nips nips2013 nips2013-216 knowledge-graph by maker-knowledge-mining

216 nips-2013-On Flat versus Hierarchical Classification in Large-Scale Taxonomies

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Author: Rohit Babbar, Ioannis Partalas, Eric Gaussier, Massih-Reza Amini

Abstract: We study in this paper ﬂat and hierarchical classiﬁcation strategies in the context of large-scale taxonomies. To this end, we ﬁrst propose a multiclass, hierarchical data dependent bound on the generalization error of classiﬁers deployed in large-scale taxonomies. This bound provides an explanation to several empirical results reported in the literature, related to the performance of ﬂat and hierarchical classiﬁers. We then introduce another type of bound targeting the approximation error of a family of classiﬁers, and derive from it features used in a meta-classiﬁer to decide which nodes to prune (or ﬂatten) in a large-scale taxonomy. We ﬁnally illustrate the theoretical developments through several experiments conducted on two widely used taxonomies. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 fr Abstract We study in this paper ﬂat and hierarchical classiﬁcation strategies in the context of large-scale taxonomies. [sent-3, score-0.291]

2 To this end, we ﬁrst propose a multiclass, hierarchical data dependent bound on the generalization error of classiﬁers deployed in large-scale taxonomies. [sent-4, score-0.485]

3 This bound provides an explanation to several empirical results reported in the literature, related to the performance of ﬂat and hierarchical classiﬁers. [sent-5, score-0.434]

4 We then introduce another type of bound targeting the approximation error of a family of classiﬁers, and derive from it features used in a meta-classiﬁer to decide which nodes to prune (or ﬂatten) in a large-scale taxonomy. [sent-6, score-0.229]

5 The target classes in such large-scale scenarios typically have an inherent hierarchical structure, usually in the form of a rooted tree, as in Directory Mozilla1 , or a directed acyclic graph, with a parentchild relationship. [sent-9, score-0.385]

6 Various classiﬁcation techniques have been proposed for deploying classiﬁers in such large-scale taxonomies, from ﬂat (sometimes referred to as big bang) approaches to fully hierarchical one adopting a complete top-down strategy. [sent-10, score-0.291]

7 Several attempts have also been made in order to develop new classiﬁcation techniques that integrate, at least partly, the hierarchy into the objective function being optimized (as [3, 5, 10, 11] among others). [sent-11, score-0.195]

8 These techniques are however costly in practice and most studies either rely on a ﬂat classiﬁer, or a hierarchical one either deployed on the original hierarchy or a simpliﬁed version of it obtained by pruning some nodes (as [15, 18])2 . [sent-12, score-0.899]

9 This intermediate decision making leads to the error propagation phenomenon causing a decrease in accuracy. [sent-14, score-0.084]

10 On the other hand, ﬂat classiﬁers rely on a single decision including all the ﬁnal categories, a single decision that is however difﬁcult to make as it involves many categories, potentially unbalanced. [sent-15, score-0.116]

11 It is thus very difﬁcult to assess which strategy is best and there is no consensus, at the time being, on to which approach, ﬂat or hierarchical, should be preferred on a particular category system. [sent-16, score-0.17]

12 In this paper, we address this problem and introduce new bounds on the generalization errors of classiﬁers deployed in large-scale taxonomies. [sent-17, score-0.158]

13 These bounds make explicit the trade-off that both ﬂat and hierarchical classiﬁers encounter in large-scale taxonomies and provide an explanation to 1 www. [sent-18, score-0.554]

14 org The study in [19] introduces a slightly different simpliﬁcation, through an embedding of both categories and documents into a common space. [sent-20, score-0.203]

15 To our knowledge, this is the ﬁrst time that such bounds are introduced and that an explanation of the behavior of ﬂat and hierarchical classiﬁers is based on theoretical grounds. [sent-22, score-0.375]

16 We also propose a well-founded way to select nodes that should be pruned so as to derive a taxonomy better suited to the classiﬁcation problem. [sent-23, score-0.303]

17 Contrary to [4] that reweighs the edges in a taxonomy through a cost sensitive loss function to achieve this goal, we use here a simple pruning strategy that modiﬁes the taxonomy in an explicit way. [sent-24, score-0.567]

18 The remainder of the paper is organized as follows: Section 2 introduces the notations used and presents the generalization error bounds for classiﬁcation in large-scale taxonomies. [sent-25, score-0.143]

19 It also presents the meta-classiﬁer we designed to select those nodes that should be pruned in the original taxonomy. [sent-26, score-0.162]

20 Section 3 illustrates these developments via experiments conducted on several taxonomies extracted from DMOZ and the International Patent Classiﬁcation. [sent-27, score-0.211]

21 In the case of hierarchical classiﬁcation, the hierarchy of classes H = (V, E) is deﬁned in the form of a rooted tree, with a root ⊥ and a parent relationship π : V \ {⊥} → V where π(v) is the parent of node v ∈ V \ {⊥}, and E denotes the set of edges with parent to child orientation. [sent-32, score-0.859]

22 For each node v ∈ V \ {⊥}, we further deﬁne the set of its sisters S(v) = {v ∈ V \ {⊥}; v = v ∧ π(v) = π(v )} and its daughters D(v) = {v ∈ V \ {⊥}; π(v ) = v}. [sent-33, score-0.219]

23 The nodes at the intermediary levels of the hierarchy deﬁne general class labels while the specialized nodes at the leaf level, denoted by Y = {y ∈ V : v ∈ V, (y, v) ∈ E} ⊂ V , constitute the set of target classes. [sent-34, score-0.364]

24 In the case of ﬂat classiﬁcation, the hierarchy H is ignored, Y = V , and the problem reduces to the classical supervised multiclass classiﬁcation problem. [sent-42, score-0.321]

25 1 A hierarchical Rademacher data-dependent bound Our main result is the following theorem which provides a data-dependent bound on the generalization error of a top-down multiclass hierarchical classiﬁer. [sent-44, score-0.914]

26 The learning problem we address is then to ﬁnd a hypothesis f from FB such that the generalization error of gf ∈ GFB , E(gf ) = E(x,y)∼D 1gf (x,y)≤0 , is minimal (1gf (x,y)≤0 is the 0/1 loss, equal to 1 if gf (x, y) ≤ 0 and 0 otherwise). [sent-55, score-0.449]

27 The following theorem sheds light on the trade-off between ﬂat versus hierarchical classiﬁcation. [sent-56, score-0.324]

28 The notion of function class capacity used here is the empirical Rademacher complexity [1]. [sent-57, score-0.098]

29 For ﬂat multiclass classiﬁcation, we recover the bounds of [12] by considering a hierarchy containing a root node with as many daughters as there are categories. [sent-65, score-0.607]

30 The generalization error is controlled in inequality (1) by a trade-off between the empirical error and the Rademacher complexity of the class of classiﬁers. [sent-68, score-0.243]

31 The Rademacher complexity term favors hierarchical classiﬁers over ﬂat k ones, as any split of a set of category of size n in k parts n1 , · · · , nk ( i=1 ni = n) is such that k 2 2 i=1 ni ≤ n . [sent-69, score-0.378]

