UserReg: A Simple but Strong Model for Rating Prediction
Haiyang Zhang, Ivan Ganchev, Nikola S. Nikolov, Mark Stevenson
aa r X i v : . [ c s . I R ] F e b USERREG: A SIMPLE BUT STRONG MODEL FOR RATING PREDICTION
Haiyang Zhang Ivan Ganchev , , ∗ Nikola S. Nikolov ∗∗ Mark Stevenson Department of Computer Science, The University of Sheffield, UK Department of Computer Systems, University of Plovdiv “Paisii Hilendarski”, Bulgaria Institute of Mathematics and Informatics - Bulgarian Academy of Sciences, Bulgaria TRC*/CSIS**,University of Limerick, Ireland
ABSTRACT
Collaborative filtering (CF) has achieved great success in the fieldof recommender systems. In recent years, many novel CF models,particularly those based on deep learning or graph techniques, havebeen proposed for a variety of recommendation tasks, such as ratingprediction and item ranking. These newly published models usuallydemonstrate their performance in comparison to baselines or existingmodels in terms of accuracy improvements. However, others havepointed out that many newly proposed models are not as strong asexpected and are outperformed by very simple baselines.This paper proposes a simple linear model based on Matrix Fac-torization (MF), called
UserReg , which regularizes users’ latent rep-resentations with explicit feedback information for rating predic-tion. We compare the effectiveness of UserReg with three linear CFmodels that are widely-used as baselines, and with a set of recentlyproposed complex models that are based on deep learning or graphtechniques. Experimental results show that UserReg achieves over-all better performance than the fine-tuned baselines considered andis highly competitive when compared with other recently proposedmodels. We conclude that UserReg can be used as a strong baselinefor future CF research.
Index Terms — Recommender Systems, Collaborative Filter-ing, Matrix Factorization
1. INTRODUCTION
Personalized recommendation techniques have become popular andare widely used in many applications, including e-commerce andonline learning. They can be deployed to help users discover use-ful information and help merchants reach valuable target users. Themost successful and widely deployed recommendation technique iscollaborative filtering (CF) due to its effectiveness, efficiency andthe fact that it can make recommendations based only on users’historical interactions and without requiring specific domain infor-mation [1, 2]. Within CF, embedding based models have been themost popular ones for over a decade [2, 3, 4]. Matrix factoriza-tion (MF) is among the simplest and most widely used embeddingbased approaches [2]. Numerous extensions to MF have been pro-posed to further improve prediction accuracy including (1) tradi-tional enhancements, such as PMF [5], BiasedMF [2] and SVD++[6], proposed a decade ago and widely considered as baselines incurrent research, and (2) hybrid models that make use of content in-formation related to users/items for achieving further improvements[7, 8, 9, 10, 11, 12, 13].
This publication has been supported by the Bulgarian National ScienceFund (BNSF) under the Grant No. KP-06-IP-CHINA/1.
In recent years, embedding based models using deep learningtechniques have become particular popular, following their successin multiple application domains such as computer vision and natu-ral language processing. Most of these models reported significantimprovements over baselines [14, 15, 16, 17, 18]. However, somerecent works have pointed out that models based on deep learn-ing are not as strong as expected while also being computationalcomplex [3, 4]. For instance, Rendle et al. [4] showed that nu-merous recommendation models published in top-level conferencesbetween 2015 and 2019 are outperformed by long-established base-lines, which were even not the best ones. We also found that baselineresults reported in some recent work are suboptimal, which alignswith these findings. Dacrema et al. [3] analyzed a number of the re-cent neural network (NN) based models for top-n recommendationand found most of them failed to outperform simple baselines.Recommendation problems can be cast as either rating predic-tion or item ranking (also known as top-n recommendation) task andmost algorithms are designed for only one of these [9]. In this paper,we focus on the rating prediction task which predicts the value ofunobserved ratings to recommend items with the highest estimatedscores. Our contributions can be summarized as follows:• We propose a conceptually and computationally simple MF-based model, UserReg, that effectively makes use of userexplicit feedback to regularize user representation in MF inorder to improve recommendation accuracy. The experimentsconducted on four widely used datasets demonstrate that ourmodel outperforms popular fine-tuned baselines and canachieve state-of-the-art performance. In particular, it outper-forms the majority of MF-based models that use additionalcontent information;• We found UserReg more efficient in both training and rec-ommendation compared to SVD++, which is considered as astrong baseline [4, 9]. We conclude that UserReg can be usedas a strong baseline for future development of CF approaches;• We found that the fine-tuned baseline results are better thanthose reported in some recent works under the same experi-mental settings and that several MF-based approaches werenot compared against strong baselines (e.g. SVD++), andwould be outperformed by them.
