Federated Recommender Systems with Learning to Rank

Abstract

Recommendation services are extensively adopted in several user-centered applications as a tool to alleviate the information overload problem and help users in orienteering in a vast space of possible choices. In such scenarios, data ownership is a crucial concern since users may not be willing to share their sensitive preferences (e.g., visited locations, read books, bought items) with a central server. Unfortunately, data harvesting and collection is at the basis of modern, state-of-the-art approaches to recommendation. To address this issue, we extend Federated Pair-wise Learning (FPL), an architecture in which users collaborate in training a central factorization model while controlling the amount of sensitive data leaving their devices. The proposed approach implements pair-wise learning-to-rank optimization by following the Federated Learning principles, conceived originally to mitigate the privacy risks of traditional machine learning.

Keywords

• eol>Federated Learning
• Recommender Systems
• Information Retrieval
• Learning to Rank

1. Introduction

Collaborative filtering (CF) models have been mainstream research in the recommender system (RS) community over the last two decades thanks to their performance accuracy [ 1, 2 ]. Among them, a prominent class uses the matrix factorization (MF) approach as the inference model. The MF model’s main aim is to uncover user and item latent representations whose linear interaction explains observed feedback. To date, the majority of existing MF models are trained in a centralized fashion causing several concerns about the privacy of user data.

The consequent data scarcity dilemma can thereby jeopardize the training of MF models. Training high-quality MF models strongly relies on suficient in-domain interaction data to ensure that enough co-occurrence information exists to shape similar behavioral/preference patterns in a user community. Although cross-domain recommendation approaches allow combating the issue of data scarcity, their applicability largely depends upon the availability of data providers that can collect/supply cross-domain in their platform (e.g., Amazon). However, these approaches remain out of focus in this work. In recent years, federated learning (FL) was proposed by Google as a mean to ofer a privacy-by-design solution [ 3, 4, 5 ] for machine-learned models. Federated learning aims to meet ML privacy shortcomings by horizontally distributing the model’s training over user devices; thus, clients exploit private data without sharing them [ 5 ]. Despite its original formulation, the FL concept is extended to a more comprehensive idea of privacy-preserving, decentralized, collaborative ML techniques [ 6 ] where diferent data partitions share the same feature space (horizontal federation) or not (vertical federation). Weiss et al. [ 7 ] state that privacy can be preserved by limiting data collection, which is one of the main privacy concerns [ 8 ]. Indeed, the accuracy of RS based on the CF paradigm is strictly dependent on the amount of user preferences available.

Our idea is to put users in control of their sensitive data by allowing them to choose the amount of information to share with the server. Hence, if data collection from the server side is reduced, other threats related to retention, sales, and unauthorized data browsing are limited. The proposed system extends FPL [ 9, 10 ] (short for Federated Pair-wise Learning), is a federated factorization model for collaborative recommendation1. It extends state-of-the-art factorization approaches to build a RS that puts users in control of their sensitive data. Users participating in the federation process can decide if and to which extent they are willing to disclose their sensitive private data (i.e., what they liked/consumed). FPL mainly leverages not-sensitive information (e.g., places the user has not visited) – which can be large and non-sensitive – to reach a competitive accuracy and, at the same time, respect a satisfactory balance between accuracy and privacy. We have carried out extensive experiments on real-world datasets [ 11 ] in the Point of Interest (PoI) domain by considering the accuracy of recommendation and diversity metrics. The experimental evaluation shows that FPL can provide high-quality recommendations, putting the user in control of the amount of sensitive data to share.

2. Approach

In this section, after a brief introduction of background technologies, we extend FPL [ 9, 10 ] (depicted in Fig. 1). To the best of our knowledge, FPL is the first attempt to put pair-wise optimization in federated recommender systems and give the users the possibility to select the trade-of between data disclosure and the recommendation utility.

