diversity is proposed to measure such properties of recommender systems, which is defined by the dissimilarity between all pairs of recommended items. In this work, user uncertainty is modeled in recommender systems to enhance different aspects of personalized ranking, by giving priorities to the items that induce user s feeling of uncertainty. 2.3 Computational Curiosity In psychology, curiosity is commonly recognized as a critical motivation that is associated with exploratory behaviors such as exploration, investigation and learning. It is an intrinsic drive towards novelty and interestingness [26]. According to Kashdan [12], curiosity benefits human beings at two levels: at the individual level, curiosity drives personal growth, as an innate love for learning; and at the social level, curiosity promotes interpersonal relationships, through infusing energy and passion into social interactions. In recent years, researchers have shown a growing interest in modeling a curious mechanism similar to human beings in artificial beings, in order to bring about the curious impact on their performances [26]. Schmidhumber [22] models artificial curiosity

3 Modeling Uncertainty Driven Curiosity for Social Recommendation WI 17, August 23-26, 217, Leipzig, Germany in the reinforcement learning framework to speed up agent learning and to build unsupervised developmental robotics. Oudeyer et al. [2] develop a curiosity mechanism for robots, which acts as intrinsic motivation to motivate robots to explore into regions with new knowledge. Saunders and Gero [21] develop a curious design agent that can arrange art exhibits to elicit the curiosity of their viewers and provide them with an aesthetically pleasing experience. Curiosity has also been instilled into virtual learning companions to enhance their believability [27, 29, 3] or realized in learning machines to improve their learning capabilities [28]. To the best of our knowledge, we are the first group to study curiosity in the context of social recommendation. We have explored surprise driven curiosity in our earlier work [25] and empirical studies have shown that curiosity helps to recommend movies that users are interested in and motivated to watch. In this work, we study another dimension of curiosity-stimulating factors, i.e., uncertainty, and explore its impact on personalized ranking. 3 THE PROPOSED METHOD An overview of the proposed recommendation model is given in Figure 2. This model takes two inputs: users historical ratings and their friend relationships. User preference is estimated based on the historical ratings and user uncertainty is evaluated using both the historical ratings and the friend relationships. After that, weighted Borda count is applied to consolidate user preference with user uncertainty to generate the personalized ranking of items. It should be noted that in our model, user preference can be estimated by any existing user preference centered recommendation techniques, such as neighborhood-based CF [8] or MF [13, 18]. Therefore, in the rest of this section, we will elaborate on the other two major components of the proposed model, i.e., uncertainty evaluation and weighted Borda count. 3.1 Modeling User Uncertainty In social recommendation context, a user s feeling of uncertainty is often elicited by the variety of ratings given by his/her friends. This kind of uncertainty can be modeled by Shannon entropy [3]. Specifically, suppose a user u has a finite set of friends f(u), and a discrete rating scale of r levels is allowed in the rating system. Let c u j (i) (j [1, 2,, r]) represent the count of ratings given to an item i by u s friends on the jth level of the rating scale. The probability of u expecting a rating of j from his/her friends for item i is given by: c u j (i) p(u, i, j) = r. (5) j=1 cu j (i) According to Shannon entropy, u s feeling of uncertainty for item i due to the diverse ratings provided by u s friends is given by: r SE(u, i) = p(u, i, j) log p(u, i, j). (6) j=1 A higher value of SE(u, i) indicates that u is more uncertain about i. Besides the variety of ratings given by u s friends, u s interest for an item i is also influenced by the total number of ratings provided by u s friends. Intuitively, when the rating varieties of two movies are the same, the user will be more attracted to the one that is more popular among his/her friends. For example, a Figure 2: Overview of the proposed recommendation model movie that aroused disputation among a large number of friends will be more curiosity-eliciting than the one that aroused disputation between only two friends. Comparing with the former case, the latter case represents a situation that the uncertainty about the rating distribution of an item is high due to the lack of evidence. Such kind of uncertainty can be modeled by the Dempster-Shafer theory and Subjective Logic [11]. Accordingly, the uncertainty of u for i s rating distribution is given by: r DS(u, i) =. (7) (i) + r r j=1 cu j A lower value of DS(u, i) indicates a higher certainty about the distribution of ratings given by u s friends for i, and one step further, it demonstrates that more evidence is available for supporting the great variety of opinions. Hence, u s feeling of uncertainty elicited by the variety of ratings should be weighted by an inverse value of DS(u, i), given by: UN(u, i) = (1 DS(u, i)) SE(u, i). (8) Therefore, UN(u, i) represents u s interests for item i caused by the feeling of uncertainty due to friends rating information. 3.2 Combining User Preference and Uncertainty A curiosity-stimulating item may not catch a user s attention unless the user is in favor of that item to some extent. For example, a user who is scared to watch horror movies may be indifferent to a horror movie discussed among his/her friends. Hence, it is necessary to generate a recommendation list that consolidates both user preference and user uncertainty.

