nips nips2012 nips2012-49 knowledge-graph by maker-knowledge-mining

49 nips-2012-Automatic Feature Induction for Stagewise Collaborative Filtering

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Author: Joonseok Lee, Mingxuan Sun, Guy Lebanon, Seung-jean Kim

Abstract: Recent approaches to collaborative ﬁltering have concentrated on estimating an algebraic or statistical model, and using the model for predicting missing ratings. In this paper we observe that different models have relative advantages in different regions of the input space. This motivates our approach of using stagewise linear combinations of collaborative ﬁltering algorithms, with non-constant combination coefﬁcients based on kernel smoothing. The resulting stagewise model is computationally scalable and outperforms a wide selection of state-of-the-art collaborative ﬁltering algorithms. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu a Abstract Recent approaches to collaborative ﬁltering have concentrated on estimating an algebraic or statistical model, and using the model for predicting missing ratings. [sent-5, score-0.238]

2 This motivates our approach of using stagewise linear combinations of collaborative ﬁltering algorithms, with non-constant combination coefﬁcients based on kernel smoothing. [sent-7, score-0.749]

3 The resulting stagewise model is computationally scalable and outperforms a wide selection of state-of-the-art collaborative ﬁltering algorithms. [sent-8, score-0.68]

4 1 Introduction Recent approaches to collaborative ﬁltering (CF) have concentrated on estimating an algebraic or statistical model, and using the model for predicting the missing rating of user u on item i. [sent-9, score-0.839]

5 Linear combinations of K models K F (K) (x) = αk fk (x) (1) k=1 where α1 , . [sent-12, score-0.184]

6 , fK ∈ F, such as boosting or stagewise linear regression and stagewise logistic regression, enjoy a signiﬁcant performance boost over the single top-performing model. [sent-18, score-0.963]

7 Stagewise models are greedy incremental models of the form (αk , fk ) = arg min Risk(F (k−1) + αk fk ), k = 1, . [sent-20, score-0.294]

8 It is somewhat surprising that ensemble methods have had relatively little success in the collaborative ﬁltering literature. [sent-25, score-0.254]

9 Generally speaking, ensemble or combination methods have shown only a minor improvement over the top-performing CF methods. [sent-26, score-0.161]

10 The cases where ensemble methods did show an improvement (for example the Netﬂix prize winner [10] and runner up), relied heavily on manual feature engineering, manual parameter setting, and other tinkering. [sent-27, score-0.306]

11 This paper follows up on an experimental discovery: different recommendation systems perform better than others for some users and items but not for others. [sent-28, score-0.274]

12 In other words, the relative strengths of two distinct CF models f1 (u, i), f2 (u, i) ∈ F depend on the user u and the item i whose rating 1 0. [sent-29, score-0.653]

13 70 40 70 100 130 160 Number of available ratings for target item 190 Figure 1: Test set loss (mean absolute error) of two simple algorithms (user average and item average) on items with different number of ratings. [sent-35, score-0.758]

14 One example of two such systems appears in Figure 1 that graphs the test-set loss of two recommendation rules (user average and item average) as a function of the number of available ratings for the recommended item i. [sent-37, score-0.822]

15 The two recommendation rules outperform each other, depending on whether the item in question has few or many ratings in the training data. [sent-38, score-0.507]

16 The inescapable conclusion is that the weights αk in the combination should be functions of u and i rather than constants K F (K) (u, i) = αk (u, i)fk (u, i) (3) k=1 where αk (u, i) ∈ R and fk ∈ F for k = 1, . [sent-40, score-0.284]

17 In this paper we explore the use of such models for collaborative ﬁltering, where the weight functions αk (u, i) are learned from. [sent-44, score-0.235]

18 A major part of our contribution is a feature induction strategy to identify feature functions expressing useful locality information. [sent-45, score-0.284]

19 2 Related Work Many memory-based CF methods predict the rating of items based on the similarity of the test user and the training users [21, 3, 6]. [sent-47, score-0.477]

20 Model-based CF includes user and item clustering [3, 29, 32], Bayesian networks [3], dependence network [5] and probabilistic latent variable models [19, 17, 33]. [sent-50, score-0.552]

21 In many cases, there is signiﬁcant manual intervention such as setting the combination weights manually. [sent-58, score-0.193]