2.1. Background Technologies

Federated Learning. Federated learning (FL) is a paradigm initially envisioned by Google [ 3, 12, 5 ] to train a machine-learning model from data distributed among a loose federation of users’ devices (e.g., personal mobile phones). The rationale is to face the increasing issues of ownership and locality of data to mitigate the privacy risks (and leaks) resulting from centralized machine learning [ 13, 14 ]. In particular, given Θ denoting the parameters of a machine learning model, we consider a learning scenario where the objective is to minimize a generic loss function (Θ). FL is a learning paradigm in which the users ∈ of a federation collaborate to solve the learning problem under the coordination of a central server without sharing or exchanging 1A public implementation of FPL is available at https://github.com/sisinflab/FedBPR/. their raw data with . From an algorithmic point of view, we start with sharing Θ with the federation of devices. Then, specific methods solve a local optimization problem on the single device, i.e., using its data, and exploiting Θ. Afterwards, the client shares the parameters of its local model with . The parameters provided by the clients are used to update Θ, which is sent back to the devices in a new iteration step.

Factorization Models and Pair-Wise Recommendation A recommendation problem

over a set of users and a set of items ℐ is defined as the activity of finding for each user ∈ an item ∈ ℐ that maximizes a utility function : × ℐ → R. In this context, X ∈ R||×|ℐ| is the user-item matrix containing for each an explicit or implicit feedback (e.g., rating or check-in, respectively) of user ∈ for item ∈ ℐ. In the work at hand, an implicit feedback scenario is considered — i.e., feedback is, e.g., purchases, visits, clicks, views, check-ins —, with X containing binary values. Therefore, = 1 and = 0 denote either user has consumed or not item , respectively.

In FPL, the underlying data model is a Factorization model, inspired by MF [ 15 ], a recommendation model that became popular in the last decade thanks to its state-of-the-art recommendation accuracy [ 16 ]. This technique aims to build a model Θ in which each user and each item is represented by the embedding vectors p and q, respectively, in the shared latent space R . The algorithm relies on the assumption that X can be factorized such that the dot product between p and q can explain any observed user-item interaction , and that any non-observed interaction can be estimated as ^(Θ) = (Θ) + p (Θ) · q(Θ) where is a term denoting the bias of the item . Among pair-wise approaches for learning-to-rank the items of a catalog, Bayesian Personalized Ranking (BPR) [ 17 ] is one of the most broadly adopted, thanks to its capabilities to correctly rank with acceptable computational complexity. In detail, given a training set defined by = {(, , ) | = 1 ∧ = 0}, BPR solves the optimization problem via the criterion mΘax ∑︀(,,)∈ ln (^ (Θ)) − ‖Θ‖2, where ^ (Θ) = ^(Θ) − ^ (Θ) is a real value modeling the relation between user , item and item , (· ) is the sigmoid function, and is a model-specific regularization parameter to prevent overfitting.

Pair-wise optimization can be applied to a wide range of recommendation models, included factorization. Hereafter, we denote the model Θ = ⟨P, Q, b⟩, where P ∈ R||× is a matrix whose -th row corresponds to the vector p, and Q ∈ R|ℐ|× is a matrix in which the -th row corresponds to the vector q. Finally, b ∈ R|ℐ| is a vector whose -th element corresponds to the value .

2.2. FPL: Federated Pair-wise Learning for Recommendation

Following the aforementioned federated learning principles, let us assume that users in consume items from a catalog ℐ and give feedback about them. is aware of the whole catalog ℐ, while only user knows her own set of consumed items. Given these conditions, the classic BPR-MF learning procedure [ 17 ] for model training can not be applied to the federated learning scheme [ 5 ]. Instead, we propose a novel learning paradigm (depicted in Figure 1) that is executed for a number of epochs and works by rounds of communication that envisages Distribution→Computation→Transmission→Aggregation sequences between the server and the clients.

