nips nips2013 nips2013-211 knowledge-graph by maker-knowledge-mining

211 nips-2013-Non-Linear Domain Adaptation with Boosting


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Author: Carlos J. Becker, Christos M. Christoudias, Pascal Fua

Abstract: A common assumption in machine vision is that the training and test samples are drawn from the same distribution. However, there are many problems when this assumption is grossly violated, as in bio-medical applications where different acquisitions can generate drastic variations in the appearance of the data due to changing experimental conditions. This problem is accentuated with 3D data, for which annotation is very time-consuming, limiting the amount of data that can be labeled in new acquisitions for training. In this paper we present a multitask learning algorithm for domain adaptation based on boosting. Unlike previous approaches that learn task-specific decision boundaries, our method learns a single decision boundary in a shared feature space, common to all tasks. We use the boosting-trick to learn a non-linear mapping of the observations in each task, with no need for specific a-priori knowledge of its global analytical form. This yields a more parameter-free domain adaptation approach that successfully leverages learning on new tasks where labeled data is scarce. We evaluate our approach on two challenging bio-medical datasets and achieve a significant improvement over the state of the art. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 This problem is accentuated with 3D data, for which annotation is very time-consuming, limiting the amount of data that can be labeled in new acquisitions for training. [sent-6, score-0.334]

2 In this paper we present a multitask learning algorithm for domain adaptation based on boosting. [sent-7, score-0.45]

3 Unlike previous approaches that learn task-specific decision boundaries, our method learns a single decision boundary in a shared feature space, common to all tasks. [sent-8, score-0.773]

4 This yields a more parameter-free domain adaptation approach that successfully leverages learning on new tasks where labeled data is scarce. [sent-10, score-0.684]

5 A possible solution is to treat each acquisition as a separate, but related classification problem, and exploit their possible relationship to learn from the supervised data available across all of them. [sent-18, score-0.277]

6 1(a,b) the task is mitochondria segmentation in both acquisitions. [sent-21, score-0.44]

7 Techniques in domain adaptation [1] and more generally multi-task learning [2, 3] seek to leverage data from a set of different yet related tasks or domains to help learn a classifier in a seemingly new task. [sent-23, score-0.64]

8 In domain adaptation, it is typically assumed that there is a fairly large amount of labeled data in one domain, commonly referred to as the source domain, and that a limited amount of supervision is available in the other, often called the target domain. [sent-24, score-0.607]

9 Our goal is to exploit the labeled data in the source domain to learn an accurate classifier in the target domain despite having only a few labeled samples in the latter. [sent-25, score-1.059]

10 1 Mitochondria Segmentation (3D stacks) (a) Striatum Path Classification (2D images to 3D stacks) (b) Hippocampus (c) Aerial road images (d) Neural Axons (OPF) Figure 1: (a,b) Slice cuts from two 3D Electron Microscopy acquisitions from different parts of the brain of a rat. [sent-27, score-0.387]

11 (c,d) 2D aerial road images and 3D neural axons from Olfactory Projection Fibers (OPF). [sent-28, score-0.391]

12 The data acquisition problem is unique to many multi-task learning problems, however, in that each task is in fact the same, but what has changed is that the features across different acquisitions have undergone some unknown transformation. [sent-30, score-0.503]

13 That is to say that each task can be well described by a single decision boundary in some common feature space that preserves the task-relevant features and discards the domain specific ones corresponding to unwanted acquisition artifacts. [sent-31, score-0.893]

14 This contrasts the more general multi-task setting where each task is comprised of both a common and task-specific boundary, even when mapped to a common feature space, as illustrated in Fig. [sent-32, score-0.28]

15 A method that can jointly optimize over the common decision boundary and shared feature space is therefore desired. [sent-34, score-0.528]

16 Linear latent variable methods such as those based on Canonical Correlation Analysis (CCA) [4, 5] can be applied to learn a shared feature space across the different acquisitions. [sent-35, score-0.381]

17 In this paper we propose a solution to the data acquisition problem and devise a method that can jointly solve for the non-linear decision boundary and transformations across tasks. [sent-39, score-0.435]

18 We assume that only the mappings are taskdependent and that in the shared space the problem is linearly separable and the decision boundary is common to all tasks. [sent-42, score-0.503]

19 We use the boosting-trick [8, 9, 10] to simultaneously learn the non-linear task-specific mappings as well as the decision boundary, with no need for specific a-priori knowledge of their global analytical form. [sent-43, score-0.262]

20 This yields a more parameter-free domain adaptation approach that successfully leverages learning on new tasks where labeled data is scarce. [sent-44, score-0.684]

21 We first consider the classification of curvilinear structures in 3D image stacks of Olfactory Projection Fibers (OPF) [11] using labeled 2D aerial road images. [sent-47, score-0.804]