32 On the other hand, the empirical error term is likely to favor ﬂat classiﬁers vs hierarchical ones, as the latter rely on a series of decisions (as many as the length of the path from the root to the chosen category in Y) and are thus more likely to make mistakes. [sent-70, score-0.529]

33 This fact is often referred to as the propagation error problem in hierarchical classiﬁcation. [sent-71, score-0.331]

34 On the contrary, ﬂat classiﬁers rely on a single decision and are not prone to this problem (even though the decision to be made is harder). [sent-72, score-0.116]

35 When the classiﬁcation problem in Y is highly unbalanced, then the decision that a ﬂat classiﬁer has to make is difﬁcult; hierarchical classiﬁers still have to make several decisions, but the imbalance problem is less severe on each of them. [sent-73, score-0.335]

36 So, in this case, even though the empirical error of hierarchical classiﬁers may be higher than the one of ﬂat ones, the difference can be counterbalanced by the Rademacher complexity term, and the bound in Theorem 1 suggests that hierarchical classiﬁers should be preferred over ﬂat ones. [sent-74, score-0.776]

37 These results have been empirically observed in different studies on classiﬁcation in largescale taxonomies and are further discussed in Section 3. [sent-76, score-0.239]

38 Similarly, one way to improve the accuracy of classiﬁers deployed in large-scale taxonomies is to modify the taxonomy by pruning (sets of) nodes [18]. [sent-77, score-0.672]

39 By doing so, one is ﬂattening part of the taxonomy and is once again trading-off the two terms in inequality (1): pruning nodes leads to reduce the number of decisions made by the hierarchical classiﬁer while maintaining a reasonable Rademacher complexity. [sent-78, score-0.782]

40 Even though it can explain several empirical results obtained so far, the bound displayed in Theorem 1 does not provide a practical way to decide on whether to prune a node or not, as it would involve the training of many classiﬁers which is impractical with large-scale taxonomies. [sent-79, score-0.341]

41 We thus turn towards another bound in the next section that will help us design a direct and simple strategy to prune nodes in a taxonomy. [sent-80, score-0.243]

42 2 Asymptotic approximation error bounds We now propose an asymptotic approximation error bound for a multiclass logistic regression (MLR) classiﬁer. [sent-82, score-0.383]

43 We ﬁrst consider the ﬂat, multiclass case (V = Y), and then show how the bounds can be combined in a typical top-down cascade, leading to the identiﬁcation of important features that control the variation of these bounds. [sent-83, score-0.164]

44 , d}, y ∈ Y \ {y }}, and using the independence assumption and the asymptotic normality of maximum likelihood estimates (see for example [17], p. [sent-98, score-0.105]

45 Lemma 1 suggests that the predicted and asymptotic posterior probabilities are close to each other, as the quantities they are based on are close to each other. [sent-104, score-0.144]

46 Thus, provided that the asymptotic posterior probabilities between the best two classes, for any given x, are not too close to each other, the generalization error of the MLR classiﬁer and the one of its asymptotic version should be similar. [sent-105, score-0.354]

47 Theorem 2 below states such a relationship, using the following function that measures the confusion between the best two classes for the asymptotic MLR classiﬁer deﬁned as : h∞ (x) = argmax P (y|x, β ∞ ) y∈Y For any given x ∈ X , the confusion between the best two classes is deﬁned as follows. [sent-106, score-0.347]

48 4 (3) 1 Deﬁnition 1 Let f∞ (x) = maxy∈Y P (y|x, β ∞ ) be the best class posterior probability for x by the 2 asymptotic MLR classiﬁer, and let f∞ (x) = maxy∈Y\h∞ (x) P (y|x, β ∞ ) be the second best class posterior probability for x. [sent-107, score-0.257]

49 We deﬁne the confusion of the asymptotic MLR classiﬁer for a category set Y as: 1 2 GY (τ ) = P(x,y)∼D (|f∞ (x) − f∞ (x)| < 2τ ) for a given τ > 0. [sent-108, score-0.215]

50 The following theorem states a relationship between the generalization error of a trained MLR classiﬁer and its asymptotic version. [sent-109, score-0.276]

51 from a probability distribution D, let i=1 hm and h∞ denote the multiclass logistic regression classiﬁers learned from a training set of ﬁnite size m and its asymptotic version respectively, and let E(hm ) and E(h∞ ) be their generalization errors. [sent-113, score-0.421]

52 d d j=1 R|Y|σ0 δm (4) y βj xj ), ∀x ∈ X and ∀y ∈ Y, and σ0 is a Proof (sketch) The difference E(hm ) − E(h∞ ) is bounded by the probability that the asymptotic MLR classiﬁer h∞ correctly classiﬁes an example (x, y) ∈ X × Y randomly chosen from D, while hm misclassiﬁes it. [sent-115, score-0.222]

53 3 A learning based node pruning strategy Let us now consider a hierarchy of classes and a top-down classiﬁer making decisions at each level of the hierarchy. [sent-122, score-0.752]

54 A node-based pruning strategy can be easily derived from the approximation bounds above. [sent-123, score-0.323]

55 Indeed, any node v in the hierarchy H = (V, E) is associated with three category sets: its sister categories with the node itself S (v) = S(v) ∪ {v}, its daughter categories, D(v), and the union of its sister and daughter categories, denoted F(v) = S(v) ∪ D(v). [sent-124, score-0.96]

56 These three sets of categories ⊥ ⊥ are the ones involved before and after the pruning of node . [sent-125, score-0.562]

57 Let us now denote the S(v) ∪ {v} v F(v) S MLR classiﬁer by hmv learned Pruning from a set of sister categories D(v) . [sent-132, score-0.263]

58 of node v and the node itself, and by hDv a MLR classiﬁer m S learned from the set of daughter categories of node v (h∞v and hDv respectively denote their asymp∞ totic versions). [sent-144, score-0.663]

59 They nevertheless exhibit the factors that play an important role in assessing whether a particular trained classiﬁer in the logistic regression family is close or not to its asymptotic version. [sent-148, score-0.138]

60 Each node v ∈ V can then be characterized by factors in the set {|Y |, mY , nY , nY , GY (. [sent-149, score-0.151]

61 ) with two simple quantities: the average cosine similarity of all the pairs of classes in Y , and the average symmetric Kullback-Leibler divergences between all the pairs in Y of class conditional multinomial distributions. [sent-152, score-0.105]

62 negative) class to a node if the pruning of that node leads to a ﬁnal performance increase (resp. [sent-154, score-0.57]

63 A meta-classiﬁer is then trained on these features using a training set from a selected class hierarchy. [sent-156, score-0.106]

64 After the learning phase, the meta-classiﬁer is applied to each node of a new hierarchy of classes so as to identify which nodes should be pruned. [sent-157, score-0.48]

65 3 Discussion We start our discussion by presenting results on different hierarchical datasets with different characteristics using MLR and SVM classiﬁers. [sent-159, score-0.337]

66 The datasets we used in these experiments are two large datasets extracted from the International Patent Classiﬁcation (IPC) dataset3 and the publicly available DMOZ dataset from the second PASCAL large scale hierarchical text classiﬁcation challenge (LSHTC2)4 . [sent-160, score-0.383]