2. MATRIX FACTORIZATION FOR RATING PREDICTION
A typical recommendation scenario involves a set of m users U = { u , u ...u m } , a set of n items I = { i , i ...i n } , and their inter-actions represented by a rating matrix R ∈ R m,n . The goal ofMF is to map both users and items into the same low-rank latentfactor space by approximating the observed ratings. The users andtems are represented by a set of feature vectors, P ∈ R m,d and Q ∈ R n,d , respectively, where d is the number of latent factors.The predicted rating of item i by user u is calculated by their dotproduct, as: ˜ r ui = P u Q Ti . The matrices P and Q are learnt by min-imizing the regularized squared error on the set of observed ratings ( u, i ) ∈ K : O MF = X ( u,i ) ∈ K (cid:16) ( r ui − ˜ r ui ) + λ ( k P u k + k Q i k ) (cid:17) (1) where λ ( k P u k + k Q i k ) is the regularization term.Several enhancements to MF have been proposed and are widelyused as baselines for comparison with newly proposed models:(1) Probabilistic matrix factorization ( PMF ) [5] formulates MFfrom a probabilistic perspective, assuming that entries of R ∈ R m,n are independent and normally distributed. The conditional distribu-tion over the observed ratings is defined as: p ( r | P, Q, σ ) = m Y u =1 n Y i =1 [ N ( r u,i | P u Q Ti , σ )] I u,i (2) where N ( x | µ, σ ) is the probability density function of the Gaus-sian distribution and I u,i is a binary indicator to check if r u,i is anobserved rating.(2) BiasedMF (also known as BiasedSVD) improves conven-tional MF by introducing bias information for users and items [2].BiasedMF predicts rating values as: ˜ r ui = P u Q Ti + µ + b u + b i (3) where µ is the global average rating, and b u and b i indicate the userbias and item bias, respectively.(3) SVD++ [6] extends BiasedMF, assuming that the rating ofuser u on item i is not only related to user u and item i , but also tothe items that u has already rated. It incorporates implicit feedbackinformation into BiasedMF: ˜ r ui = ( P u + | R u | − X j ∈ R u y j ) Q Ti + b ui (4) where b ui = µ + b u + b i represents the bias term, y j ∈ R d representsthe implicit influence of implicit feedback by user u , and R u is theset of items user u has rated.
3. USERREG
The basic form of MF assumes that the rating r ui is only based on thelatent representation of user u and item i . Some advanced forms ofMF go one step further by assuming r ui also relies on other context,e.g. users’ implicit feedback in SVD++ [6], users’ social relations[8, 9, 19], or side information of users and items [15, 10]. Similarto the previous works, the assumptions behind the proposed modelare that (1) r ui is not only related to user u and item i but also toother items that user u has shown interest in (e.g. items that receivedhigh ratings by user u ); and (2) the latent feature vector of user u should be close to the set of items of interest to that user. In line withthese assumptions, the proposed model UserReg incorporates userexplicit feedback into MF as a regularization term to constrain theMF objective function: O UR = 12 X u ∈ U X i ∈ R u ( r ui − ˜ r ui ) + β X u ∈ U || P u − | I ( u ) | − X j ∈ I ( u ) Q j || F + λ X u ∈ U k P u k F + X i ∈ I k Q i k F + X u ∈ U k b u k + X i ∈ I k b i k ) (5) where R u is the set of items rated by user u , I ( u ) is the set ofitems user u is interested in (we use items with a rating higherthan the average), β > is a regularization parameter that con-trols the influence of user feedback, and k · k F is the Frobeniusnorm. The regularization term aims to minimize the distance k P u − | I ( u ) | − P j ∈ I ( u ) Q j || F , such that the latent representa-tion for user u is close to the average representation of items that u has shown interest in, P u ≈ | I ( u ) | − P j ∈ I ( u ) Q j . Therefore, thedot product of P u and Q i can be approximated as: h P u , Q i i ≈ h| I ( u ) | − X j ∈ I ( u ) Q j , Q i i = | I ( u ) | − X j ∈ I ( u ) h Q j , Q i i (6) That is, the predicted rating of item i by user u without consideringtheir bias can be roughly viewed as the average similarity betweenitem i and item j , where j ∈ I ( u ) (similarly to the factored itemsimilarity model (FISM) proposed in [20]). Optimization.