Training data Ku

Client u

Client-side

User-Factor Vector (pu)

BPR Optimization Δ( Δ( ) )

Item-Factor

Matrix (Q) Δ( ) Δ( ) Δ( Δ( ) ) Δ( )

Server S

Server-side Σ

In the FPL setting, a global model Θ is built on such that Θ = ⟨Q, b⟩, where Q ∈ R|ℐ|× and b ∈ R|ℐ| are the item-factor matrix and the bias vector (introduced in Section 2.1). On the other hand, on each device in the federation, FPL builds a model Θ = ⟨p⟩, which corresponds to the representation of user in a latent space of dimensionality . It is noteworthy that, in FPL, only user holds the embedding vector p; therefore, each user autonomously computes her personalized item ranking, by combining the global model Θ, sent by to the devices in the federation, with her local model Θ. In such a setting, each user holds her own private feedback dataset x ∈ Rℐ , which — compared with a centralized recommender system — corresponds to the -th row of matrix X. Each FPL client hosts a user-specific training set : × ℐ × ℐ defined by = {(, , ) | = 1 ∧ = 0}, where represents the -th element of . Please note that, in the following, we refer to + = ∑︀∈ |{ | = 1}| as the number of positive interactions.

The number of rounds of communication performed in each learning epoch is a parameter denoted by the symbol rpe (round-per-epoch). Each round of communication is envisioned as a four-step protocol, described in the following.

1. Distribution. randomly selects a subset of users − ⊆ Θ. and delivers them the model 2. Computation. Each user generates triples (, , ) from her dataset and for each of them performs BPR stochastic optimization to compute the updates for the local p vector of Θ, and for p, , p , and of the received Θ, following: Δ =

− ^ 1 + − ^ · ^ − , with ^ = ⎧(q − q ) if = p, ⎪ ⎪ ⎪⎪⎪⎪p if = q, ⎨

− p ⎪⎪⎪⎪1 if = , ⎪ ⎪⎩− 1 if = .

if = q , (1) It is worth noticing that Rendle [ 17 ] suggests, in a centralized scenario, to adopt a uniform distribution (over ) to choose the training triples randomly. The purpose is to avoid data is traversed item-wise or user-wise, since this may lead to slow convergence. Conversely, in a federated approach, we required to train the model user-wise since the training of each round of communication is performed separately on each client knowing only data in . This is the reason why, in FPL, the designer can control of the number of triples used for training, to tune the degree of local computation — i.e., how much the sampling is user-wise traversing. 3. Transmission. The clients in − send back to a portion of the updates for the computed item factor vector and item bias. More in detail, since the training output of a triple (, , ) in BPR lets the server distinguish the consumed item from the non-consumed one (for example just by analyzing the positive and the negative sign of Δ and Δ ), while they show the same absolute value, we argue that sending all the updates computed by may allow to reconstruct thus raising a privacy issue. Since our primary goal is to put users in control of their data, FPL proposes a solution to overcome this vulnerability. By sending the sole update (Δq , Δ ) of each training triples (, , ), user would share with indistinguishably negative or missing values, which are assumed to be non-sensitive data. Furthermore, in FPL we introduce the parameter , which allows users to control of the number of consumed items to share with the central server . The parameter works as a probability that clients send also a specific positive item update (Δq, Δ) in addition to (Δq , Δ ). 4. Global aggregation. aggregates all the received updates in Q and b to build the new model Θ ← Θ + ∑︀∈− ΔΘ, with being the learning rate (each row of the matrix Q and each element of b is updated by summing up the contribution of all clients in − for the corresponding item).

3. Experimental Setup

In this section, we introduce the experimental setting designed to analyze the performance of FPL. To this extent, we introduce the choice of the datasets with a brief analysis of their characteristics. Then, we describe the state-of-the-art algorithms we have involved. For the sake of reproducibility, for each method, we report the explored hyper-parameters in a specific section. Lastly, we present the evaluation protocol, and the metrics considered in the study.

3.1. Datasets

The evaluation of FPL needs to meet some particular constraints: the availability of transaction data to obtain a reliable experimental setting and a domain that guarantees the presence of data the user may prefer to protect. In our view, the optimal domain would be that of the Point-of-Interest (PoI), which concerns data that users usually perceive as sensitive. Among the many available datasets, we think that a very good candidate is the Foursquare dataset [ 11 ]. Indeed, it is often considered as a reference for evaluating PoI recommendation models.

To mimic a federation of devices in a single country, we have extracted check-ins for three countries, namely Brazil, Canada, and Italy. Since our only constraint was to obtain datasets with diferent size/sparsity characteristics, we took the liberty of choosing three countries of recent RecSys conference venues. To fairly evaluate FPL against the baselines, we have kept users with more than 20 interactions2. Moreover, we have split the datasets by adopting a realistic temporal hold-out 80-20 splitting on a per-user basis [ 18, 19 ]. Table 1 shows the characteristics of the resulting training sets.