67 We created 4 datasets from LSHTC2 by splitting randomly the ﬁrst layer nodes (11 in total) of the original hierarchy in disjoint subsets. [sent-163, score-0.307]

68 The classes for the IPC and LSHTC2 datasets are organized in a hierarchy in which the documents are assigned to the leaf categories only. [sent-164, score-0.485]

69 CR denotes the complexity ratio between hierarchical and ﬂat classiﬁcation, given by the Rademacher complexity term in Theorem 1: v∈V \Y |D(v)|(|D(v)| − 1) / (|Y|(|Y| − 1)); the same constants B, R and L are used in the two cases. [sent-166, score-0.382]

70 On the other hand, the ratio of empirical errors (last column of Table 1) obtained with top-down hierarchical classiﬁcation over ﬂat classiﬁcation when using SVM 3 4 http://www. [sent-168, score-0.353]

71 The comparison of the complexity and error ratios on all the datasets thus suggests that the ﬂat classiﬁcation strategy may be preferred on IPC, whereas the hierarchical one is more likely to be efﬁcient on the LSHTC datasets. [sent-190, score-0.552]

72 To test our simple node pruning strategy, we learned binary classiﬁers aiming at deciding whether to prune a node, based on the node features described in the previous section. [sent-192, score-0.622]

73 The label associated to each node in this training set is deﬁned as +1 if pruning the node increases the accuracy of the hierarchical classiﬁer by at least 0. [sent-193, score-0.86]

74 1, and -1 if pruning the node decreases the accuracy by more than 0. [sent-194, score-0.382]

75 The meta-classiﬁer is then trained to learn a mapping from the vector representation of a node (based on the above features) and the labels {+1; −1}. [sent-198, score-0.184]

76 We used the ﬁrst two datasets of LSHTC2 to extract the training data while LSHTC2-3, 4, 5 and IPC were employed for testing. [sent-199, score-0.082]

77 We compare the fully ﬂat classiﬁer (FL) with the fully hierarchical (FH) top-down Pachinko machine, a random pruning (RN) and the proposed pruning method (PR) . [sent-204, score-0.753]

78 For the random pruning we restrict the procedure to the ﬁrst two levels and perform 4 random prunings (this is the average number of prunings that are performed in our approach). [sent-205, score-0.321]

79 For each dataset we perform 5 independent runs for the random pruning and we record the best performance. [sent-206, score-0.231]

80 On all LSHTC datasets ﬂat classiﬁcation performs worse than the fully hierarchy top-down classiﬁcation, for all classiﬁers. [sent-209, score-0.241]

81 These results are in line with complexity and empirical error ratios for SVM estimated on different collections and shown in table 1 as well as with the results obtained in [14, 7] over the same type of taxonomies. [sent-210, score-0.133]

82 Further, the work by [14] demonstrated that class hierarchies on LSHTC datasets suffer from rare categories problem, i. [sent-211, score-0.309]

83 , 80% of the target categories in such hierarchies have less than 5 documents assigned to them. [sent-213, score-0.219]

84 As a result, ﬂat methods on such datasets face unbalanced classiﬁcation problems which results in smaller error ratios; hierarchical classiﬁcation should be preferred in this case. [sent-214, score-0.488]

85 This is in agreement with the conclusions obtained in recent studies, as [2, 9, 16, 6], in which the datasets considered do not have rare categories and are more well-balanced. [sent-253, score-0.229]

86 The proposed hierarchy pruning strategy aims to adapt the given taxonomy structure for better classiﬁcation while maintaining the ancestor-descendant relationship between a given pair of nodes. [sent-254, score-0.621]

87 As shown in Table 2, this simple learning based pruning strategy leads to statistically signiﬁcant better results for all three classiﬁers compared to both the original taxonomy and a randomly pruned one. [sent-255, score-0.522]

88 A similar result is reported in [18] through a pruning of an entire layer of the hierarchy, which can be seen as a generalization, even though empirical in nature, of the pruning strategy retained here. [sent-256, score-0.608]

89 Another interesting approach to modify the original taxonomy is presented in [21]. [sent-257, score-0.141]

90 4 Conclusion We have studied in this paper ﬂat and hierarchical classiﬁcation strategies in the context of largescale taxonomies, through error generalization bounds of multiclass, hierarchical classiﬁers. [sent-259, score-0.752]

91 The ﬁrst theorem we have introduced provides an explanation to several empirical results related to the performance of such classiﬁers. [sent-260, score-0.11]

92 We have also introduced a well-founded way to simplify a taxonomy by selectively pruning some of its nodes, through a meta-classiﬁer. [sent-261, score-0.372]

93 The features retained in this meta-classiﬁer derive from the error generalization bounds we have proposed. [sent-262, score-0.172]

94 The experimental results reported here (as well as in other papers) are in line with our theoretical developments and justify the pruning strategy adopted. [sent-263, score-0.349]

95 This is the ﬁrst time, to our knowledge, that a data dependent error generalization bound is proposed for multiclass, hierarchical classiﬁers and that a theoretical explanation is provided for the performance of ﬂat and hierarchical classiﬁcation strategies in large-scale taxonomies. [sent-264, score-0.767]

96 In particular, there is, up to now, no consensus on which classiﬁcation scheme, ﬂat or hierarchical, to use on a particular category system. [sent-265, score-0.085]

97 One of our main conclusions is that top-down hierarchical classiﬁers are well suited to unbalanced, large-scale taxonomies, whereas ﬂat ones should be preferred for well-balanced taxonomies. [sent-266, score-0.38]

98 Lastly, our theoretical development also suggests possibilities to grow a hierarchy of classes from a (large) set of categories, as has been done in several studies (e. [sent-267, score-0.296]

