acl acl2010 acl2010-161 knowledge-graph by maker-knowledge-mining

161 acl-2010-Learning Better Data Representation Using Inference-Driven Metric Learning


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Author: Paramveer S. Dhillon ; Partha Pratim Talukdar ; Koby Crammer

Abstract: We initiate a study comparing effectiveness of the transformed spaces learned by recently proposed supervised, and semisupervised metric learning algorithms to those generated by previously proposed unsupervised dimensionality reduction methods (e.g., PCA). Through a variety of experiments on different realworld datasets, we find IDML-IT, a semisupervised metric learning algorithm to be the most effective.

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 A Mountain View, CA, USA The Technion, Haifa, Israel dhi l lon@ cis . [sent-9, score-0.066]

2 i l Abstract We initiate a study comparing effectiveness of the transformed spaces learned by recently proposed supervised, and semisupervised metric learning algorithms to those generated by previously proposed unsupervised dimensionality reduction methods (e. [sent-15, score-0.898]

3 Through a variety of experiments on different realworld datasets, we find IDML-IT, a semisupervised metric learning algorithm to be the most effective. [sent-18, score-0.387]

4 1 Introduction Because of the high-dimensional nature of NLP datasets, estimating a large number of parameters (a parameter for each dimension), often from a limited amount of labeled data, is a challenging task for statistical learners. [sent-19, score-0.061]

5 Faced with this challenge, various unsupervised dimensionality reduction methods have been developed over the years, e. [sent-20, score-0.175]

6 Recently, several supervised metric learning algorithms have been proposed (Davis et al. [sent-23, score-0.389]

7 , 2010) is another such method which exploits labeled as well as unlabeled data during metric learning. [sent-26, score-0.416]

8 These methods learn a Mahalanobis distance metric to compute distance between a pair of data instances, which can also be interpreted as learning a transformation of the input data, as we shall see in Section 2. [sent-27, score-0.597]

9 In this paper, we address that gap: we compare effectiveness of classifiers trained on the transformed spaces learned by metric learning methods to those generated by previously proposed unsupervised dimensionality reduction methods. [sent-31, score-0.786]

10 We find IDML-IT, a semi-supervised metric learning algorithm to be the most effective. [sent-32, score-0.314]

11 1 Relationship between Metric Learning and Linear Projection We first establish the well-known equivalence between learning a Mahalanobis distance measure and Euclidean distance in a linearly transformed space of the data (Weinberger and Saul, 2009). [sent-34, score-0.449]

12 Let A be a d d positive definite matrix which parameAte brieze as d t×hed M poahsiatilavneo dbeifsi distance, dA(xi, xj), a bme-tween instances xi and xj, as shown in Equation 1. [sent-35, score-0.514]

13 Since A is positive definite, we can decompose it as A = P>P, where P is another matrix of size d × d. [sent-36, score-0.238]

14 In this paper, we are interested in learning a better representation of the data (i. [sent-38, score-0.044]

15 , projection matrix P), and we shall achieve that goal by learning the corresponding Mahalanobis distance parameter A. [sent-40, score-0.487]

16 We shall now review two recently proposed metric learning algorithms. [sent-41, score-0.41]

17 , 2007) assumes the availability of prior knowledge about inter-instance distances. [sent-46, score-0.04]

18 In this scheme, two instances are considered similar if the Mahalanobis distance between them is upper bounded, i. [sent-47, score-0.249]

19 Similarly, thweor ein ustances are considered dissimilar if the distance between them is larger than certain threshold l, i. [sent-50, score-0.093]

20 Similar instances are represented by se)t S ≥, w l. [sent-53, score-0.156]

21 In addition to prior knowledge about interinstance distances, sometimes prior information about the matrix A, denoted by A0, itself may also be available. [sent-55, score-0.27]

22 In such cases, we would like the learned matrix A to be as close as possible to the prior matrix A0. [sent-59, score-0.492]

23 ITML combines these two types of prior information, i. [sent-60, score-0.04]

24 , knowledge about inter-instance distances, and prior matrix A0, in order to learn the matrix A by solving the optimization problem shown in (2). [sent-62, score-0.42]

25 exactly solving the problem in (2) is not possible, slack variables may be introduced to the ITML objective. [sent-68, score-0.028]

26 Let X be the d n matrix of n instances in a dL-edtim Xen bseio tnhael space. [sent-73, score-0.346]

27 mOauttr oxf othfe n n instances, nl instances are labeled, while the remaining nu instances are unlabeled, with n = nl + nu. [sent-74, score-0.752]