4 WI 17, August 23-26, 217, Leipzig, Germany Wu et al. To reflect both user preference and user uncertainty in the consolidated recommendation lists, we assume two voters, one ranking items solely based on user preference and the other ranking items solely based on user uncertainty. Then, we adopt a weighted Borda count [23], a classic election method, to combine the rankings provided by the two voters. Specifically, suppose there are n items that have not been experienced by the target user u. L p(u) is the ranking list of the n items provided by the first voter, based on the descending order of predicted ratings generated by a user preference centered technique, e.g., neighborhood-based CF [8] or MF [13, 18]. L un(u) is the ranking list of the n items provided by the second voter, based on the descending order of uncertainty generated using the proposed method. For an item i, rank(l p(u), i) and rank(l un(u), i) represent the ranking position of i in L p(u) and L un(u) respectively. Borda count assigns two scores to i based on its ranking position in the two lists: Score p(u, i) = n rank(l p(u), i) + 1; (9) Score un(u, i) = n rank(l un(u), i) + 1, where Score p(u, i) is obtained using L p(u) and Score un(u, i) is obtained using L un(u). With this scheme, the item ranked first in each list will receive a score of n and the item ranked last in each list will receive a score of 1. A weighted sum of Score p(u, i) and Score un(u, i) gives the combined opinion from both user preference and user uncertainty: Score(u, i) = (1 ) Score p(u, i) + Score un(u, i), (1) where is the weight for balancing between user preference and user uncertainty. A high value of indicates more consideration of user uncertainty for recommendation. Finally, items are reranked based on a descending order of Score(u, i). The algorithm for the proposed recommender system is shown in Algorithm 1. Line 2 is to calculate u s predicted rating for each item i using Matrix Factorization (MF) as a reflection of u s preference for i. Lines 3-8 are to calculate the uncertainty for each item i in the system. In particular, line 4 is to find the number of u s friends who provided ratings for i with rating level j, where F (u) is the set of u s friends. Then the uncertainty for i is calculated following the way as presented in Section 1. Lines 9-1 are to sort the set of user preferences and user uncertainty in descending order, respectively. Lines are to combine user preference and uncertainty using Borda count following the approach as presented in Section 3.2. Finally, user u will get a top-n recommendation list L u. 4 EXPERIMENTS In this section, we evaluate the proposed method by comparing its performance with other state-of-the-art methods. 4.1 Datasets We use two publicly available large-scale datasets: Douban [19] and Flixster [1] to study the performance of the proposed recommendation model. Both datasets contain user-item ratings and the social network connecting different users. We preprocessed the datasets by removing the large portion of users who have social relations but no expressed ratings because our approach is interested in friends rating behaviors. The statistics of the two datasets are summarized in Table Procedure: Recommend(R, F, r,, u) Input : R, user-item ratings; F, user-user friendship; r, the number of rating levels;, weight combining uncertainty and preference; u, the target user; Output : L u, recommendation list for u; ˆR = MF (R); foreach item i do foreach rating level j r do c u j (i) = {(v, i) R(v, i) == j and v F (u)} ; p(u, i, j) = SE(u, i) = 6 r DS(u, i) = cu j (i) rj=1 c u j (i) ; j=1 r rj=1 c u ; j (i)+r p(u, i, j) log p(u, i, j); UN(u, i) = (1 DS(u, i)) SE(u, i); L p(u) = sort({ ˆR(u, i) all items i}); L un(u) = sort({un(u, i) all items i}); foreach item i do Score p(u, i) = n rank(l p(u), i) + 1; Score un(u, i) = n rank(l un(u), i) + 1; Score(u, i) = (1 ) Score p(u, i)+ Score un(u, i); L u = top-n(sort({score(u, i) all items i})); Algorithm 1: Algorithm for Recommendation. 