99 Discriminative learning of relaxed hierarchy for large-scale visual recognition. [sent-332, score-0.195]

100 Improving hierarchical SVMs by hierarchy ﬂattening and lazy classiﬁcation. [sent-373, score-0.486]

similar papers computed by tfidf model

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Interestingly, one line of communication theory seeks to unify agenda setting and framing by viewing frames as a second-level kind of agenda [1]: just as agenda setting is about which objects of discussion are salient, framing is about the salience of attributes of those objects. The key is that what communications theorists consider an attribute in a discussion can itself be an object, as well. For example, “mistaken convictions” is one attribute of the death penalty discussion, but it can also be viewed as an object of discussion in its own right. This two-level view leads naturally to the idea of using a hierarchical topic model to formalize both agendas and frames within a uniform setting. In this paper, we introduce a new model to do exactly that. The model is predictive: it represents the idea of alternative or competing perspectives via a continuous-valued response variable. Although inspired by the study of political discourse, associating texts with “perspectives” is more general and has been studied in sentiment analysis, discovery of regional variation, and value-sensitive design. We show experimentally that the model’s hierarchical structure improves prediction of perspective in both a political domain and on sentiment analysis tasks, and we argue that the topic hierarchies exposed by the model are indeed capturing structure in line with the theory that motivated the work. 1 ߨ ݉ ߠௗ ߙ ߰ௗ ߛ ‫ݐ‬ௗ௦ ‫ݖ‬ௗ௦௡ ‫ݓ‬ௗ௦௡ ܿௗ௧ ܰௗ௦ ∞ ߩ ܵௗ ‫ݕ‬ௗ ‫ܦ‬ ߱ ߟ௞ ߬௩ ܸ 1. For each node k ∈ [1, ∞) in the tree (a) Draw topic φk ∼ Dir(βk ) (b) Draw regression parameter ηk ∼ N (µ, σ) 2. For each word v ∈ [1, V ], draw τv ∼ Laplace(0, ω) 3. For each document d ∈ [1, D] (a) Draw level distribution θd ∼ GEM(m, π) (b) Draw table distribution ψd ∼ GEM(α) (c) For each table t ∈ [1, ∞), draw a path cd,t ∼ nCRP(γ) (d) For each sentence s ∈ [1, Sd ], draw a table indicator td,s ∼ Mult(ψd ) i. For each token n ∈ [1, Nd,s ] A. Draw level zd,s,n ∼ Mult(θd ) B. Draw word wd,s,n ∼ Mult(φcd,td,s ,zd,s,n ) ¯ ¯ (e) Draw response yd ∼ N (η T zd + τ T wd , ρ): ߶௞ ∞ ߤ i. zd,k = ¯ ߪ ߚ ii. wd,v = ¯ 1 Nd,· 1 Nd,· Sd s=1 Sd s=1 Nd,s n=1 I [kd,s,n = k] Nd,s n=1 I [wd,s,n = v] Figure 1: S H L DA’s generative process and plate diagram. Words w are explained by topic hierarchy φ, and response variables y are explained by per-topic regression coefﬁcients η and global lexical coefﬁcients τ . 2 S H L DA: Combining Supervision and Hierarchical Topic Structure Jointly capturing supervision and hierarchical topic structure falls under a class of models called supervised hierarchical latent Dirichlet allocation. These models take as input a set of D documents, each of which is associated with a response variable yd , and output a hierarchy of topics which is informed by yd . Zhang et al. [6] introduce the S H L DA family, focusing on a categorical response. In contrast, our novel model (which we call S H L DA for brevity), uses continuous responses. At its core, S H L DA’s document generative process resembles a combination of hierarchical latent Dirichlet allocation [7, HLDA] and the hierarchical Dirichlet process [8, HDP]. HLDA uses the nested Chinese restaurant process (nCRP(γ)), combined with an appropriate base distribution, to induce an unbounded tree-structured hierarchy of topics: general topics at the top, speciﬁc at the bottom. A document is generated by traversing this tree, at each level creating a new child (hence a new path) with probability proportional to γ or otherwise respecting the “rich-get-richer” property of a CRP. A drawback of HLDA, however, is that each document is restricted to only a single path in the tree. Recent work relaxes this restriction through different priors: nested HDP [9], nested Chinese franchises [10] or recursive CRPs [11]. In this paper, we address this problem by allowing documents to have multiple paths through the tree by leveraging information at the sentence level using the twolevel structure used in HDP. More speciﬁcally, in the HDP’s Chinese restaurant franchise metaphor, customers (i.e., tokens) are grouped by sitting at tables and each table takes a dish (i.e., topic) from a ﬂat global menu. In our S H L DA, dishes are organized in a tree-structured global menu by using the nCRP as prior. Each path in the tree is a collection of L dishes (one for each level) and is called a combo. S H L DA groups sentences of a document by assigning them to tables and associates each table with a combo, and thus, models each document as a distribution over combos.1 In S H L DA’s metaphor, customers come in a restaurant and sit at a table in groups, where each group is a sentence. A sentence wd,s enters restaurant d and selects a table t (and its associated combo) with probability proportional to the number of sentences Sd,t at that table; or, it sits at a new table with probability proportional to α. After choosing the table (indexed by td,s ), if the table is new, the group will select a combo of dishes (i.e., a path, indexed by cd,t ) from the tree menu. Once a combo is in place, each token in the sentence chooses a “level” (indexed by zd,s,n ) in the combo, which speciﬁes the topic (φkd,s,n ≡ φcd,td,s ,zd,s,n ) producing the associated observation (Figure 2). S H L DA also draws on supervised LDA [12, SLDA] associating each document d with an observable continuous response variable yd that represents the author’s perspective toward a topic, e.g., positive vs. negative sentiment, conservative vs. liberal ideology, etc. This lets us infer a multi-level topic structure informed by how topics are “framed” with respect to positions along the yd continuum. 1 We emphasize that, unlike in HDP where each table is assigned to a single dish, each table in our metaphor is associated with a combo–a collection of L dishes. We also use combo and path interchangeably. 2 Sd Sd,t ߶ଵ ߟଵ dish ߶ଵଵ ߟଵଵ ߶ଵଶ ߟଵଶ ߶ଵଵଵ ߟଵଵଵ ߶ଵଵଶ ߟଵଵଶ ߶ଵଶଵ ߟଵଶଵ ߶ଵଶଶ ߟଵଶଶ table ܿௗ௧ ‫1=ݐ‬ ‫2=ݐ‬ ‫1=ݐ‬ ‫2=ݐ‬ ‫3=ݐ‬ ‫1=ݐ‬ ‫2=ݐ‬ ‫ݐ‬ௗ௦ ‫2=ݏ 1=ݏ‬ ‫ܵ = ݏ‬ଵ ‫3=ݏ 2=ݏ 1=ݏ‬ ݀=1 ݇ௗ௦௡ ‫ܵ = ݏ‬ଶ ‫ܵ = ݏ‬஽ ݀=2 ߶ଵ ߟଵ ݀=‫ܦ‬ customer group (token) (sentence) restaurant (document) ߶ଵଵ ߟଵଵ ݀=1 ‫1=ݏ‬ ߶ଵଵଵ ߟଵଵଵ combo (path) Nd,s Nd,·,l Nd,·,>l Nd,·,≥l Mc,l Cc,l,v Cd,x,l,v φk ηk τv cd,t td,s zd,s,n kd,s,n L C+ Figure 2: S H L DA’s restaurant franchise metaphor. # sentences in document d # groups (i.e. sentences) sitting at table t in restaurant d # tokens wd,s # tokens in wd assigned to level l # tokens in wd assigned to level > l ≡ Nd,·,l + Nd,·,>l # tables at level l on path c # word type v assigned to level l on path c # word type v in vd,x assigned to level l Topic at node k Regression parameter at node k Regression parameter of word type v Path assignment for table t in restaurant d Table assignment for group wd,s Level assignment for wd,s,n Node assignment for wd,s,n (i.e., node at level zd,s,n on path cd,td,s ) Height of the tree Set of all possible paths (including new ones) of the tree Table 1: Notation used in this paper Unlike SLDA, we model the response variables using a normal linear regression that contains both pertopic hierarchical and per-word lexical