28 Let S be ×× a n n diagonal matrix with Sii = 1iff instance xi is labeled. [sent-75, score-0.393]

29 Y is the n m matrix storing training label information, ei fn any. [sent-77, score-0.257]

30 , output moaft any classifier, dw litahdenoting score of label lat node i. [sent-80, score-0.067]

31 The ITML metric learning algorithm, which we reviewed in Section 2. [sent-82, score-0.314]

32 2, is supervised in nature, and hence it does not exploit widely available unlabeled data. [sent-83, score-0.16]

33 , 2010), a recently proposed metric learning framework which combines an existing supervised metric learning algorithm (such as ITML) along with transductive graph-based label inference to learn a new distance metric from labeled as well as unlabeled data combined. [sent-85, score-1.37]

34 In self-training styled iterations, IDML alternates between metric learning and label inference; with output of label inference used during next round of metric learning, and so on. [sent-86, score-0.769]

35 IDML starts out with the assumption that existing supervised metric learning algorithms, such Yˆ m Yˆil as ITML, can learn a better metric if the number of available labeled instances is increased. [sent-87, score-0.876]

36 Since we are focusing on the semi-supervised learning (SSL) setting with nl labeled and nu unlabeled instances, the idea is to automatically label the unlabeled instances using a graph based SSL algorithm, and then include instances with low assigned label entropy (i. [sent-88, score-1.073]

37 , high confidence label assignments) in the next round of metric learning. [sent-90, score-0.388]

38 The number of instances added in each iteration depends on the threshold β1 . [sent-91, score-0.156]

39 This process is continued until no new instances can be added to the set of labeled instances, which can happen when either all the instances are already exhausted, or when none of the remaining unlabeled instances can be assigned labels with high confidence. [sent-92, score-0.692]

40 In Line 3, any supervised metric learner, such as ITML, may be used as the METRICLEARNER. [sent-94, score-0.345]

41 Using the distance metric learned in Line 3, a new k-NN graph is constructed in Line 4 , whose edge weight matrix is stored in W. [sent-95, score-0.661]

42 , Uii = 0, ∀i) 10: return A cian, and D is a diagonal matrix with Dii = Pj Wij. [sent-103, score-0.227]

43 The constraint, = in (3) mPakes sure that labels on training instances are not changed during inference. [sent-104, score-0.19]

44 , = 0) is considered a new labeled training instance, i. [sent-107, score-0.061]

45 , Uii = 1, for next round of metric learning if the instance has been assigned labels with high confidence in the current iteration, i. [sent-109, score-0.432]

46 Finally in Line 7, training instance label) )in ≤foβr m). [sent-114, score-0.033]

47 This iterative process is continued till no new labeled instance can be added, i. [sent-116, score-0.138]

48 1 Setup SˆYˆ0, TableE1:KWDBe icaVtobcerasKoDhkcsenBritcpsonD1i74m8f35 t9eh258n4e613s 9id5oantseBaY luae ns ecd inSec- tion 3. [sent-122, score-0.028]

49 All datasets are binary with 1500 total instances in each. [sent-123, score-0.239]

50 Description of the datasets used during experiments in Section 3 are presented in Table 1. [sent-124, score-0.083]

51 The first four datasets Electronics, Books, Kitchen, and DVDs are from the sentiment domain and previously used in (Blitzer et al. [sent-125, score-0.083]

52 For details regarding features and data pre-processing, we refer the reader to the origin of these datasets cited above. [sent-128, score-0.083]

53 We experiment with the following ways of estimating transformation matrix P: Original2: We set P = I, where I the is d d identity matrix. [sent-131, score-0.23]

54 RP: The data is first projected into a lower dimensional space using the Random Projection (RP) method (Bingham and Mannila, 2001). [sent-133, score-0.16]

55 Dimensionality of the target space was set at = as prescribed in d0 ? [sent-134, score-0.056]

56 We use the projection matrix constructed by RP as P. [sent-137, score-0.293]

57 25 for the experiments in Section 3, which has the effect of projecting the data into a much lower dimensional space (84 for the experiments in this section). [sent-140, score-0.141]

58 This presents an interesting evaluation setting as we already run evaluations in much higher di- mensional space (e. [sent-141, score-0.056]

59 PCA: Data instances are first projected into a lower dimensional space using Principal Components Analysis (PCA) (Jolliffe, 2002) . [sent-144, score-0.316]