4.2 Metrics Table 1: Statistics of the Datasets. Douban Flixster # users 129,49 1,49,58 # movies 58,541 66,726 # ratings 16,83,839 8,196,77 # friend links 1,692,952 7,58,819 # ratings per user # ratings per movie # friend per user To evaluate the ability of the proposed method on recommending interesting items, we focus on studying the properties of the personalized ranking of recommended items. More specifically, we adopt precision, coverage, and diversity for evaluation. Precision evaluates the ability of a recommender system to recommend items that users will explore, which is defined as the percentage of top-n items that have observed rating in the testing set [5]. Here, a historical rating for an item can be treated as an evidence showing that the user indeed got interested to explore the item [31]. A higher precision indicates a higher chance that the user will explore the recommended items and finally give ratings for them. Therefore, precision can reflect to what extent the recommended items interest

5 Modeling Uncertainty Driven Curiosity for Social Recommendation WI 17, August 23-26, 217, Leipzig, Germany the user. Precision of a recommendation list is given by P (L(u)) = {i i L(u) R(u, i) RT (u)} L(u) 1% (11) where L(u) is the set of items recommended to a user u and R T (u) is the set of ratings given by u in the testing set. is defined as the percentage of items in the database that is covered by the top-n recommendations for all the target users. It is a system-level measure that reflects the ability of a recommender system on recommending long-tail items [9]. is also referred to as the aggregate diversity [1], given by: C = u U L(u) 1% (12) T otal where is the operator that takes the union of sets, returns the cardinality of a set and T otal is the total number of items in the recommender system. Diversity is defined as the average dissimilarity between all pairs of the top-n items [6]. Let U(i, j) represent the set of users who have rated both items i and j. The dissimilarity between two items i and j is determined by the dissimilarity between ratings given to them by the set of users who have rated both, given by: D(i, j) = u U(i,j) ( abs(r(u,i) R(u,j)) R m ), (13) U(i, j) where R m is the maximum rating scale difference. Diversity reflects the ability of the recommender system on recommending idiosyncratic items. 4.3 Methods For the prediction of user preferences, we adopt MF, due to its high recommendation accuracy and its efficiency when dealing with largescale user-item rating matrices [18]. Accordingly, we compare our method with the baseline MF method [13], three ranking methods for improving recommendation diversity [2] and two variations of the surprise driven curiosity recommendation [25]: MF: the baseline MF method. PopR: the item popularity based ranking, which ranks items whose ratings are predicted above the ranking threshold T H based on their popularity. AbsLikeR: the item absolute likeability based ranking, which ranks items whose ratings are predicted above the ranking threshold T H based on how many users liked them (i.e., rated the item above T H). RelLikeR: the item relative likeability based ranking, which ranks items whose ratings are predicted above the ranking threshold T H based on the percentage of the users who liked them (i.e., rated the item above T H). SC Max: The surprise driven curiosity recommendation model with bold strategy for curiosity evaluation. SC Ave: The surprise driven curiosity recommendation model with average strategy for curiosity evaluation. UC: the proposed uncertainty driven curiosity recommendation model. For the MF parameters, we set the learning rate γ to.1, the regularization parameter λ to.2, and the latent factor dimension d to 1. 