22 The primary difference is the manual selection of features in [26] as opposed to automatic induction of local features in our paper that leads to a signiﬁcant improvement in prediction quality. [sent-60, score-0.4]

23 Model combination based on locality has been proposed in other machine learning topics, such as classiﬁcation [31, 18] or sensitivity estimation [2]. [sent-61, score-0.133]

24 2 3 Combination of CF Methods with Non-Constant Weights Recalling the linear combination (3) from Section 1, we deﬁne non-constant combination weights αk (u, i) that are functions of the user and item that are being predicted. [sent-62, score-0.744]

25 We propose the following algebraic form αk (u, i) = βk hk (u, i), βk ∈ R, hk ∈ H (4) where βk is a parameter and hk is a function selected from a family H of candidate feature functions. [sent-63, score-0.567]

26 The combination (3) with non-constant weights (4) enables some CF methods fk to be emphasized for some user-item combinations through an appropriate selection of the βk parameters. [sent-64, score-0.324]

27 Substituting (4) into (3) we get K F (K) (u, i) = βk hk (u, i) fk (u, i), βk ∈ R, hk ∈ H, fk ∈ F. [sent-66, score-0.544]

28 (5) k=1 Note that since hk and fk are selected from the sets of CF methods and feature functions respectively, we may have fj = fl or hj = hl for j = l. [sent-67, score-0.365]

29 This is similar to boosting and other stagewise algorithms where one feature or base learner may be chosen multiple times, effectively updating its associate feature functions and parameters. [sent-68, score-0.598]

30 The total weight function associated with a particular f ∈ F is k:fk =f βk hk (u, i). [sent-69, score-0.151]

31 , βK ) is least squares β ∗ = arg min β∈C F (K) (u, i) − Ru,i 2 , (6) u,i where Ru,i denotes the rating of user u on item i in the training data and the summation ranges over all ratings in the training set. [sent-73, score-0.691]

32 A variation of (6), where β is constrained such that αk (u, i) ≥ 0, and K k=1 αk (u, i) = 1 endows F with the following probabilistic interpretation F (u, i) = Ep {f | u, i} , (7) where f represents a random draw from F, with probabilities p(f |u, i) proportional to k:fk =f βk hk (u, i). [sent-74, score-0.125]

33 4 Inducing Local Features In contrast to [26] that manually deﬁned 25 features, we induce the features hk from data. [sent-76, score-0.244]

34 The features hk (u, i) should emphasize users u and items i that are likely to lead to variations in the relative strength of the f1 , . [sent-77, score-0.372]

35 We consider below two issues: (i) deﬁning the set H of candidate features, and (ii) a strategy for selecting features from H to add to the combination F . [sent-81, score-0.217]

36 1 Candidate Feature Families H We denote the sets of users and items by U and I respectively, and the domain of f ∈ F and h ∈ H as Ω = U × I. [sent-83, score-0.148]

37 There are several possible choices for the distance functions in (8) between users and between items. [sent-89, score-0.103]

38 For simplicity, we use in our experiments the angular distance x, y x · y d(x, y) = arc cos (9) where the inner products above are computed based on the user-item rating matrix expressing the training set (ignoring entries not present in both arguments). [sent-90, score-0.13]

39 Their values decay linearly with the distance from their mode (truncated at zero), and feature a bandwidth parameter h, controlling the rate of decay. [sent-92, score-0.103]

40 The unimodal feature functions (8) capture locality in the Ω space by measuring proximity to a mode, representing a user u∗ , an item i∗ , or a user-item pair. [sent-94, score-0.725]

41 We deﬁne the family of candidate features H as all possible additive mixtures or max-mixtures of the functions (8), parameterized by ∗ ∗ a set of multiple modes ω ∗ = {ω1 , . [sent-95, score-0.183]

42 ,r Using this deﬁnition, features functions hk (u, i) ∈ H are able to express a wide variety of locality information involving multiple potential modes. [sent-102, score-0.301]

43 We discuss next the strategy for identifying useful features from H and adding them to the model F in a stagewise manner. [sent-103, score-0.522]