60 Following (Weinberger and Saul, 2009), dimensionality of the projected space was set at 250 for all experiments. [sent-145, score-0.232]

61 In this case, we used the projection matrix generated by PCA as P. [sent-146, score-0.293]

62 ITML: A is learned by applying ITML (see Section 2. [sent-147, score-0.072]

63 2) on the Original space (above), and then we decompose A as A = to obtain P. [sent-148, score-0.104]

64 P>P 2Note that “Original” in the results tables refers to original space with features occurring more than 20 times. [sent-149, score-0.056]

65 All hyperparameters are tuned on a separate random split. [sent-156, score-0.205]

66 All hyperparameters are tuned on a separate random split. [sent-162, score-0.205]

67 IDML-IT: A is learned by applying IDML (Algorithm 1) (see Section 2. [sent-163, score-0.072]

68 3) on the Original space (above); with ITML used as METRICLEARNER in IDML (Line 3 in Algorithm 1). [sent-164, score-0.056]

69 In this case, we treat the set of test instances (without their gold labels) as the unlabeled data. [sent-165, score-0.241]

70 In other words, we essentially work in the transductive setting (Vapnik, 2000). [sent-166, score-0.052]

71 Once again, we decompose A as A = P>P to obtain P. [sent-167, score-0.048]

72 We also experimented with the supervised large-margin metric learning algorithm (LMNN) presented in (Weinberger and Saul, 2009). [sent-168, score-0.389]

73 Each input instance, x, is now pro- jected into the transformed space as Px. [sent-170, score-0.188]

74 We now train different classifiers on this transformed space. [sent-171, score-0.132]

75 2 Supervised Classification We train a SVM classifier, with an RBF kernel, on the transformed space generated by the projection matrix P. [sent-174, score-0.481]

76 SVM hyperparameter, C and RBF kernel bandwidth, were tuned on a separate development split. [sent-175, score-0.147]

77 Experimental results with 50 and 100 labeled instances are shown in Table 2, and Table 3, respectively. [sent-176, score-0.217]

78 3 Semi-Supervised Classification In this section, we trained the GRF classifier (see Equation 3), a graph-based semi-supervised learning (SSL) algorithm (Zhu et al. [sent-180, score-0.073]

79 , 2003), using Gaussian kernel parameterized by A = P>P to set edge weights. [sent-181, score-0.07]

80 During graph construction, each node was connected to its k nearest neighbors, with k treated as a hyperparameter and tuned on a separate development set. [sent-182, score-0.21]

81 Experimental results with 50 and 100 labeled instances are shown in Table 4, and Table 5, respectively. [sent-183, score-0.217]

82 As before, we experimented with nl = 50 and nl = 100. [sent-184, score-0.314]

83 Once again, we observe that IDML-IT is the most effective method, with the GRF classifier trained on the data representation learned by IDML-IT achieving best performance in all settings. [sent-185, score-0.101]

84 All hyperparameters are tuned on a separate random split. [sent-189, score-0.205]

85 All results are averaged over using different methods (see Section 3. [sent-191, score-0.059]

86 All hyperparameters are tuned on a separate random split. [sent-194, score-0.205]

87 4 Conclusion In this paper, we compared the effectiveness of the transformed spaces learned by recently proposed supervised, and semi-supervised metric learning algorithms to those generated by previously proposed unsupervised dimensionality reduction methods (e. [sent-195, score-0.825]

88 Through a variety of experiments on different real-world NLP datasets, we demonstrated that supervised as well as semisupervised classifiers trained on the space learned by IDML-IT consistently result in the lowest classification errors. [sent-199, score-0.276]

89 Random projection in dimensionality reduction: applications to image and text data. [sent-210, score-0.222]

90 Distance metric learning for large margin nearest neighbor classification. [sent-261, score-0.344]


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Abstract: In this paper, we study the problem of using an annotated corpus in English for the same natural language processing task in another language. While various machine translation systems are available, automated translation is still far from perfect. To minimize the noise introduced by translations, we propose to use only key ‘reliable” parts from the translations and apply structural correspondence learning (SCL) to find a low dimensional representation shared by the two languages. We perform experiments on an EnglishChinese sentiment classification task and compare our results with a previous cotraining approach. To alleviate the problem of data sparseness, we create extra pseudo-examples for SCL by making queries to a search engine. Experiments on real-world on-line review data demonstrate the two techniques can effectively improvetheperformancecomparedtoprevious work.

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