The model parameters are learned by applying gra-dient descent (GD) across all users and items in the training set asfollows: ∂O UR ∂b u = X i ∈ R u e ui + λb u (7) ∂O UR ∂b i = X u ∈ U i e ui + λb i (8) ∂O UR ∂P u = X i ∈ R u e ui Q i + β ( P u − | I ( u ) | − X j ∈ I ( u ) Q j ) + λP u (9) ∂O UR ∂Q i = X u ∈ U i e ui P u + λQ i (10)where e ui = ˜ r ui − r ui and U i is the set of users that have rated item i . The pseudocode for learning UserReg is presented in Algorithm1, where γ is the learning rate. Algorithm 1:
Parameter updating for UserReg. while O UR not converged do compute the gradients according to (7)-(10) b u ← b u − γ ∂O UR ∂b u , u = 1 ...mb i ← b i − γ ∂O UR ∂b i , i = 1 ...nP u ← P u − γ ∂O UR ∂P u , u = 1 ...mQ i ← Q i − γ ∂O UR ∂Q i , i = 1 ...n endComputational Complexity Analysis. The main computationalcost in each iteration of learning UserReg depends on the compu-tational cost for computing the objective function and the gradients.Let m be the total number of users and r the average number of rat-ings for each user. Then, | R | ≈ m × r and the computational com-plexity of the objective function for UserReg is O ( mrd + mrld ) ,where l is the average number of items a user is interested in. Thecomplexity for computing the gradients according to (7)-(10) is O ( mr ) , O ( mr ) , O ( mrd + mld ) , and O ( mrd ) , respectively. Thecomputation complexity of UserReg is O ( mrd + mld ) for one iter-ation. Due to r, l, d ≪ m , the overall computational complexity islinear with respect to the number of users. Comparison with Other Similar Baselines.
The models that areclosely related to UserReg are SVD++ [6] and FISM [20]. Com-pared to SVD++, UserReg: (1) predicts the rating of r ui based onnot only user u , item i and the set of items that u has rated, butlso considers the explicit ratings of items that has been rated by u and filters out the items that u dislikes; (2) incorporates the influ-ence of items that a user liked as a regularization term, such that theprediction function remains the same with BiasedMF (equation (3)),which is more computationally efficient for rating prediction; and (3)it is more computational efficient in training, as the training compu-tational complexity of SVD++ is linear with respect to the numberof ratings [6] while in UserReg it is linear as regards the numberof users. Despite the fact that FISM and UserReg are designed fordifferent recommendation tasks (item ranking vs. rating prediction),their key difference is the matrices they factorize. FISM is an item-oriented model that learns the item latent factors by factorizing theitem similarity matrix, while UserReg learns latent factors for bothusers and items by factorizing the user-item rating matrix and regu-larizing the user presentations by the set of items user likes.
4. PERFORMANCE COMPARISON4.1. Datasets
We evaluated the performance of UserReg using two extensivelystudied Movielens benchmark datasets (ML-100K and ML-1M) and two datasets that are widely used for sparsity and cold startproblems: FilmTrust [9] and the Yelp . FilmTrust contains both userratings of items and social relations between users. The Yelp dataset,from the business domain, contains user ratings on businesses andattribute information of users and businesses. Main characteristicsof the four datasets are shown in Table 1. Table 1 : Descriptive statistics of the rating data in each dataset.