44 2 Feature Induction Strategy Adapting the stagewise learning approach to the model (5) we have K F (K) (u, i) = βk hk (u, i) fk (u, i), (12) k=1 (βk , hk , fk ) = F (k−1) (u, i) + βk hk (u, i)fk (u, i) − Ru,i arg min βk ∈R,hk ∈H,fk ∈F 2 . [sent-105, score-1.113]

45 (u,i)∈R It is a well-known fact that stagewise algorithms sometimes outperform non-greedy algorithms due to resistance to overﬁtting (see [22], for example). [sent-106, score-0.471]

46 We address this difﬁculty by restricting H to a ﬁnite collection of additive or max-mixtures kernels with r modes, randomly sampled from the users or items present in the training data. [sent-113, score-0.169]

47 Our experiments conclude that it is possible to ﬁnd useful features from a surprisingly small number of randomly-chosen samples. [sent-114, score-0.099]

48 CONST combines all candidate algorithms with constant weights as in (1). [sent-122, score-0.127]

49 FWLS combines all candidate algorithms with non-constant weights as in (3) [26]. [sent-123, score-0.127]

50 FEAT applies the feature induction techniques discussed in Section 4. [sent-126, score-0.138]

51 To evaluate whether the automatic feature induction in FEAT works better or worse than manually constructed features, we used in FWLS and STAGE manual features similar to the ones in [26] (excluding features requiring temporal data). [sent-127, score-0.426]

52 Examples include number of movies rated per user, number of users rating each movie, standard deviation of the users’ ratings, and standard deviation of the item’s ratings. [sent-128, score-0.183]

53 The feature induction in FEAT used a feature space H with additive multi-mode smoothing kernels as described in Section 4 (for simplicity we avoided kernels unimodal in both u and i). [sent-129, score-0.258]

54 The family H included 200 randomly sampled features (a new sample was taken for each of the iterations in the stagewise algorithms). [sent-130, score-0.547]

55 The r in (11) was set to 5% of user or item count, and bandwidth h values of 0. [sent-131, score-0.56]

56 The stagewise algorithm continues until either ﬁve consecutive trials fail to improve the RMSE on validation set, or the iteration number reaches 100, which occur only in a few cases. [sent-134, score-0.444]

57 We used similar L2 regularization for all methods (both stagewise and non-stagewise), where the regularization parameter was selected among 5 different values based on a validation set. [sent-135, score-0.469]

58 More speciﬁcally, we sub-sampled from the most active M users and the most often rated N items to obtain pre-speciﬁed data density levels |R|/|Ω|. [sent-138, score-0.21]

59 As shown in Table 2, we varied either the user or item count in the set {1000, 1500, 2000, 2500, 3000}, holding the other variable ﬁxed at 1000 and the density at 1%, which is comparable density of the original Netﬂix dataset. [sent-139, score-0.732]

60 5% Density Figure 2: Performance trend with varied user count (left), item count (middle), and density (right) on Netﬂix dataset. [sent-340, score-0.821]

61 For stagewise methods, the 80% train set was divided to 60% training set and 20% validation set, used to determine when to stop the stagewise addition process. [sent-341, score-0.909]

62 The 10% of training set is used to select regularization parameter for both stagewise and non-stagewise. [sent-343, score-0.465]

63 • STAGE FWLS: Figure 2 indicates that stagewise combinations where features are chosen with replacement are more accurate. [sent-351, score-0.577]

64 The selection with replacement allow certain features to be selected more than once, correcting a previous inaccurate parameter setting. [sent-352, score-0.141]

65 • FEAT STAGE: Making use of induced features improves prediction accuracy further from stagewise optimization with manually-designed features. [sent-353, score-0.573]

66 Overall, our experiments indicate that the combination with non-constant weights and feature induction (FEAT) outperforms three baselines (the best single method, standard combinations with constant weight, and the FWLS method using manually constructed features [26]). [sent-354, score-0.456]

67 4 0 200 400 600 800 item (sorted by algorithm 1) 1000 0. [sent-372, score-0.312]

68 7 0 200 400 600 800 item (sorted by algorithm 2) 1000 0. [sent-373, score-0.312]

69 4 0 200 400 600 800 item (sorted by algorithm 8) 0. [sent-375, score-0.312]

70 We conclude that our proposed combination outperforms state-of-the-art methods, and several previously proposed combination methods. [sent-402, score-0.173]