regression parameters. The hierarchical regression parameters are just like topics’ regression parameters in SLDA: each topic k (here, a tree node) has a parameter ηk , and the model uses the empirical distribution over the nodes that generated a document as the regressors. However, the hierarchy in S H L DA makes it possible to discover relationships between topics and the response variable that SLDA’s simple latent space obscures. Consider, for example, a topic model trained on Congressional debates. Vanilla LDA would likely discover a healthcare category. SLDA [12] could discover a pro-Obamacare topic and an anti-Obamacare topic. S H L DA could do that and capture the fact that there are alternative perspectives, i.e., that the healthcare issue is being discussed from two ideological perspectives, along with characterizing how the higher level topic is discussed by those on both sides of that ideological debate. Sometimes, of course, words are strongly associated with extremes on the response variable continuum regardless of underlying topic structure. Therefore, in addition to hierarchical regression parameters, we include global lexical regression parameters to model the interaction between speciﬁc words and response variables. We denote the regression parameter associated with a word type v in the vocabulary as τv , and use the normalized frequency of v in the documents to be its regressor. Including both hierarchical and lexical parameters is important. For detecting ideology in the US, “liberty” is an effective indicator of conservative speakers regardless of context; however, “cost” is a conservative-leaning indicator in discussions about environmental policy but liberal-leaning in debates about foreign policy. For sentiment, “wonderful” is globally a positive word; however, “unexpected” is a positive descriptor of books but a negative one of a car’s steering. S H L DA captures these properties in a single model. 3 Posterior Inference and Optimization Given documents with observed words w = {wd,s,n } and response variables y = {yd }, the inference task is to ﬁnd the posterior distribution over: the tree structure including topic φk and regression parameter ηk for each node k, combo assignment cd,t for each table t in document d, table assignment td,s for each sentence s in a document d, and level assignment zd,s,n for each token wd,s,n . We approximate S H L DA’s posterior using stochastic EM, which alternates between a Gibbs sampling E-step and an optimization M-step. More speciﬁcally, in the E-step, we integrate out ψ, θ and φ to construct a Markov chain over (t, c, z) and alternate sampling each of them from their conditional distributions. In the M-step, we optimize the regression parameters η and τ using L-BFGS [13]. Before describing each step in detail, let us deﬁne the following probabilities. For more thorough derivations, please see the supplement. 3 • First, deﬁne vd,x as a set of tokens (e.g., a token, a sentence or a set of sentences) in document d. The conditional density of vd,x being assigned to path c given all other assignments is −d,x Γ(Cc,l,· + V βl ) L −d,x fc (vd,x ) = l=1 −d,x Γ(Cc,l,v + Cd,x,l,v + βl ) V −d,x Γ(Cc,l,· + Cd,x,l,· + V βl ) (1) −d,x Γ(Cc,l,v + βl ) v=1 where superscript −d,x denotes the same count excluding assignments of vd,x ; marginal counts −d,x are represented by ·’s. For a new path cnew , if the node does not exist, Ccnew ,l,v = 0 for all word types v. • Second, deﬁne the conditional density of the response variable yd of document d given vd,x being −d,x assigned to path c and all other assignments as gc (yd ) =  1 N Nd,· ηc,l · Cd,x,l,· + ηcd,td,s ,zd,s,n + wd,s,n ∈{wd \vd,x }  Sd Nd,s L τwd,s,n , ρ (2) s=1 n=1 l=1 where Nd,· is the total number of tokens in document d. For a new node at level l on a new path cnew , we integrate over all possible values of ηcnew ,l . Sampling t: For each group wd,s we need to sample a table td,s . The conditional distribution of a table t given wd,s and other assignments is proportional to the number of sentences sitting at t times the probability of wd,s and yd being observed under this assignment. This is P (td,s = t | rest) ∝ P (td,s = t | t−s ) · P (wd,s , yd | td,s = t, w−d,s , t−d,s , z, c, η) d ∝ −d,s −d,s −d,s Sd,t · fcd,t (wd,s ) · gcd,t (yd ), for existing table t; (3) −d,s −d,s α · c∈C + P (cd,tnew = c | c−d,s ) · fc (wd,s ) · gc (yd ), for new table tnew . For a new table tnew , we need to sum over all possible paths C + of the tree, including new ones. For example, the set C + for the tree shown in Figure 2 consists of four existing paths (ending at one of the four leaf nodes) and three possible new paths (a new leaf off of one of the three internal nodes). The prior probability of path c is: P (cd,tnew = c | c−d,s ) ∝       L l=2 −d,s Mc,l −d,s Mc,l−1 + γl−1  γl∗    −d,s M ∗ cnew ,l∗ + γl , l∗ l=2 for an existing path c; (4) −d,s Mcnew ,l , for a new path cnew which consists of an existing path −d,s Mcnew ,l−1 + γl−1 from the root to a node at level l∗ and a new node. Sampling z: After assigning a sentence wd,s to a table, we assign each token wd,s,n to a level to choose a dish from the combo. The probability of assigning wd,s,n to level l is −s,n P (zd,s,n = l | rest) ∝ P (zd,s,n = l | zd )P (wd,s,n , yd | zd,s,n = l, w−d,s,n , z −d,s,n , t, c, η) (5) The ﬁrst factor captures the probability that a customer in restaurant d is assigned to level l, conditioned on the level assignments of all other customers in restaurant d, and is equal to P (zd,s,n = −s,n l | zd ) = −d,s,n mπ + Nd,·,l −d,s,n π + Nd,·,≥l l−1 −d,s,n (1 − m)π + Nd,·,>j −d,s,n π + Nd,·,≥j j=1 , The second factor is the probability of observing wd,s,n and yd , given that wd,s,n is assigned to level −d,s,n −d,s,n l: P (wd,s,n , yd | zd,s,n = l, w−d,s,n , z −d,s,n , t, c, η) = fcd,t (wd,s,n ) · gcd,t (yd ). d,s d,s Sampling c: After assigning customers to tables and levels, we also sample path assignments for all tables. This is important since it can change the assignments of all customers sitting at a table, which leads to a well-mixed Markov chain and faster convergence. The probability of assigning table t in restaurant d to a path c is P (cd,t = c | rest) ∝ P (cd,t = c | c−d,t ) · P (wd,t , yd | cd,t = c, w−d,t , c−d,t , t, z, η) (6) where we slightly abuse the notation by using wd,t ≡ ∪{s|td,s =t} wd,s to denote the set of customers in all the groups sitting at table t in restaurant d. The ﬁrst factor is the prior probability of a path given all tables’ path assignments c−d,t , excluding table t in restaurant d and is given in Equation 4. The second factor in Equation 6 is the probability of observing wd,t and yd given the new path −d,t −d,t assignments, P (wd,t , yd | cd,t = c, w−d,t , c−d,t , t, z, η) = fc (wd,t ) · gc (yd ). 4 Optimizing η and τ : We optimize the regression parameters η and τ via the likelihood, 1 L(η, τ ) = − 2ρ D 1 ¯ ¯ (yd − η zd − τ wd ) − 2σ T d=1 T K+ 2 (ηk − µ)2 − k=1 1 ω V |τv |, (7) v=1 where K + is the number of nodes in the tree.2 This maximization is performed using L-BFGS [13]. 