6% of the data are randomly selected for training and the rest 4% of data are used for testing. For the ranking methods, a higher value of the ranking threshold T H will make the recommendation results more similar to the baseline MF. In order to allow the different ranking criteria to make effects and also to ensure that the recommended items are generally preferred by the target users, we set the ranking threshold T H to 4.5. Note that we do not report the results of conservative strategy for surprise driven curiosity recommendation because the results obtained by the conservative strategy is very similar to the average strategy as is shown in [25]. All the results are reported based on top-1 recommendations. The selection strategy for the weight of Borda count will be discussed in the following subsection. 4.4 Analysis of In this experiment, we empirically study the impact of the weight for Borda count on the performance of the proposed method UC. balances between user preferences and user uncertainty when making decisions. Intuitively, a higher value of indicates that the proposed recommender system considers more of user uncertainty for recommendation and thus incorporates more curiosity effects into the recommendation results. On the other hand, a lower value of leads to a more similar list to the baseline method MF that uses only the estimated preference for ranking. In order to find the best performing, we conduct grid search from to 1 with an interval of.1 for both Douban and Flixster datasets. The experimental results are shown in Figure 3. It can be observed from Figure 3 that the best performing differs for different metrics. Taking the Douban dataset for example (Figure 3(a)(b)(c)), the best performing for precision is.9, for coverage is.6 and for diversity is 1. This means that the impacts of uncertainty on the three metrics are not equally strong. For douban dataset, uncertainty has a strong impact on diversity as its value increases monotonously when increases. In contrast, the trends for precision and coverage first climb upwards and then go downwards, which means that the best performing values could only be achieved when there is a balanced consideration between user preferences and user uncertainty. Based on the above observations, in the following experiments, we report the results by the best performing. 4.5 Performance Comparison In this experiment, we compare the performance of the proposed uncertainty driven curiosity recommendation model UC with the state-of-the-art methods. The results are shown in Table 2. The best performing values for each metric are highlighted in bold. From Table 2, it can be observed that the proposed method performs greatly better than all the state-of-the-art methods in terms of precision and diversity. Specifically, for Douban dataset, UC achieves the precision of.82, which is at least two magnitude levels higher than that of the baseline MF and ranking methods PopR, AbsLikeR and RelLikeR. The baseline method and the ranking methods achieve rather low values of precision, which means that they could rarely recommend items that have observed ratings in the testing set. The observed ratings in the testing set, no matter low or high, are evidence showing that the user indeed got interested to watch those movies. Hence, the values of precision demonstrate that the proposed method is much more efficient in predicting items

6 WI 17, August 23-26, 217, Leipzig, Germany Wu et al Precision Diversity (a) Douban Precision (b) Douban (c) Douban Diversity Precision Diversity (d) Flixster Precision (e) Flixster (f) Flixster Diversity Figure 3: Impact of on the performance of UC Table 2: Performance comparison between the state-of-the-art methods and the proposed method. Dataset Douban Flixster Metrics Baseline Ranking Methods Surprise Uncertainty MF PopR AbsLikeR RelLikeR SC Max SC Ave UC Precision 6.491e e e e Diversity e Precision Diversity that users may have the intention to watch. Similarly, UC achieves the diversity of.222, which is also remarkably higher than the baseline MF and ranking methods PopR, AbsLikeR and RelLikeR. It demonstrates that UC is much more efficient in recommending idiosyncratic items. UC also beats the surprise driven curiosity recommendation methods SC Max and SC Ave in terms of precision and diversity, which shows that uncertainty has a stronger impact on these two aspects than surprise does. In