22 We then perform mitochondria segmentation in large 3D Electron Microscopy (EM) stacks of neural rat tissue, demonstrating the ability of our algorithm to leverage labeled data from different data acquisitions on this challenging task. [sent-48, score-0.954]

23 On both datasets our approach obtains a significant improvement over using labeled data from either domain alone and outperforms recent multi-task learning baseline methods. [sent-49, score-0.372]

24 2 Related Work Initial ideas to multi-task learning exploited supervised data from related tasks to define a form of regularization in the target problem [2, 12]. [sent-50, score-0.265]

25 MTL assumes a single, pre-defined transformation φ(x) : X → Z and learns shared and task-specific linear boundaries in Z, namely β o , β 1 and β 2 ∈ Z. [sent-52, score-0.273]

26 In contrast, our DA approach learns a single linear boundary β in a common feature space Z, and task-specific mappings φ1 (x), φ2 (x) : X → Z. [sent-53, score-0.328]

27 as auxiliary problems [13], are used to learn a latent representation and find discriminative features shared across tasks. [sent-55, score-0.34]

28 This representation is then transferred to the target task to help regularize the solution and learn from fewer labeled examples. [sent-56, score-0.399]

29 More recent multi-task learning methods jointly optimize over both the shared and task-specific components of each task [3, 14, 10, 15]. [sent-62, score-0.22]

30 In particular, for each task their approach computes a linear decision boundary defined as a linear combination between a shared hyperplane, shared across tasks, and a task-specific one in either the original or a kernelized feature space. [sent-64, score-0.759]

31 For each task they optimize for a shared and task-specific decision boundary similar to [3], except nonlinearities are modeled using a boosted feature space. [sent-67, score-0.678]

32 As with other methods, however, additional parameters are required to control the degree of sharing between tasks that can be difficult to set, especially when one or more tasks have only a few labeled samples. [sent-68, score-0.338]

33 For many problems, such as those common to domain adaptation [1], the decision problem is in fact the same across tasks, however, the features of each task have undergone some unknown transformation. [sent-69, score-0.857]

34 Feature-based approaches seek to uncover this transformation by learning a mapping between the features across tasks [18, 19, 7]. [sent-70, score-0.237]

35 A cross-domain Mahalanobis distance metric was introduced in [18] that leverages across-task correspondences to learn a transformation from the source to target domain. [sent-71, score-0.36]

36 Shared latent variable models have also been proposed to learn a shared representation across multiple feature sources or tasks [4, 19, 6, 7, 21]. [sent-73, score-0.484]

37 In this paper, we exploit the boosting-trick [10] to handle non-linearities and learn a shared representation across tasks, overcoming these limitations. [sent-75, score-0.262]

38 This results in a more parameter-free, scalable domain adaptation approach that can leverage learning on new tasks where labeled data is scarce. [sent-76, score-0.702]

39 3 Our Approach We consider the problem of learning a binary decision function from supervised data collected across multiple tasks or domains. [sent-77, score-0.34]

40 In our setting, each task is an instance of the same underlying decision problem, however, its features are assumed to have undergone some unknown non-linear transformation. [sent-78, score-0.356]

41 , T tasks, where i=1 i t xt ∈ RD represents a feature vector for sample i in task t and yi ∈ {−1, 1} its label. [sent-82, score-0.33]

42 For each task, i we seek to learn a non-linear transformation, φt (xt ), that maps xt to a common, task-independent feature space, Z, accounting for any unwanted feature shift. [sent-83, score-0.385]

43 In what follows, we set H to be the set of regression trees or stumps [8] that in combination with τ t can be used to model highly complex, non-linear transformations. [sent-101, score-0.325]

44 Assuming that the problem is linearly separable in Z the predictive function ft (·) : RD → R for each task can then be written as M ft (x) = β φt (xt ) = βj hj (xt − τjt ) (2) j=1 where β ∈ RM is a linear decision boundary in Z that is common to all tasks. [sent-102, score-0.74]

45 This contrasts previous approaches to multi-task learning such as [3, 10] that learn a separate decision boundary per task and, as we show later, is better suited for problems in domain adaptation. [sent-103, score-0.748]

46 We learn the functions ft (·) by minimizing the exponential loss on the training data across each task T β ∗ , Γ∗ = min β,Γ L(β, Γt ; X t ), (3) t=1 where Nt t Nt t exp − L(β, Γ ; X ) = t yi ft (xt ) i i=1 M t exp − yi = i=1 βj hj (xt − τjt ) , i (4) j=1 t t and Γ = [Γ1 , . [sent-104, score-0.736]