4 Data: Congress, Products, Films We conduct our experiments using three datasets: Congressional ﬂoor debates, Amazon product reviews, and movie reviews. For all datasets, we remove stopwords, add bigrams to the vocabulary, and ﬁlter the vocabulary using tf-idf.3 • U.S Congressional ﬂoor debates: We downloaded debates of the 109th US Congress from GovTrack4 and preprocessed them as in Thomas et al. [14]. To remove uninterestingly non-polarized debates, we ignore bills with less than 20% “Yea” votes or less than 20% “Nay” votes. Each document d is a turn (a continuous utterance by a single speaker, i.e. speech segment [14]), and its response variable yd is the ﬁrst dimension of the speaker’s DW- NOMINATE score [15], which captures the traditional left-right political distinction.5 After processing, our corpus contains 5,201 turns in the House, 3,060 turns in the Senate, and 5,000 words in the vocabulary.6 • Amazon product reviews: From a set of Amazon reviews of manufactured products such as computers, MP 3 players, GPS devices, etc. [16], we focused on the 50 most frequently reviewed products. After ﬁltering, this corpus contains 37,191 reviews with a vocabulary of 5,000 words. We use the rating associated with each review as the response variable yd .7 • Movie reviews: Our third corpus is a set of 5,006 reviews of movies [17], again using review ratings as the response variable yd , although in this corpus the ratings are normalized to the range from 0 to 1. After preprocessing, the vocabulary contains 5,000 words. 5 Evaluating Prediction S H L DA’s response variable predictions provide a formally rigorous way to assess whether it is an improvement over prior methods. We evaluate effectiveness in predicting values of the response variables for unseen documents in the three datasets. For comparison we consider these baselines: • Multiple linear regression (MLR) models the response variable as a linear function of multiple features (or regressors). Here, we consider two types of features: topic-based features and lexicallybased features. Topic-based MLR, denoted by MLR - LDA, uses the topic distributions learned by vanilla LDA as features [12], while lexically-based MLR, denoted by MLR - VOC, uses the frequencies of words in the vocabulary as features. MLR - LDA - VOC uses both features. • Support vector regression (SVM) is a discriminative method [18] that uses LDA topic distributions (SVM - LDA), word frequencies (SVM - VOC), and both (SVM - LDA - VOC) as features.8 • Supervised topic model (SLDA): we implemented SLDA using Gibbs sampling. The version of SLDA we use is slightly different from the original SLDA described in [12], in that we place a Gaussian prior N (0, 1) over the regression parameters to perform L2-norm regularization.9 For parametric models (LDA and SLDA), which require the number of topics K to be speciﬁed beforehand, we use K ∈ {10, 30, 50}. We use symmetric Dirichlet priors in both LDA and SLDA, initialize The superscript + is to denote that this number is unbounded and varies during the sampling process. To ﬁnd bigrams, we begin with bigram candidates that occur at least 10 times in the corpus and use Pearson’s χ2 -test to ﬁlter out those that have χ2 -value less than 5, which corresponds to a signiﬁcance level of 0.025. We then treat selected bigrams as single word types and add them to the vocabulary. 2 3 4 http://www.govtrack.us/data/us/109/ 5 Scores were downloaded from http://voteview.com/dwnomin_joint_house_and_senate.htm 6 Data will be available after blind review. 7 The ratings can range from 1 to 5, but skew positive. 8 9 http://svmlight.joachims.org/ This performs better than unregularized SLDA in our experiments. 5 Floor Debates House-Senate Senate-House PCC ↑ MSE ↓ PCC ↑ MSE ↓ Amazon Reviews PCC ↑ MSE ↓ Movie Reviews PCC ↑ MSE ↓ SVM - LDA 10 SVM - LDA 30 SVM - LDA 50 SVM - VOC SVM - LDA - VOC 0.173 0.172 0.169 0.336 0.256 0.861 0.840 0.832 1.549 0.784 0.08 0.155 0.215 0.131 0.246 1.247 1.183 1.135 1.467 1.101 0.157 0.277 0.245 0.373 0.371 1.241 1.091 1.130 0.972 0.965 0.327 0.365 0.395 0.584 0.585 0.970 0.938 0.906 0.681 0.678 MLR - LDA 10 MLR - LDA 30 MLR - LDA 50 MLR - VOC MLR - LDA - VOC 0.163 0.160 0.150 0.322 0.319 0.735 0.737 0.741 0.889 0.873 0.068 0.162 0.248 0.191 0.194 1.151 1.125 1.081 1.124 1.120 0.143 0.258 0.234 0.408 0.410 1.034 1.065 1.114 0.869 0.860 0.328 0.367 0.389 0.568 0.581 0.957 0.936 0.914 0.721 0.702 SLDA 10 SLDA 30 SLDA 50 0.154 0.174 0.254 0.729 0.793 0.897 0.090 0.128 0.245 1.145 1.188 1.184 0.270 0.357 0.241 1.113 1.146 1.939 0.383 0.433 0.503 0.953 0.852 0.772 S H L DA 0.356 0.753 0.303 1.076 0.413 0.891 0.597 0.673 Models Table 2: Regression results for Pearson’s correlation coefﬁcient (PCC, higher is better (↑)) and mean squared error (MSE, lower is better (↓)). Results on Amazon product reviews and movie reviews are averaged over 5 folds. Subscripts denote the number of topics for parametric models. For SVM - LDA - VOC and MLR - LDA - VOC, only best results across K ∈ {10, 30, 50} are reported. Best results are in bold. the Dirichlet hyperparameters to 0.5, and use slice sampling [19] for updating hyperparameters. For SLDA , the variance of the regression is set to 0.5. For S H L DA , we use trees with maximum depth of three. We slice sample m, π, β and γ, and ﬁx µ = 0, σ = 0.5, ω = 0.5 and ρ = 0.5. We found that the following set of initial hyperparameters works reasonably well for all the datasets in our experiments: m = 0.5, π = 100, β = (1.0, 0.5, 0.25), γ = (1, 1), α = 1. We also set the regression parameter of the root node to zero, which speeds inference (since it is associated with every document) and because it is reasonable to assume that it would not change the response variable. To compare the performance of different methods, we compute Pearson’s correlation coefﬁcient (PCC) and mean squared error (MSE) between the true and predicted values of the response variables and average over 5 folds. For the Congressional debate corpus, following Yu et al. [20], we use documents in the House to train and test on documents in the Senate and vice versa. Results and analysis Table 2 shows the performance of all models on our three datasets. Methods that only use topic-based features such as SVM - LDA and MLR - LDA do poorly. Methods only based on lexical features like SVM - VOC and MLR - VOC outperform methods that are based only on topic features signiﬁcantly for the two review datasets, but are comparable or worse on congressional debates. This suggests that reviews have more highly discriminative words than political speeches (Table 3). Combining topic-based and lexically-based features improves performance, which supports our choice of incorporating both per-topic and per-word regression parameters in S H L DA. In all cases, S H L DA achieves strong performance results. For the two cases where S H L DA was second best in MSE score (Amazon reviews and House-Senate), it outperforms other methods in PCC. Doing well in PCC for these two datasets is important since achieving low MSE is relatively easier due to the response variables’ bimodal distribution in the ﬂoor debates and positively-skewed distribution in Amazon reviews. For the ﬂoor debate dataset, the results of the House-Senate experiment are generally better than those of the Senate-House experiment, which is consistent with previous results [20] and is explained by the greater number of debates in the House. 