comparison, UC shows a less strong impact on coverage and SC Ave achieves the best performing coverage for both Douban and Flixster datasets. It is an interesting phenomena that uncertainty beats surprise in terms of diversity but surprise beats uncertainty in terms of coverage, wherein coverage is also named aggregated diversity in several works [2]. Diversity evaluates the dissimilarity between items in each recommendation lists. In contrast, coverage evaluates the dissimilarity between recommendation lists. It means that uncertainty instills high dissimilarity to individual items of each recommendation list but tends to recommend similar lists to users. An explanation for this phenomenon is that uncertainty is calculated based on the opinions of a group of people (within a friend circle), and these opinion patterns are similar between groups (or friend circles). It means that an item causing high uncertainty in

7 Modeling Uncertainty Driven Curiosity for Social Recommendation WI 17, August 23-26, 217, Leipzig, Germany MF PopR AbsLikeR RelLikeR SSAve SSMax UC Precision Diversity Precision [1,2] [21,4] [41,6] [61,8] [81,1] 1+ (a) Douban Precision [1,2] [21,4] [41,6] [61,8] [81,1] 1+ (d) Flixster Precision.1 [1,2] [21,4] [41,6] [61,8] [81,1] (b) Douban.1 [1,2] [21,4] [41,6] [61,8] [81,1] 1+ (e) Flixster Diversity.25.5 [1,2] [21,4] [41,6] [61,8] [81,1] (c) Douban Diversity [1,2] [21,4] [41,6] [61,8] [81,1] 1+ (f) Flixster Diversity Figure 4: Impact of friend degree on algorithm performance one group also causes high uncertainty in other groups, and therefore is recommended repetitively to many users in these groups, which leads to a comparatively low coverage value. 4.6 Impact of Friend As the proposed method is closely related to the behavior of the target user s friends, it is worth analyzing the impact of the number of friends, i.e., friend degree, on the recommendation results. In our experiments, we separate users into 6 degree groups: the first group consists of users with degrees from 1 to 2, the second group from 21 to 4, the third group from 41 to 6, the fourth group from 61 to 8, the fifth group from 81 to 1, and the sixth group above 1. We do not continue dividing users with degree above 1 into groups because users with degree above 12 represent less than 1% of the total number of users in the dataset. Since the number of users decreases in larger degree groups, to make the comparisons fair, we randomly select 1 users from each degree group for reporting the coverage value. The experimental results are shown in Figure 4. It can be observed from Figure 4(a)(d) that the proposed method UC consistently outperform all the other methods for precision across all the degree groups for both Douban and Flixster datasets. It can be clearly seen from Figure 4(d) that the ranking methods even perform worse than the baseline method for precision in Flixster dataset. It confirms the superior performance of the proposed method on recommending interesting items that users may want to explore and finally give ratings to. Figure 4(b)(e) show that the proposed method consistently outperform all the other methods for diversity across all the degree groups for the two datasets. By comparing Figure 4(b) and Figure 4(e), it can also be seen that the performance of ranking methods on diversity depends on the datasets being evaluated. For example, the AbsLikeR and RelLikeR perform better than the baseline method in terms of diversity in Douban dataset but perform worse in Flixster dataset. The experimental results demonstrate that the proposed method show overall robust performance for precision and diversity in different degree groups. However, from Figure 4(c)(f), it can be shown that surprise driven curiosity methods SC Max and SC Ave show a comparatively superior performance in terms of coverage. This result matches with the result interpretation of Table 2. Let us analyze the impact of friend degree. It can be observed from Figure 4(a)(c)(d)(f) that there is a general trend for UC: a larger degree tends to achieve a higher value for precision and diversity. However, there is no such a trend observed for the baseline method or the ranking methods. The performance of the baseline method and the ranking methods stays similar for all the degree groups. This is due to the fact that the baseline method and the ranking methods do not explicitly consider social information during recommendation. On the contrary, from Figure 4(b)(e), it can be observed that the