47 Luckily, this is a problem for which boosting is particularly well suited [8], as it has been demonstrated to be an effective method for constructing a highly accurate classifier from a possibly large collection of weak prediction functions. [sent-113, score-0.282]

48 We propose to use gradient boosting [8, 9] to solve for ft (·). [sent-116, score-0.311]

49 (3), ˜ ˜ ˜ the goal at each boosting iteration is to find the weak learner h ∈ H and the set of {τ 1 , . [sent-120, score-0.241]

50 , τ T } that minimize T  2 t t ˜ ˜ wik h(xt − τ t ) − rik  ,  t=1  Nt (5) i=1 t t t t t where wik and rik can be computed by differentiating the loss of Eq. [sent-123, score-0.54]

51 (4), obtaining wik = e−yi ft (xi ) t t ˜ and {τ 1 , . [sent-124, score-0.264]

52 Once h 4 Algorithm 1 Non-Linear Domain Adaptation with Boosting t t Input: Training samples and labels for T tasks X t = {(xt , yi )}N i i=1 Number of iterations K, shrinkage factor 0 < γ ≤ 1 1: Set ft (·) = 0 ∀ t = 1, . [sent-128, score-0.339]

53 , T 2: for k = 1 to K do 3: t t t t t Let wik = e−yi ft (xi ) and rik = yi Nt T 4: Find ˜ ˜ ˜ h(·), τ 1 , . [sent-131, score-0.463]

54 , τ T = t t wik h(xt − τ t ) − rik i argmin h∈H,τ 1 ,. [sent-134, score-0.27]

55 ,τ T t=1 i=1 T 5: Nt t ˜ i ˜ exp − yi ft (xt ) + α h(xt − τ t ) i Find α through line search: α = argmin ˜ ˜ α 2 t=1 i=1 6: ˜ Set β = γ α ˜ 7: ˜˜ ˜ Update ft (·) = ft (·) + β h( · − τ t ) ∀ t = 1, . [sent-137, score-0.475]

56 Shrinkage may be applied to help regularize the solution, particularly when using powerful weak learners such as regression trees [8]. [sent-145, score-0.241]

57 In the next section we show that regression trees and boosted stumps can be used efficiently to minimize Eq. [sent-154, score-0.436]

58 1 Weak Learners Regression trees have proven very effective when used as weak learners with gradient boosting [23]. [sent-157, score-0.376]

59 Decision stumps represent a special case of single-level regression trees. [sent-159, score-0.241]

60 In cases where feature dimensionality D is very large, decision stumps may be preferred over regression trees to reduce training time. [sent-161, score-0.625]

61 ,τ T }  Nt Nt t t 1{xt [n]−τ t } wik η1 − rik i  i=1 2  t t ¯{xt [n]−τ t } wik η2 − rik 2  , (6) 1 i + i=1 where x[n] ∈ R denotes the value of the nth dimension of x, 1{·} is the indicator function, and ¯{·} = 1 − 1{·} . [sent-169, score-0.54]

62 classic regression trees is that, besides learning the values of 1 η1 , η2 and n, our approach requires the tree to also learn a threshold τ t ∈ R per task. [sent-173, score-0.223]

63 5 Decision Stumps: Decision stumps consist of a single split and return values η1 , η2 = ±1. [sent-177, score-0.241]

64 If also t rik = ±1, which is true when boosting with the exponential loss, then it can be demonstrated that minimizing Eq (6) can be separated into T independent minimization problems for all D attributes for each n. [sent-178, score-0.317]

65 This makes decision stumps feasible for large-scale applications with very high dimensional feature spaces. [sent-181, score-0.423]

66 4 Evaluation We evaluated our approach on two challenging domain adaptation problems for which annotation is very time-consuming, representative of the problems we seek to address. [sent-184, score-0.443]

67 We consider the detection of 3D curvilinear structures in 3D image stacks of Olfactory Projection Fibers (OPF) using 2D aerial road images (see Fig. [sent-188, score-0.739]

68 For this problem, the task is to predict whether a tubular path between two image locations belongs to a curvilinear structure. [sent-190, score-0.301]

69 We used a publiclyavailable dataset [11] of 2D aerial images of road networks as the source domain and 3D stacks of Olfactory Projection Fibers (OPF) from the DIADEM challenge as the target domain. [sent-191, score-1.033]

70 The source domain consists of six fully-labeled 2D aerial road images and the target domain contains eight fully-labeled 3D stacks. [sent-192, score-1.028]

71 We aim at using large amounts of labeled data from 2D road images to leverage learning in the 3D stacks. [sent-193, score-0.383]

72 The goal of this task is to segment mitochondria from large 3D Electron Microscopy (EM) stacks of 5 nm voxel size, acquired from the brain of a rat. [sent-197, score-0.633]

