{"title": "Active Learning by Querying Informative and Representative Examples", "book": "Advances in Neural Information Processing Systems", "page_first": 892, "page_last": 900, "abstract": "Most active learning approaches select either informative or representative unlabeled instances to query their labels. Although several active learning algorithms have been proposed to combine the two criterions for query selection, they are usually ad hoc in finding unlabeled instances that are both informative and representative. We address this challenge by a principled approach, termed QUIRE, based on the min-max view of active learning. The proposed approach provides a systematic way for measuring and combining the informativeness and representativeness of an instance. Extensive experimental results show that the proposed QUIRE approach outperforms several state-of -the-art active learning approaches.", "full_text": "Active Learning by Querying\n\nInformative and Representative Examples\n\nSheng-Jun Huang1\n\nRong Jin2\n\nZhi-Hua Zhou1\n\n1National Key Laboratory for Novel Software Technology,\n\nNanjing University, Nanjing 210093, China\n\n2Department of Computer Science and Engineering,\nMichigan State University, East Lansing, MI 48824\n\n{huangsj, zhouzh}@lamda.nju.edu.cn\n\nrongjin@cse.msu.edu\n\nAbstract\n\nMost active learning approaches select either informative or representative unla-\nbeled instances to query their labels. Although several active learning algorithms\nhave been proposed to combine the two criteria for query selection, they are usu-\nally ad hoc in \ufb01nding unlabeled instances that are both informative and repre-\nsentative. We address this challenge by a principled approach, termed QUIRE,\nbased on the min-max view of active learning. The proposed approach provides\na systematic way for measuring and combining the informativeness and represen-\ntativeness of an instance. Extensive experimental results show that the proposed\nQUIRE approach outperforms several state-of -the-art active learning approaches.\n\n1\n\nIntroduction\n\nIn this work, we focus on the pool-based active learning, which selects an unlabeled instance from\na given pool for manually labeling. There are two main criteria, i.e., informativeness and represen-\ntativeness, that are widely used for active query selection. Informativeness measures the ability of\nan instance in reducing the uncertainty of a statistical model, while representativeness measures if\nan instance well represents the overall input patterns of unlabeled data [16]. Most active learning\nalgorithms only deploy one of the two criteria for query selection, which could signi\ufb01cantly limit the\nperformance of active learning: approaches favoring informative instances usually do not exploit the\nstructure information of unlabeled data, leading to serious sample bias and consequently undesirable\nperformance for active learning; approaches favoring representative instances may require querying\na relatively large number of instances before the optimal decision boundary is found. Although sev-\neral active learning algorithms [19, 8, 11] have been proposed to \ufb01nd the unlabeled instances that\nare both informative and representative, they are usually ad hoc in measuring the informativeness\nand representativeness of an instance, leading to suboptimal performance.\n\nIn this paper, we propose a new active learning approach by QUerying Informative and Represen-\ntative Examples (QUIRE for short). The proposed approach is based on the min-max view of active\nlearning [11], which provides a systematic way for measuring and combining the informativeness\nand the representativeness. The interesting feature of the proposed approach is that it measures both\nthe informativeness and representativeness of an instance by its prediction uncertainty: the informa-\ntiveness of an instance x is measured by its prediction uncertainty based on the labeled data, while\nthe representativeness of x is measured by its prediction uncertainty based on the unlabeled data.\n\nThe rest of this paper is organized as follows: Section 2 reviews the related work on active learning;\nSection 3 presents the proposed approach in details; experimental results are reported in Section 4;\nSection 5 concludes this work with issues to be addressed in the future.\n\n1\n\n\f(a) A binary classi\ufb01cation\n\n(b) An approach favoring\n\nproblem\n\ninformative instances\n\n(c) An approach favoring\nrepresentative instances\n\n(d) Our approach\n\nFigure 1: An illustrative example for selecting informative and representative instances\n\n2 Related Work\n\nQuerying the most informative instances is probably the most popular approach for active learning.