6 Qualitative Analysis: Agendas and Framing/Perspective Although a formal coherence evaluation [21] remains a goal for future work, a qualitative look at the topic hierarchy uncovered by the model suggests that it is indeed capturing agenda/framing structure as discussed in Section 1. In Figure 3, a portion of the topic hierarchy induced from the Congressional debate corpus, Nodes A and B illustrate agendas—issues introduced into political discourse—associated with a particular ideology: Node A focuses on the hardships of the poorer victims of hurricane Katrina and is associated with Democrats, and text associated with Node E discusses a proposed constitutional amendment to ban ﬂag burning and is associated with Republicans. Nodes C and D, children of a neutral “tax” topic, reveal how parties frame taxes as gains in terms of new social services (Democrats) and losses for job creators (Republicans). 6 E ﬂag constitution freedom supreme_court elections rights continuity american_ﬂag constitutional_amendm ent gses credit_rating fannie_mae regulator freddie_mac market ﬁnancial_services agencies competition investors fannie bill speaker time amendment chairman people gentleman legislation congress support R:1.1 R:0 A minimum_wage commission independent_commissio n investigate hurricane_katrina increase investigation R:1.0 B percent tax economy estate_tax capital_gains money taxes businesses families tax_cuts pay tax_relief social_security affordable_housing housing manager fund activities funds organizations voter_registration faithbased nonproﬁts R:0.4 D:1.7 C death_tax jobs businesses business family_businesses equipment productivity repeal_permanency employees capital farms D REPUBLICAN billion budget children cuts debt tax_cuts child_support deﬁcit education students health_care republicans national_debt R:4.3 D:2.2 DEMOCRAT D:4.5 Figure 3: Topics discovered from Congressional ﬂoor debates. Many ﬁrst-level topics are bipartisan (purple), while lower level topics are associated with speciﬁc ideologies (Democrats blue, Republicans red). For example, the “tax” topic (B) is bipartisan, but its Democratic-leaning child (D) focuses on social goals supported by taxes (“children”, “education”, “health care”), while its Republican-leaning child (C) focuses on business implications (“death tax”, “jobs”, “businesses”). The number below each topic denotes the magnitude of the learned regression parameter associated with that topic. Colors and the numbers beneath each topic show the regression parameter η associated with the topic. Figure 4 shows the topic structure discovered by S H L DA in the review corpus. Nodes at higher levels are relatively neutral, with relatively small regression parameters.10 These nodes have general topics with no speciﬁc polarity. However, the bottom level clearly illustrates polarized positive/negative perspective. For example, Node A concerns washbasins for infants, and has two polarized children nodes: reviewers take a positive perspective when their children enjoy the product (Node B: “loves”, “splash”, “play”) but have negative reactions when it leaks (Node C: “leak(s/ed/ing)”). transmitter ipod car frequency iriver product transmitters live station presets itrip iriver_aft charges international_mode driving P:6.6 tried waste batteries tunecast rabbit_ears weak terrible antenna hear returned refund returning item junk return A D router setup network expander set signal wireless connect linksys connection house wireless_router laptop computer wre54g N:2.2 N:1.0 tivo adapter series adapters phone_line tivo_wireless transfer plugged wireless_adapter tivos plug dvr tivo_series tivo_box tivo_unit P:5.1 tub baby water bath sling son daughter sit bathtub sink newborn months bath_tub bathe bottom N:8.0 months loves hammock splash love baby drain eurobath hot ﬁts wash play infant secure slip P:7.5 NEGATIVE N:0 N:2.7 B POSITIVE time bought product easy buy love using price lot able set found purchased money months transmitter car static ipod radio mp3_player signal station sound music sound_quality volume stations frequency frequencies C leaks leaked leak leaking hard waste snap suction_cups lock tabs difﬁcult bottom tub_leaks properly ring N:8.9 monitor radio weather_radio night baby range alerts sound sony house interference channels receiver static alarm N:1.7 hear feature static monitors set live warning volume counties noise outside alert breathing rechargeable_battery alerts P:6.2 version hours phone F ﬁrmware told spent linksys tech_support technical_supportcusto mer_service range_expander support return N:10.6 E router ﬁrmware ddwrt wrt54gl version wrt54g tomato linksys linux routers ﬂash versions browser dlink stable P:4.8 z22 palm pda palm_z22 calendar software screen contacts computer device sync information outlook data programs N:1.9 headphones sound pair bass headset sound_quality ear ears cord earbuds comfortable hear head earphones ﬁt N:1.3 appointments organized phone lists handheld organizer photos etc pictures memos track bells books purse whistles P:5.8 noise_canceling noise sony exposed noise_cancellation stopped wires warranty noise_cancelling bud pay white_noise disappointed N:7.6 bottles bottle baby leak nipples nipple avent avent_bottles leaking son daughter formula leaks gas milk comfortable sound phones sennheiser bass px100 px100s phone headset highs portapros portapro price wear koss N:2.0 leak formula bottles_leak feeding leaked brown frustrating started clothes waste newborn playtex_ventaire soaked matter N:7.9 P:5.7 nipple breast nipples dishwasher ring sippy_cups tried breastfeed screwed breastfeeding nipple_confusion avent_system bottle P:6.4 Figure 4: Topics discovered from Amazon reviews. Higher topics are general, while lower topics are more speciﬁc. The polarity of the review is encoded in the color: red (negative) to blue (positive). Many of the ﬁrstlevel topics have no speciﬁc polarity and are associated with a broad class of products such as “routers” (Node D). However, the lowest topics in the hierarchy are often polarized; one child topic of “router” focuses on upgradable ﬁrmware such as “tomato” and “ddwrt” (Node E, positive) while another focuses on poor “tech support” and “customer service” (Node F, negative). The number below each topic is the regression parameter learned with that topic. In addition to the per-topic regression parameters, S H L DA also associates each word with a lexical regression parameter τ . Table 3 shows the top ten words with highest and lowest τ . The results are unsuprising, although the lexical regression for the Congressional debates is less clear-cut than other 10 All of the nodes at the second level have slightly negative values for the regression parameters mainly due to the very skewed distribution of the review ratings in Amazon. 7 datasets. As we saw in Section 5, for similar datasets, S H L DA’s context-speciﬁc regression is more useful when global lexical weights do not readily differentiate documents. Dataset Floor Debates Amazon Reviews Movie Reviews Top 10 words with positive weights bringing, private property, illegally, tax relief, regulation, mandates, constitutional, committee report, illegal alien highly recommend, pleased, love, loves, perfect, easy, excellent, amazing, glad, happy hilarious, fast, schindler, excellent, motion pictures, academy award, perfect, journey, fortunately, ability Top 10 words with negative weights bush administration, strong opposition, ranking, republicans, republican leadership, secret, discriminate, majority, undermine waste, returned, return, stopped, leak, junk, useless, returning, refund, terrible bad, unfortunately, supposed, waste, mess, worst, acceptable, awful, suppose, boring Table 3: Top words based on the global lexical regression coefﬁcient, τ . For the ﬂoor debates, positive τ ’s are Republican-leaning while negative τ ’s are Democrat-leaning. 