3.2. Baselines

To evaluate the eficacy of FPL, we have conducted the experiments by considering nonpersonalized methods (random and most popular recommendation), and diferent recommendation approaches, including the centralized BPR-MF implementation [ 17 ], VAE [ 20 ], and FCF [21], which is, to date, the only federated recommendation approach based on MF (since no source code is available, we reimplemented and considered it in the reader’s interest). To evaluate the impact of feedback deprivation on recommendation accuracy, we have evaluated diferent values of in the range [0.0, 1.0]. We remember that = 0.0 means is not sharing any update (Δq, Δ) with regarding her positive items feedback, while = 1.0 means is sharing the updates on all positive items. Hence, we have considered four diferent configurations regarding computation and communication: • sFPL: it aims to reproduce the stochastic learning approach of centralized factorization model with pair-wise learning, where the central model is updated sequentially; therefore, we set | − | = 1 to involve just one random client per round, and it extracts solely one triple (, , ) from its dataset ( = 1) for the training phase; 2The limitations of the Collaborative Filtering in a cold-start user setting are well-known in the literature. • sFPL+: we increase client local computation by raising to + the number of triples || extracted from by each client involved in the round of communication; • pFPL: we enable parallelism by involving all clients in each round of communication ( − = ); we keep = 1; • pFPL+: we extend pFPL by letting each client sample = + triples from ; the || rationale is that the overall training samples are exactly +, as in centralized BPR-MF. In Rendle et al. [ 17 ], authors suggest to set the number of triples in one epoch of BPR to +, which corresponds to the number of optimizations steps. A particular choice is to randomly sampling = + triples per user. To make a federated training epoch of FPL comparable to BPR and amo|ng| diferent configurations, we set rpe to obtain always the same number of interactions between clients and server in one epoch. This value is equal to the overall number of optimization steps in one epoch of the centralized pair-wise learning. In detail, we set = + and then rpe = · | − | which results in = + for sFPL, and = + for pFPL. |− |

3.3. Reproducibility

For the splitting strategy, we have adopted a temporal hold-out 80/20 to separate our datasets in training and test set. Moreover, to find the most promising learning rate , we have further split the training set, adopting a temporal hold-out 80/20 strategy on a user basis to extract her validation set. VAE has been trained by considering three autoencoder topologies, with the following number of neurons per layer: 200-100-200, 300-100-300, 600-200-600. We have chosen candidate models by considering the best models after training for 50, 100, and 200 epochs, respectively. For the factorization models, we have performed a grid search in BPRMF for ∈ {0.005, 0.05, 0.5} varying the number of latent factors in {10, 20, 50}. Then, to ensure a fair comparison, we have exploited the same learning rate and number of latent factors to train FPL and FCF, and we explored the models in the range of {10, . . . , 50} iterations. We have set user- and positive item-regularization parameter to 210 of the learning rate. The negative item-regularization parameter is 2010 of the learning rate, as suggested in mymedialite3 implementation as well as by Anelli et al. [22].

3.4. Evaluation Metrics

We have evaluated the performance of FPL under the accuracy and diversity perspective. The accuracy of the models is measured by exploiting Precision ( @ ) and Recall (@ ). They respectively represent, for each user, the proportion of relevant recommended items in the recommendation list, and the fraction of relevant items that have been altogether suggested. We have assessed the statistical significance of results by adopting Student’s paired T-test considering p-values < 0.054. The results are in general statistically significant but the differences among BPR-MF, sFPL, and pFPL, which is a very important result. To measure the diversity of recommendations, we have measured the Item Coverage (@ ), and the Gini 3http://www.mymedialite.net/ 4The complete results are available at https://github.com/sisinflab/fpl-results/.

Random 0.00013 Top-Pop 0.01909 BPR-MF 0.07702 VAE * FCF sFPL sFPL+ pFPL pFPL+

PR Best obtained for each the proposed FPL variations for Brazil, Canada, and Italy are: sFPL = (0.5, 0.1, 0.4), pFPL = (0.8, 0.1, 1) * VAE does not always produce recommendations for all the users. For Italy, the reported results cover the 14% of the users. For this reason, it is not marked with bold in the table.