\nExemplar approaches include query-by-committee [17, 6, 10], uncertainty sampling [13, 12, 18, 2]\nand optimal experimental design [9, 20]. The main weakness of these approaches is that they are\nunable to exploit the abundance of unlabeled data and the selection of query instances is solely\ndetermined by a small number of labeled examples, making it prone to sample bias. Another school\nof active learning is to select the instances that are most representative to the unlabeled data. These\napproaches aim to exploit the cluster structure of unlabeled data [14, 7], usually by a clustering\nmethod. The main weakness of these approaches is that their performance heavily depends on the\nquality of clustering results [7].\n\nSeveral active learning algorithms tried to combine the informativeness measure with the represen-\ntativeness measure for \ufb01nding the optimal query instances. In [19], the authors propose a sampling\nalgorithm that exploits both the cluster information and the classi\ufb01cation margins of unlabeled in-\nstances. One limitation of this approach is that since clustering is only performed on the instances\nwithin the classi\ufb01cation margin, it is unable to exploit the unlabeled instances outside the margin.\nIn [8], Donmez et al. extended the active learning approach in [14] by dynamically balancing the\nuncertainty and the density of instances for query selection. This approach is ad hoc in combining\nthe measure of informativeness and representativeness for query selection, leading to suboptimal\nperformance.\n\nOur work is based on the min-max view of active learning, which was \ufb01rst proposed in the study of\nbatch mode active learning [11]. Unlike [11] which measures the representativeness of an instance\nby its similarity to the remaining unlabeled instances, our proposed measure of representativeness\ntakes into account the cluster structure of unlabeled instances as well as the class assignments of the\nlabeled examples, leading to a better selection of unlabeled instances for active learning.\n\n3 QUIRE: QUery Informative and Representative Examples\n\nWe start with a synthesized example that illustrates the importance of querying instances that are\nboth informative and representative for active learning. Figure 1 (a) shows a binary classi\ufb01cation\nproblem with each class represented by a different legend. We examine three different active learning\nalgorithms by allowing them to sequentially select 15 data points. Figure 1 (b) and (c) show the\ndata points selected by an approach favoring informative instances (i.e., [18]) and by an approach\nfavoring representative instances (i.e., [7]), respectively. As indicated by Figure 1 (b), due to the\nsample bias, the approach preferring informative instances tends to choose the data points close to\nthe horizontal line, leading to incorrect decision boundaries. On the other hand, as indicated by\nFigure 1 (c), the approach preferring representative instances is able to identify the approximately\ncorrect decision boundary but with a slow convergence. Figure 1 (d) shows the data points selected\nby the proposed approach that favors data points that are both informative and representative. It is\nclear that the proposed algorithm is more ef\ufb01cient in \ufb01nding the accurate decision boundary than the\nother two approaches.\n\nWe denote by D = {(x1, y1), (x2, y2), \u00b7 \u00b7 \u00b7 , (xnl , ynl ), xnl+1, \u00b7 \u00b7 \u00b7 , xn} the training data set that\nconsists of nl labeled instances and nu = n \u2212 nl unlabeled instances, where each instance\nxi = [xi1, xi2, \u00b7 \u00b7 \u00b7 , xid]\u22a4 is a vector of d dimension and yi \u2208 {\u22121, +1} is the class label of xi.\n\n2\n\n\fActive learning selects one instance xs from the pool of unlabeled data to query its class label. For\nconvenience, we divide the data set D into three parts: the labeled data Dl, the currently selected\ninstance xs, and the rest of the unlabeled data Du. We also use Da = Du \u222a {xs} to represent all\nthe unlabeled instances. We use y = [yl, ys, yu] for the class label assignment of the entire data set,\nwhere yl, ys and yu are the class labels assigned to Dl, xs and Du, respectively. Finally, we denote\nby ya = [ys, yu] the class assignment for all the unlabeled instances.\n\n3.1 The Framework\n\nTo motivate the proposed approach, we \ufb01rst re-examine the margin-based active learning from the\nviewpoint of min-max [11]. Let f \u2217 be a classi\ufb01cation model trained by the labeled examples, i.e.,\n\nf \u2217 = arg min\n\nf \u2208H\n\n\u03bb\n2\n\n|f |2\n\nH +\n\nnlXi=1\n\n\u2113(yi, f (xi)),\n\n(1)\n\nwhere H is a reproducing kernel Hilbert space endowed with kernel function \u03ba(\u00b7, \u00b7) : Rd \u00d7 Rd \u2192 R.\n\u2113(z) is the loss function. Given the classi\ufb01er f \u2217, the margin-based approach chooses the unlabeled\ninstance closest to the decision boundary, i.e.,\n\ns\u2217 = arg min\nnl