71 To see how feature induction works in detail, we illustrate an example with a case where the user count and item count equals 1000. [sent-403, score-0.881]

72 Figure 3 shows the average weight distribution that each user or item receives under three CF methods: user average, item average, and NLPMF. [sent-404, score-1.112]

73 We focused on these three methods since they are frequently selected by the stagewise algorithm. [sent-405, score-0.469]

74 The x axis variables in the three panels are sorted in the order of decreasing weights of selected algorithm. [sent-406, score-0.155]

75 2 Trend Analysis Figure 2 graphs the RMSE of the different combination methods as a function of the user count, item count, and density. [sent-412, score-0.607]

76 • As expected, prediction accuracy for all combination methods and for the top single method improves with the user count, item count, and density. [sent-414, score-0.648]

77 • The performance gap between the best single algorithm and the combinations tends to decrease with larger user and item count. [sent-415, score-0.586]

78 This is a manifestation of the law of diminishing returns, and the fact that the size of a suitable family H capturing locality information increases with the user and item count. [sent-416, score-0.613]

79 Thus, the stagewise procedure becomes more challenging computationally, and less accurate since in our experiment we sampled same number of compositions from H, rather than increasing it for larger data. [sent-417, score-0.444]

80 • We note that all combination methods and the single best CF method improve performance as the density increases. [sent-418, score-0.129]

81 7 • Comparing the left and middle panels of Figure 2 implies that having more users is more informative than having more items. [sent-420, score-0.124]

82 3 Scalability Our proposed stagewise algorithm is very efﬁcient, when compared to other feature selection algorithms such as step-wise or subset selection. [sent-423, score-0.515]

83 In our experiments, we sampled from the space of candidate features a small subset of features that was considered for addition (the random subset is different in each iteration of the stagewise algorithm). [sent-425, score-0.663]

84 In the limit K → ∞, such a sampling scheme would recover the optimal ensemble as each feature will be selected for consideration inﬁnitely often. [sent-426, score-0.138]

85 Our experiments conclude that this scheme works well also in practice and results in signiﬁcant improvement to the state-of-the-art even for a relatively small sample of feature candidates such as 200. [sent-427, score-0.141]

86 Viewed from another perspective, this implies that randomly selecting such a small subset of features each iteration ensures the selection of useful features. [sent-428, score-0.098]

87 In fact, the features induced in this manner were found to be more useful than the manually crafted features in the FWLS algorithm [26]. [sent-429, score-0.225]

88 7 Summary We started from an observation that the relative performance of different candidate recommendation systems f (u, i) depends on u and i, for example on the activity level of user u and popularity of item i. [sent-430, score-0.741]

89 This motivated the development of combination of recommendation systems with non-constant weights that emphasize different candidates based on their relative strengths in the feature space. [sent-431, score-0.395]

90 In contrast to the FWLS method that focused on manual construction of features, we developed a feature induction algorithm that works in conjunction with stagewise least-squares. [sent-432, score-0.655]

91 We formulate a family of feature function, based on the discrete analog of triangular kernel smoothing. [sent-433, score-0.103]

92 This family captures a wide variety of local information and is thus able to model the relative strengths of the different CF methods and how they change across Ω. [sent-434, score-0.101]

93 The combination with induced features outperformed any of the base candidates as well as other combination methods in literature. [sent-435, score-0.304]

94 This includes the recently proposed FWLS method that uses manually constructed feature function. [sent-436, score-0.113]

95 As our candidates included many of the recently proposed state-of-the-art recommendation systems our conclusions are signiﬁcant for the engineering community as well as recommendation system scientists. [sent-437, score-0.298]

96 Dependency networks for inference, collaborative ﬁltering, and data visualization. [sent-467, score-0.192]

97 Factorization meets the neighborhood: a multifaceted collaborative ﬁltering model. [sent-488, score-0.192]

98 Factor in the neighbors: Scalable and accurate collaborative ﬁltering. [sent-493, score-0.192]

99 Grouplens: an open architecture for collaborative ﬁltering of netnews. [sent-570, score-0.192]

100 Hybrid collaborative ﬁltering algorithms using a mixture of experts. [sent-613, score-0.215]

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