0.1 0.5

(a) Brazil 1 F 0.06 0.05 0.04 1 0.1 0.5

(c) Italy 1 F sFPL+, light blue is pFPL, light green is pFPL+.

Index (@ ). provides the number of diverse items recommended to users. It also conveys the sense of the degree of personalization [23]. measures distributional inequality, i.e., how unequally diferent items a RS provides users with [ 24]. A higher value of [ 18 ] corresponds to higher personalization.

4. Discussion

The main goal of the experiments is assessing whether it is possible to obtain a recommendation performance comparable to a centralized pair-wise learning approach while allowing the users to control their data. In this respect, Table 2 shows the accuracy and diversity results of the comparison between the state-of-the-art baselines and the four configurations of FPL presented in Section 3. By focusing on accuracy metrics, we may notice that User-kNN outperforms the other approaches in the three datasets, while the performance of Item-kNN and BPR-MF approximately settle in the same range of values. This is possibly due to the user-item ratio [25], that favors the user-based schemes (see Table 1). On the other hand, it is important to investigate the diferences of FPL with respect to BPR-MF, which is a pair-wise centralized approach, being FPL the first federated pair-wise recommender based on a factorization model. The performance of BPR-MF against FPL, in the configuration sFPL, shows how precision and recall in sFPL are slightly outperforming BPR-MF for the three datasets. This result is surprising since the two methods share the sequential training, but sFPL exploits a reduced to 0.5, 0.1, and 0.4, respectively, for Brazil, Canada, and Italy. This behavior is more evident in Figure 2, where the harmonic mean between Precision and Recall (F1) is plotted for diferent values of . If we look at the dark blue line, we may observe how the best result does not correspond to = 1. In the last three rows of Table 2, we explore an increasing of the local computation (sFPL+), or an increased parallelism (pFPL), or a combination of both (pFPL+). In detail, we observe that sFPL+ takes advantage of the increased local computation, and FPL significantly outperforms BPR-MF for the three datasets; for instance, for Canada, we observe an interesting increase in precision. Instead, when comparing pFPL with sFPL, we observe that the increased parallelism does not afect the performance significantly. Even then, the increased local computation boosts the Precision and Recall performance, up to 24% for precision in the Italy dataset. The results confirm that the proposed system can generate recommendations with a quality that is comparable with the centralized pair-wise learning approach. Moreover, the increased local computation causes a considerable improvement in the accuracy of recommendation. On the other side, the training parallelism does not significantly afects results. Finally, when the local computation is combined with parallelism, the results show a further improvement.

Afterwards, we varied in the range {0.1, . . . , 1.0} to assess how removal of the updates for consumed items afects the final recommendation accuracy, and we plotted the accuracy performance by considering F1 in Figure 2. As previously observed, the best performance rarely corresponds to = 1. On the contrary, a general trend can be observed: the training reaches a peak for a certain value of — depending on the dataset —, and then the system performance decays in accuracy when increasing the amount of shared positive updates. In rare cases, e.g., sFPL, and pFPL for Brazil dataset, the decay is absent, but results that are very close for diferent values of . The general behavior suggests that the system learning exploits the updates of positive items to absorb information about popularity. This consideration is coherent with the mathematical formulation of the learning procedure, and it is also supported by the observation that for Canada and Italy FPL reaches the peak before with respect to Brazil. Indeed, Canada and Italy datasets are less sparse than Brazil, and the increase of information about positive items may lead to push up too much the popular items (this is a characteristic of pair-wise learning), while the same behavior in Brazil can be observed for values of very close to 1. The same mathematical background, for sFPL+ and pFPL+ with Brazil dataset, which is very sparse, explains the higher value of needed to reach good performance. Here, the lack of positive information with a vast catalog of items, confuses the training that cannot exploit item popularity. Now, we can positively assert that user can receive high-quality recommendations also when decides to disclose a small amount of her sensitive data. However, it should be noted that the more the dataset is sparse, the more the amount of sensitive data should be large.