8 WI 17, August 23-26, 217, Leipzig, Germany Wu et al. coverage value tends to decline when degree increases. This empirically shows that when friend circle is large, those highly disputable movies (with high user uncertainty) tend to be repetitively recommended to a large proportion of users who are mutually friends, which leads to decreasing coverage values. The experimental results empirically show that the proposed approach remarkably enhance recommendation precision and diversity. From an intuitive point of view, the proposed approach can achieve such improvements because it not only relies on the similarity information as in traditional recommendation techniques but also considers the uncertainty information for recommendation. The incorporation of such uncertainty information makes the items that may not best match the user s usual preferences but rather elicit the user s interest be ranked at top. Therefore, the recommendation precision and diversity can be remarkably improved. 5 CONCLUSION AND FUTURE WORK In this paper, we pointed out that user preference is not the single factor that influences a person s interests and highlighted curiosity as another important factor. Accordingly, we model user uncertainty, which is one of the key stimulating factors for curiosity, in social recommendation context. We modeled user uncertainty elicited by friends rating information using Shannon entropy and Damster- Shafer theory. Weighted Borda count was employed to consolidate the rankings produced by user preference and user uncertainty respectively. The performance of the proposed method was evaluated using two large-scale real world datasets, i.e., Douban and Flixster, on properties of personalized ranking. The experimental results demonstrated that the consideration of user uncertainty largely improves recommendation precision and diversity. From the experimental results, we observed that uncertainty driven curiosity has superior performance in terms of precision and diversity, whereas surprise driven curiosity has superior performance in terms of coverage. For future work, we will study how surprise and uncertainty could be combined together so as to enhance the performance in all the three aspects. Moreover, according to Berlyne s stimulus selection theory [4], there are other factors besides uncertainty and surprise that also stimulate curiosity, including but are not limited to novelty, conflict, etc. In the future, we will explore those interesting curiosity-stimulating factors in recommender systems. 6 ACKNOWLEDGMENTS This research is supported by the National Research Foundation, Prime Ministers Office, Singapore under its IDM Futures Funding Initiative. This research is also partially supported by the NTU- PKU Joint Research Institute, a collaboration between Nanyang Technological University and Peking University that is sponsored by a donation from the Ng Teng Fong Charitable Foundation. REFERENCES [1] Panagiotis Adamopoulos and Alexander Tuzhilin On unexpectedness in recommender systems: Or how to expect the unexpected. RecSys 11 (211), [2] Gediminas Adomavicius and YoungOk Kwon Improving aggregate recommendation diversity using ranking-based techniques. IEEE Transactions on Knowledge and Data Engineering 24, 5 (212), [3] David R Anderson. 28. Information Theory and Entropy. Springer New York. [4] Daniel E. Berlyne Conflict, arousal, and curiosity. McGraw-Hill Book Company. [5] Jesús Bobadilla, Fernando Ortega, Antonio Hernando, and Abraham Gutiérrez Recommender systems survey. Knowledge-Based Systems 46 (213), [6] Keith Bradley and Barry Smyth. 