Dataset
ML-100K 943 1,682 100,000 6.31%ML-1M 6,040 3,952 1,000,209 4.19%FilmTrust 1,508 2,071 35,497 1.14%Yelp 16,239 14,284 198,379 0.08%Following [14, 21, 17], the performance of rating predic-tion is measured using the
Root Mean Square Error (RMSE): q | Z | P ( u,i ) ∈ Z ( r ui − ˜ r ui ) , where Z is the set of observed ratingsin the test set. A smaller value of RMSE indicates better predictiveaccuracy of the corresponding model. Experiments were conducted in two groups: (1) on the Movielensdatasets, as they are more general benchmarks used for variouskinds of recommendation approaches; (2) on FilmTrust and Yelp,which are usually used for attribute-aware recommendations. Foreach dataset, we used experimental settings, including data splits,employed by the majority of previous models that have used thatdataset. For the state-of-the-art models, we directly used the resultsreported in the corresponding papers using the same experimentalsettings. For the baselines (PMF, BaisedMF, SVD++), as the resultsreported vary between different works with the same experimentalsettings, we obtained the results with fine-tuned parameters usingthe LibRec library [22]. For fair comparison, we set the number oflatent factors in all MF-based models to . Each experiment was http://grouplens.org/datasets/movielens/ http://yelp.com/dataset-change/ Table 2 : The RMSE resutls on Movielens-100K and ML-1M w.r.t. different training test splits. (The first group are baselines, whereasthe second group are newly proposed models, all are shown in as-cending order by year of publication. ct. indicates whether contentinformation is needed for the corresponding model.) (a) ML-100K
Model 90/10 ct. Model 80/20 ct.PMF 0.909 no PMF 0.918 noBiasedMF 0.908 no BiasedMF 0.917 noSVD++ 0.903 no SVD++ 0.914 noNNMF (3HL) 0.907 no GRALS 0.945 yesAutoSVD 0.901 yes mSDA-CF yesAutoSVD++ 0.904 yes GC-MC 0.910 noNFM 0.910 no sRGCNN 0.929 yesGraphRec no IGMC 0.905 noUserReg 0.901 no UserReg 0.906 no (b) ML-1M
Model 90/10 50/50 ct.PMF 0.871 0.879 noBiasedMF 0.851 0.876 noSVD++ 0.850 0.874 noNNMF (3HL) 0.846 - noI-AutoRec 0.831 - noCF-NADE (2HL) - noAutoSVD 0.864 0.877 yesAutoSVD++ 0.848 0.875 yesNFM 0.858 0.881 noGC-MC 0.832 - noGraphRec 0.845 noIGMC 0.857 - noUserReg 0.845 0.872 noconducted five times and the average RMSE was taken as the finalresult.
In addition to the three baselines, we also compared UserReg againstmultiple state-of-the-art rating prediction models. GraphRec[18]and IGMC[17] are the two most recently proposed CF modelsfor rating prediction task using ML-100K and ML-1M. Based on[18, 17], we found a richer set of rating prediction models thatpresent state-of-the-art results, including (1) graph neural networks(GNNs) based ones: GRALS [23], GC-MC [24], sRGCNN [25] and(2) neural network based CF models: mSDA-CF [26], NNMF (3HL)[21], AutoSVD [15], AutoSVD++ [15], NFM [27], CF-NADE [16],I-AutoRec [14]. Following the experimental settings employed bythe majority of these models, we used 90/10 and 80/20 train/testsplits on ML-100K, and 90/10 and 50/50 train/test splits on ML-1M.For ML-100K, we used the hyper-parameters- λ = 0 . and β =12 for both data splits. For ML-1M, we used λ = 0 . and β = 8 for the 90/10 train/test split, and λ = 0 . , β = 5 for the 50/50split. The results are depicted in Table 2, where the best performancefigures are shown in bold (results of recent models were taken from[14, 15, 17, 18]).According to the results, UserReg outperforms the three base-ines on both datasets and achieves performance competitive withthe state-of-the-art models which are either complicated hybrid CFmodels or use content information. On ML-100K, UserReg outper-forms most of the recent models, except mSDA-CF, GraphRec andIGMC, among which mSDA-CF use additional content information,and GraphRec and IGMC are based on GNNs. On ML-1M, User-Reg cannot catch up with some of the NN-based models, such asI-AutoRec, CF-NADE, but still outperforms more than half of theremaining models. In particular, on both datasets UserReg achievesbetter performance than AutoSVD and AutoSVD++, which are pow-erful hybrid models [18] that integrate MF with a contractive auto-encoder to tackle data sparsity in CF.We also noticed that baseline results we obtained are better thanthose reported in most of the aforementioned recent works using thesame experiment settings, which indicates that the baselines are notproperly fine-tuned and the results in these works are suboptimal.Moreover, baseline results in more recent works are usually directlytaken from previous studies, e.g. [18, 17] that used results for