5. Conclusion and Future Work

Inspired by the potential ubiquity of the federated learning paradigm, we extend FPL, a novel federated learning framework that exploits pair-wise learning for factorization models. To this purpose, we have designed a model to leave the user-specific information of the original factorization model in the clients’ devices. With FPL, a user may be completely in control of her sensitive data and could share no positive feedback with the centralized server. The framework can be envisioned as a general factorization model in which clients can tune the amount of information shared among devices. We have conducted an exploratory, but extensive, experimental evaluation to analyze the degree of accuracy, the diversity of the recommendation results, the trade-of between accuracy, and amount of shared transactions. We have assessed that the proposed model shows performance comparable with several state-of-the-art baselines and the classic centralized factorization model with pair-wise learning. The evaluation shows that clients may share a small portion of their data with the server and still receive highperformance recommendations. We believe that the proposed privacy-oriented paradigm may open the doors to a new class of ubiquitous recommendation engines. [21] M. Ammad-ud-din, E. Ivannikova, S. A. Khan, W. Oyomno, Q. Fu, K. E. Tan, A. Flanagan, Federated collaborative filtering for privacy-preserving personalized recommendation system, CoRR abs/1901.09888 (2019). arXiv:1901.09888. [22] V. W. Anelli, T. D. Noia, E. D. Sciascio, C. Pomo, A. Ragone, On the discriminative power of hyper-parameters in cross-validation and how to choose them, in: Proc. of the 13th ACM Conf. on Recommender Systems, ACM, 2019, pp. 447–451. [23] G. Adomavicius, Y. Kwon, Improving aggregate recommendation diversity using rankingbased techniques, IEEE Trans. Knowl. Data Eng. 24 (2012) 896–911. [24] P. Castells, N. J. Hurley, S. Vargas, Novelty and diversity in recommender systems, in: F. Ricci, L. Rokach, B. Shapira (Eds.), Recommender Systems Handbook, Springer, 2015, pp. 881–918. [25] G. Adomavicius, J. Zhang, Impact of data characteristics on recommender systems performance, ACM Trans. Management Inf. Syst. 3 (2012) 3:1–3:17. URL: https://doi.org/10.1145/ 2151163.2151166. doi:10.1145/2151163.2151166.

References

[1] B. McFee , L. Barrington , G. R. G. Lanckriet , Learning content similarity for music recommendation , IEEE Trans. Audio, Speech & Language Processing 20 ( 2012 ) 2207 - 2218 .

[2] J. Yuan , W. Shalaby , M. Korayem , D. Lin , K. AlJadda , J. Luo, Solving cold-start problem in large-scale recommendation engines: A deep learning approach , in: 2016 IEEE Int. Conf. on Big Data, BigData 2016 , Washington DC , USA, December 5- 8 , 2016 , IEEE Computer Society, 2016 , pp. 1901 - 1910 .

[3] J. Konecný , B. McMahan , D. Ramage , Federated optimization: Distributed optimization beyond the datacenter , CoRR abs/1511 .03575 ( 2015 ). arXiv: 1511 . 03575 .

[4] V. W. Anelli , Y. Deldjoo , T. Di Noia , A. Ferrara , Towards efective device-aware federated learning , in: International Conference of the Italian Association for Artificial Intelligence , Springer, 2019 , pp. 477 - 491 .

[5] H. B. McMahan , E. Moore , D. Ramage , S. Hampson , et al., Communication-eficient learning of deep networks from decentralized data , arXiv preprint arXiv:1602.05629 ( 2016 ).

[6] Q. Yang , Y. Liu , T. Chen , Y. Tong, Federated machine learning: Concept and applications , ACM TIST 10 ( 2019 ) 12 : 1 - 12 : 19 .

[7] S. Weiss , The need for a paradigm shift in addressing privacy risks in social networking applications , in: IFIP International Summer School on the Future of Identity in the Information Society , Springer, 2007 , pp. 161 - 171 .

[8] A. J. P. Jeckmans , M. Beye , Z. Erkin , P. H. Hartel , R. L. Lagendijk , Q. Tang , Privacy in recommender systems , in: N. Ramzan , R. van Zwol, J. Lee , K. Clüver , X. Hua (Eds.), Social Media Retrieval, Computer Communications and Networks , Springer, 2013 , pp. 263 - 281 .