21. Improving recommendation diversity. In Proceedings of International Conference on Artificial Intelligence and Computer Science (21), [7] Mouzhi Ge, Carla Delgado-Battenfeld, and Dietmar Jannach. 21. Beyond accuracy: Evaluating recommender systems by coverage and serendipity. RecSys (21), [8] Jonathan L. Herlocker, Joseph A. Konstan, Al Borchers, and John Riedl An algorithmic framework for performing collaborative filtering. SIGIR (1999), [9] Jonathan L. Herlocker, Joseph A. Konstan, Loren G. Terveen, and John T. Riedl. 24. Evaluating collaborative filtering recommender systems. ACM Transactions on Information Systems 22, 1 (24), [1] Mohsen Jamali and Martin Ester A transitivity aware matrix factorization model for recommendation in social networks. IJCAI (211), [11] Audun Jøsang. 21. A logic for uncertain probabilities. Fuzziness and Knowledge-Based Systems 9, 3 (21), [12] Todd Kashdan. 29. Curious?: Discover the missing ingredient to a fulfilling life. HarperCollins New York. [13] Yehuda Koren, Robert Bell, and Chris Volinsky. 29. Matrix factorization techniques for recommender systems. Computer 8 (29), [14] George Lekakos and Petros Caravelas. 28. A hybrid approach for movie recommendation. Multimedia Tools and Applications 36, 1-2 (28), [15] Huayu Li, Richang Hong, Defu Lian, Zhiang Wu, Meng Wang, and Yong Ge A Relaxed Ranking-Based Factor Model for Recommender System from Implicit Feedback. IJCAI (216), 1 7. [16] Ming Li, Benjamin Dias, Wael El-Deredy, and Paulo J.G. Lisboa. 27. A probabilistic model for item-based recommender systems. In Proceedings of The ACM Recommender Systems Conference (27), [17] Haifeng Liu, Zheng Hu, Ahmad Mian, Hui Tian, and Xuzhen Zhu A new user similarity model to improve the accuracy of collaborative filtering. Knowledge-Based Systems 56 (214), [18] Xin Luo, Yunni Xia, and Qingsheng Zhu Incremental collaborative filtering recommender based on regularized matrix factorization. Knowledge-Based Systems 27 (212), [19] Hao Ma, Dengyong Zhou, Chao Liu, Michael R. Lyu, and Irwin King Recommender systems with social regularization. WSDM (211), [2] Perre-Yves Oudeyer, Frederic Kaplan, and Verena Hafner. 27. Intrinsic motivation systems for autonomous mental development. IEEE Trans. on Evolutionary Computation 11, 2 (27), [21] R Saunders and John S Gero. 21. A curious design agent. In Proceedings of the Conference on Computer Aided Architectural Design Research in Aisa 1 (21), [22] Jrgen Schmidhuber. 26. Developmental robotics, optimal artificial curiosity, creativity, music, and the fine arts. Connection Science 18, 2 (26), [23] Merijn Van Erp and Lambert Schomaker. 2. Variants of the borda count method for combining ranked classifier hypotheses. In proceedings of International Workshop on Frontiers in Handwriting Recognition (2). [24] Xin Wang, Congfu Xu, Yunhui Guo, and Hui Qian Constrained Preference Embedding for Item Recommendation. IJCAI (216), 1 7. [25] Qiong Wu, Siyuan Liu, Chunyan Miao, Yuan Liu, and Cyril Leung A social curiosity inspired recommendation model to improve precision, coverage and diversity. In Proceedings of IEEE/ACM/WIC International Conference on Web Intelligence (216), [26] Qiong Wu and Chunyan Miao Curiosity: From psychology to computation. Comput. Surveys 46, 2 (213), 18. [27] Qiong Wu and Chunyan Miao Modeling curiosity-related emotions for virtual peer learners. Computational Intelligence Magazine 8, 2 (213), [28] Qiong Wu and Chunyan Miao C-ELM: A Curious Extreme Learning Machine for Classification Problems. In Proceedings of The International Conference on Extreme Learning Machine (215), [29] Qiong Wu, Chunyan Miao, and Zhiqi Shen A curious learning companion in virtual learning environment. In Proceedings of IEEE International Conference on Fuzzy Systems (212), 1 8. [3] Qiong Wu, Chunyan Miao, Xuehong Tao, and MG Helander A curious companion for elderly gamers. In Proceedings of Southeast Asian Network of Ergonomics Societies Conference (SEANES) (212), 1 5. [31] Xiangyu Zhao, Zhendong Niu, and Wei Chen Interest before liking: Twostep recommendation approaches. Knowledge-Based Systems 48 (213),