PMFand BiasedMF taken from [15]. However, the baselines in previousworks (e.g. [15]) were not properly fine-tuned, leading to the prop-agation of suboptimal baselines. This aligns with the findings statedin [3] that the baseline results reported in previous works should beused with care. As FilmTrust and Yelp are popular datasets for attribute-aware CFstudies, besides baselines, we compared the performance of User-Reg to some recently reported hybrid MF-based models that useadditional content information. TrustSVD [9], which is one of themost influencing trust-enriched MF. Additionally, we choose threemore popular social relation enriched MF-based models, i.e. RSTE[7], SoReg [8], and TrustMF [19], for performance comparison onFilmTrust. Yelp is widely used in studies on heterogeneous infor-mation networks (HINs). Besides HERec [10], which is the state-of-art HIN-based MF model, three other MF-based models that useHINs to construct context information were chosen for comparisonon Yelp, namely HeteMF [11], SemRec [13] and DSR [12]. We setthe train/test split as 80/20 on both datasets. Results on FilmTrust aretaken directly from [9] and results on Yelp are taken from [10]. ForUserReg, we used λ = 0 . and β = 1 on FilmTrust, and λ = 0 . and β = 10 on Yelp. The obtained RMSE results are reported inTable 3. Table 3 : The RMSE results on FilmTrust and Yelp for different mod-els, shown in ascending order by year of publication.Model FilmTrust Model YelpPMF 0.968 PMF 1.482BiasedMF 0.804 BiasedMF 1.096SVD++ 0.802 SVD++ 1.097RSTE 0.835 HeteMF 1.280SoReg 0.838 SemRec 1.177TrustSVD
DSR 1.201TrustMF 0.819 HERec 1.112UserReg 0.798 UserReg
The major findings are: (1) UserReg performs consistently bet-ter than the baselines on both datasets; (2) UserReg outperforms allstate-of-the-art models (except TrustSVD on FilmTrust), despite thefact that it does not use any content information; (3) BiasedMF and
Training Ratio l og ( t r a i n i ng t i m e ) BiasedMFSVD++UserReg training ratio l og ( t r a n i ng ti m e ) (a) value of R M SE β R M S E (b) Fig. 1 : (a) A comparison of execution time on ML-1M with d = 5 .(b) The impact of parameter β on RMSE in UserReg.SVD++ show better performance than most of the recently proposedmodels, and to the best of our knowledge, they have not been usedas baselines for comparative study in the HIN-based research. Figure 1a shows the training time comparison (on a log scale) be-tween BiasedMF, SVD++ and UserReg, carried out on ML-1M. Theexecution time required by UserReg is significantly lower than thatof SVD++, despite the latter being considered a strong baseline forrating prediction [4]. Compared to BiasedMF and SVD++, UserRegprovides a better trade-offs between recommendation effectivenessand efficiency.
The parameter β plays an important role in UserReg by controllingthe impact of user feedback. In the extreme case when β = 0 , User-Reg equals BiasedMF and the user feedback has no influence on thepredicted rating. When β is set to a relatively large value, the learn-ing process is dominated by the influence of the items liked by theuser. In order to analyse the impact of β , we exprimented with itsvalues in the range (0 , on ML-1M with a 90/10 data split. Fig-ure 1b shows the impact of β on RMSE. With the increase of β , theprediction accuracy initially improves but later degrades, wherebythe best performance is achieved for β = 8 . Similar trends werefound on other experimental settings and other datasets described.This indicates that the proper incorporation of user feedback helpsimprove the recommendation accuracy.
5. CONCLUSION
This paper has proposed a simple MF-based model, UserReg, thatoutperforms the fine-tuned baselines considered and achieves com-petitive results when compared to other more computationally com-plex state-of-the-art models. UserReg has the potential to be usedas a strong baseline in the future development of rating predictionrecommendations. In addition, findings have been presented thatsome of the baseline results reported in a number of newly publishedworks are suboptimal. Moreover, some recent MF-based modelshave not been compared against strong baselines (BiasedMF andSVD++) as otherwise would be simply outperformed by them. Theconclusion is that baselines used for performance comparison shouldbe chosen and fine-tuned with care in the future CF development. . REFERENCES [1] Simon Funk, “Netflix update: Try this at home,” 2006.[2] Yehuda Koren, Robert Bell, and Chris Volinsky, “Matrix fac-torization techniques for recommender systems,”
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