73 As in the path classification problem, 3D annotations are time-consuming and exploiting already-annotated stacks is essential to speed up analysis. [sent-198, score-0.315]

74 The source domain is a fully-labeled EM stack from the Striatum region of 853x506x496 voxels with 39 labeled mitochondria. [sent-199, score-0.524]

75 The target domain consists of two stacks acquired from the Hippocampus, one a training volume of size 1024x653x165 voxels and the other a test volume that is 1024x883x165 voxels, with 10 and 42 labeled mitochondria in each respectively. [sent-200, score-1.195]

76 However, differences in appearance and geometry of the structures may potentially adversely affect classifier accuracy when 2D-trained ones are applied to 3D stacks, which motivates domain adaptation. [sent-207, score-0.287]

77 We use half of the target domain for training and half for testing. [sent-208, score-0.441]

78 This results in balanced sets of 30k samples for training in the source domain, and 20k for training and 20k for testing in the target domain. [sent-210, score-0.411]

79 To simulate the lack of training data, we randomly pick an equal number of positive and negative samples for training from the target domain. [sent-211, score-0.327]

80 The HGD codewords are extracted from the road images and used for both domains to generate consistent feature vectors. [sent-212, score-0.31]

81 We employ gradient boosted trees, which in our experiments outperformed boosted stumps and kernel SVMs. [sent-213, score-0.503]

82 Pooling TD only Full TD Test error 8% 6% 4% 2% 20 30 40 70 100 150 250 Number of training samples in TD 500 1000 Figure 3: Path Classification: Median, lower and upper quartiles of the test error as the number of training samples is varied. [sent-215, score-0.252]

83 Our approach nears Full TD performance with as few as 70 training samples in the target domain and significantly outperforms the baseline methods. [sent-216, score-0.484]

84 For mitochondria segmentation we use the boosting-based method of [27], which is optimized for 3D stacks and whose source code is publicly available. [sent-222, score-0.69]

85 Similar to [27], we group voxels into supervoxels to reduce training and testing time, which yields 15k positive and 275k negative supervoxel samples in the source domain. [sent-224, score-0.323]

86 In the target domain it renders 12k negative training samples. [sent-225, score-0.441]

87 To simulate a real scenario, we create 10 different transfer learning problems using the samples from one mitochondria at a time as positives, which translates into approximately 300 positive training supervoxels each. [sent-226, score-0.439]

88 We compare to linear Canonical Correlation Analysis (CCA) and Kernel CCA (KCCA) [4] for learning a shared latent space on the path classification dataset, and use a Radial Basis kernel function for KCCA, which is a commonly used kernel. [sent-232, score-0.33]

89 The data size and dimensionality of the mitochondria dataset is prohibitive for these methods, and instead we compare to Mean-Variance Normalization (MVN) and Histogram Matching (HM) that are common normalizations one might apply to compensate for acquisition artifacts. [sent-234, score-0.42]

90 The next best competitor is the multi-task method of [10], although it exhibits a much higher variance than our approach and performs poorly when only provided a few labeled target examples. [sent-241, score-0.25]

91 In contrast, our method yields a higher performance without the need for such priors and is able to faithfully leverage the source domain data to learn from relatively few examples in the target domain, outperforming the baseline methods. [sent-252, score-0.569]

92 Our approach is very close to Full TD in performance when using as few as 70 training samples, even though the Full TD classifier was trained with 20k samples from the target domain. [sent-255, score-0.244]

93 [10] suggests that modeling the domain shift using shared and task-specific boundaries, as is commonly done in multi-task learning methods, is not a good model for domain adaptation problems such as the ones shown in Fig. [sent-260, score-0.791]

94 This gets accentuated by the parameter tuning required by [10], done through crossvalidation, that performs poorly when only afforded a few labeled samples in the target domain and yields a longer training time. [sent-262, score-0.692]

95 The method of [10] took 25 minutes to train, while our approach only took between 2 and 15 minutes, depending on the amount of labeled target data. [sent-263, score-0.334]

96 5 Conclusion In this paper we presented an approach for performing non-linear domain adaptation with boosting. [sent-272, score-0.41]

97 Our method learns a task-independent decision boundary in a common feature space, obtained via a non-linear mapping of the features in each task. [sent-273, score-0.454]

98 This contrasts recent approaches that learn taskspecific boundaries and is better suited for problems in domain adaptation where each task is of the same decision problem, but whose features have undergone an unknown transformation. [sent-274, score-0.973]

99 We evaluated our approach on two challenging bio-medical datasets where it achieved a significant gain over using labeled data from either domain alone and outperformed recent multi-task learning methods. [sent-276, score-0.405]

100 : A literature survey on domain adaptation of statistical classifiers. [sent-278, score-0.41]


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