7 Related Work S H L DA joins a family of LDA extensions that introduce hierarchical topics, supervision, or both. Owing to limited space, we focus here on related work that combines the two. Petinot et al. [22] propose hierarchical Labeled LDA (hLLDA), which leverages an observed document ontology to learn topics in a tree structure; however, hLLDA assumes that the underlying tree structure is known a priori. SSHLDA [23] generalizes hLLDA by allowing the document hierarchy labels to be partially observed, with unobserved labels and topic tree structure then inferred from the data. Boyd-Graber and Resnik [24] used hierarchical distributions within topics to learn topics across languages. In addition to these “upstream” models [25], Perotte et al. [26] propose a “downstream” model called HSLDA , which jointly models documents’ hierarchy of labels and topics. HSLDA ’s topic structure is ﬂat, however, and the response variable is a hierarchy of labels associated with each document, unlike S H L DA’s continuous response variable. Finally, another body related body of work includes models that jointly capture topics and other facets such as ideologies/perspectives [27, 28] and sentiments/opinions [29], albeit with discrete rather than continuously valued responses. Computational modeling of sentiment polarity is a voluminous ﬁeld [30], and many computational political science models describe agendas [5] and ideology [31]. Looking at framing or bias at the sentence level, Greene and Resnik [32] investigate the role of syntactic structure in framing, Yano et al. [33] look at lexical indications of sentence-level bias, and Recasens et al. [34] develop linguistically informed sentence-level features for identifying bias-inducing words. 8 Conclusion We have introduced S H L DA, a model that associates a continuously valued response variable with hierarchical topics to capture both the issues under discussion and alternative perspectives on those issues. The two-level structure improves predictive performance over existing models on multiple datasets, while also adding potentially insightful hierarchical structure to the topic analysis. Based on a preliminary qualitative analysis, the topic hierarchy exposed by the model plausibly captures the idea of agenda setting, which is related to the issues that get discussed, and framing, which is related to authors’ perspectives on those issues. We plan to analyze the topic structure produced by S H L DA with political science collaborators and more generally to study how S H L DA and related models can help analyze and discover useful insights from political discourse. Acknowledgments This research was supported in part by NSF under grant #1211153 (Resnik) and #1018625 (BoydGraber and Resnik). Any opinions, ﬁndings, conclusions, or recommendations expressed here are those of the authors and do not necessarily reﬂect the view of the sponsor. 8 References [1] McCombs, M. The agenda-setting role of the mass media in the shaping of public opinion. North, 2009(05-12):21, 2002. [2] McCombs, M., S. Ghanem. The convergence of agenda setting and framing. In Framing public life. 2001. [3] Baumgartner, F. R., S. L. De Boef, A. E. Boydstun. The decline of the death penalty and the discovery of innocence. Cambridge University Press, 2008. [4] Blei, D. M., A. Ng, M. Jordan. Latent Dirichlet allocation. JMLR, 3, 2003. [5] Grimmer, J. A Bayesian hierarchical topic model for political texts: Measuring expressed agendas in Senate press releases. Political Analysis, 18(1):1–35, 2010. [6] Zhang, J. Explore objects and categories in unexplored environments based on multimodal data. Ph.D. thesis, University of Hamburg, 2012. [7] Blei, D. M., T. L. Grifﬁths, M. I. Jordan. The nested Chinese restaurant process and Bayesian nonparametric inference of topic hierarchies. J. ACM, 57(2), 2010. [8] Teh, Y. W., M. I. Jordan, M. J. Beal, et al. Hierarchical Dirichlet processes. JASA, 101(476), 2006. [9] Paisley, J. W., C. Wang, D. M. Blei, et al. Nested hierarchical Dirichlet processes. arXiv:1210.6738, 2012. [10] Ahmed, A., L. Hong, A. Smola. The nested Chinese restaurant franchise process: User tracking and document modeling. In ICML. 2013. [11] Kim, J. H., D. Kim, S. Kim, et al. Modeling topic hierarchies with the recursive Chinese restaurant process. In CIKM, pages 783–792. 2012. [12] Blei, D. M., J. D. McAuliffe. Supervised topic models. In NIPS. 2007. [13] Liu, D., J. Nocedal. On the limited memory BFGS method for large scale optimization. Math. Prog., 1989. [14] Thomas, M., B. Pang, L. Lee. Get out the vote: Determining support or opposition from Congressional ﬂoor-debate transcripts. In EMNLP. 2006. [15] Lewis, J. B., K. T. Poole. Measuring bias and uncertainty in ideal point estimates via the parametric bootstrap. Political Analysis, 12(2), 2004. [16] Jindal, N., B. Liu. Opinion spam and analysis. In WSDM. 2008. [17] Pang, B., L. Lee. Seeing stars: Exploiting class relationships for sentiment categorization with respect to rating scales. In ACL. 2005. [18] Joachims, T. Making large-scale SVM learning practical. In Adv. in Kernel Methods - SVM. 1999. [19] Neal, R. M. Slice sampling. Annals of Statistics, 31:705–767, 2003. [20] Yu, B., D. Diermeier, S. Kaufmann. Classifying party afﬁliation from political speech. JITP, 2008. [21] Chang, J., J. Boyd-Graber, C. Wang, et al. Reading tea leaves: How humans interpret topic models. In NIPS. 2009. [22] Petinot, Y., K. McKeown, K. Thadani. A hierarchical model of web summaries. In HLT. 2011. [23] Mao, X., Z. Ming, T.-S. Chua, et al. SSHLDA: A semi-supervised hierarchical topic model. In EMNLP. 2012. [24] Boyd-Graber, J., P. Resnik. Holistic sentiment analysis across languages: Multilingual supervised latent Dirichlet allocation. In EMNLP. 2010. [25] Mimno, D. M., A. McCallum. Topic models conditioned on arbitrary features with Dirichlet-multinomial regression. In UAI. 2008. [26] Perotte, A. J., F. Wood, N. Elhadad, et al. Hierarchically supervised latent Dirichlet allocation. In NIPS. 2011. [27] Ahmed, A., E. P. Xing. Staying informed: Supervised and semi-supervised multi-view topical analysis of ideological perspective. In EMNLP. 2010. [28] Eisenstein, J., A. Ahmed, E. P. Xing. Sparse additive generative models of text. In ICML. 2011. [29] Jo, Y., A. H. Oh. Aspect and sentiment uniﬁcation model for online review analysis. In WSDM. 2011. [30] Pang, B., L. Lee. Opinion Mining and Sentiment Analysis. Now Publishers Inc, 2008. [31] Monroe, B. L., M. P. Colaresi, K. M. Quinn. Fightin’words: Lexical feature selection and evaluation for identifying the content of political conﬂict. Political Analysis, 16(4):372–403, 2008. [32] Greene, S., P. Resnik. More than words: Syntactic packaging and implicit sentiment. In NAACL. 2009. [33] Yano, T., P. Resnik, N. A. Smith. Shedding (a thousand points of) light on biased language. In NAACL-HLT Workshop on Creating Speech and Language Data with Amazon’s Mechanical Turk. 2010. [34] Recasens, M., C. Danescu-Niculescu-Mizil, D. Jurafsky. Linguistic models for analyzing and detecting biased language. In ACL. 2013. 9

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