[9] V. W. Anelli , Y. Deldjoo , T. Di Noia , A. Ferrara , F. Narducci , How to put users in control of their data in federated top-n recommendation with learning to rank , in: Proceedings of the 36th Annual ACM Symposium on Applied Computing , SAC '21, Association for Computing Machinery, New York, NY, USA, 2021 , p. 1359 - 1362 . URL: https://doi.org/10. 1145/3412841.3442010. doi: 10 .1145/3412841.3442010.

[10] V. W. Anelli , Y. Deldjoo , T. D. Noia , A. Ferrara , F. Narducci , Federank: User controlled feedback with federated recommender systems , in: D. Hiemstra , M. Moens , J. Mothe , R. Perego , M. Potthast , F. Sebastiani (Eds.), Advances in Information Retrieval - 43rd European Conference on IR Research , ECIR 2021 , Virtual Event , March 28 - April 1, 2021 , Proceedings, Part I , volume 12656 of Lecture Notes in Computer Science, Springer, 2021 , pp. 32 - 47 . URL: https://doi.org/10.1007/978-3- 030 -72113- 8 _3. doi: 10 .1007/978-3- 030 -72113-8\_3.

[11] D. Yang , D. Zhang , B. Qu , Participatory cultural mapping based on collective behavior data in location-based social networks , ACM TIST 7 ( 2016 ) 30 : 1 - 30 : 23 .

[12] J. Konecný , H. B. McMahan , D. Ramage , P. Richtárik , Federated optimization: Distributed machine learning for on-device intelligence , CoRR abs/1610 .02527 ( 2016 ). arXiv: 1610 . 02527 .

[13] K. Bonawitz , H. Eichner , W. Grieskamp , D. Huba , A. Ingerman , V. Ivanov , C. Kiddon , J. Konecný , S. Mazzocchi , H. B. McMahan , T. V. Overveldt , D. Petrou , D. Ramage , J. Roselander , Towards federated learning at scale: System design , CoRR abs/ 1902 .01046 ( 2019 ). arXiv: 1902 .01046.

[14] P. Kairouz , H. B. McMahan , B. Avent , A. Bellet , M. Bennis , A. N. Bhagoji , K. Bonawitz , Z. Charles , G. Cormode, R. Cummings , et al., Advances and open problems in federated learning , arXiv preprint arXiv: 1912 . 04977 ( 2019 ).

[15] Y. Koren , R. M. Bell , C. Volinsky , Matrix factorization techniques for recommender systems , IEEE Computer 42 ( 2009 ) 30 - 37 .

[16] D. kumar Bokde , S. Girase , D. Mukhopadhyay , Role of matrix factorization model in collaborative filtering algorithm: A survey , CoRR abs/1503 .07475 ( 2015 ). arXiv: 1503 . 07475 .

[17] S. Rendle , C. Freudenthaler , Z. Gantner , L. Schmidt-Thieme , BPR: bayesian personalized ranking from implicit feedback , in: J. A. Bilmes , A. Y. Ng (Eds.), UAI 2009, Proc. of the Twenty-Fifth Conf. on Uncertainty in Artificial Intelligence , Montreal, QC, Canada, June 18-21, 2009 , AUAI Press, 2009 , pp. 452 - 461 .

[18] A. Gunawardana , G. Shani, Evaluating recommender systems , in: F. Ricci , L. Rokach , B. Shapira (Eds.), Recommender Systems Handbook , Springer, 2015 , pp. 265 - 308 .

[19] V. W. Anelli , T. D. Noia , E. D. Sciascio , A. Ragone , J. Trotta , Local popularity and time in top-n recommendation , in: European Conf. on Information Retrieval , volume 11437 , Springer, 2019 , pp. 861 - 868 .

[20] D. Liang , R. G. Krishnan , M. D. Hofman , T. Jebara, Variational autoencoders for collaborative filtering , in: Proceedings of the 2018 World Wide Web Conference , 2018 , pp. 689 - 698 .