We propose a new approach to address the text classification problems when learning with partial labels is beneficial. Instead of offering each training sample a set of candidate labels, we assign negative-oriented labels to the ambiguous training examples if they are unlikely fall into certain classes. We construct our new maximum likelihood estimators with self-correction property, and prove that under some conditions, our estimators converge faster. Also we discuss the advantages of applying one of our estimator to a fully supervised learning problem. The proposed method has potential applicability in many areas, such as crowdsourcing, natural language processing and medical image analysis.
In real life, one may have different type of labels @cite_7 , in which circumstance, semi-supervised learning or partial-label problems need to be considered @cite_18 . There are several methods to encode the partial label information into the learning framework. For the partial label data set, one can define a new loss combining all information of the possible labels, for example, in @cite_15 , the authors modify the traditional @math loss [ L(w)= 1 n+m [ i=1 ^nl(x_i,y_i,w)+ i=1 ^ml(x_i,Y_i,w) ], ] where @math is the possible label set for @math and @math is a non-negative loss function, and in @cite_18 , they defined convex loss for partial labels as: [ L _ (g(x),y) = ( 1 |y| a y g_a(x) )+ a y (-g_a(x)), ] where @math is a convex function, @math is a singleton, and @math is a score function for label @math as input @math . A modification of the likelihood function is as well an approach to this problem and @cite_3 gives the following optimization problem using Naive Bayes method [ ^*= y_i S_i p(y|x_i, ) ] where @math is the possible labels for @math .
@cite_18 @cite_3 @cite_7 @cite_15
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We address the problem of partially-labeled multiclass classification, where instead of a single label per instance, the algorithm is given a candidate set of labels, only one of which is correct. Our setting is motivated by a common scenario in many image and video collections, where only partial access to labels is available. The goal is to learn a classifier that can disambiguate the partially-labeled training instances, and generalize to unseen data. We define an intuitive property of the data distribution that sharply characterizes the ability to learn in this setting and show that effective learning is possible even when all the data is only partially labeled. Exploiting this property of the data, we propose a convex learning formulation based on minimization of a loss function appropriate for the partial label setting. We analyze the conditions under which our loss function is asymptotically consistent, as well as its generalization and transductive performance. We apply our framework to identifying faces culled from web news sources and to naming characters in TV series and movies; in particular, we annotated and experimented on a very large video data set and achieve 6 error for character naming on 16 episodes of the TV series Lost. In this paper, we address the problem of learning when some cases are fully labeled while other cases are only partially labeled, in the form of partial labels. Partial labels are represented as a set of possible labels for each training example, one of which is the correct label. We introduce a discriminative learning approach that incorporates partial label information into the conventional margin-based learning framework. The partial label learning problem is formulated as a convex quadratic optimization minimizing the L2-norm regularized empirical risk using hinge loss. We also present an efficient algorithm for classification in the presence of partial labels. Experiments with different data sets show that partial label information improves the performance of classification when there is traditional fully-labeled data, and also yields reasonable performance in the absence of any fully labeled data. The choice of the loss function is critical in extreme multi-label learning where the objective is to annotate each data point with the most relevant subset of labels from an extremely large label set. Unfortunately, existing loss functions, such as the Hamming loss, are unsuitable for learning, model selection, hyperparameter tuning and performance evaluation. This paper addresses the issue by developing propensity scored losses which: (a) prioritize predicting the few relevant labels over the large number of irrelevant ones; (b) do not erroneously treat missing labels as irrelevant but instead provide unbiased estimates of the true loss function even when ground truth labels go missing under arbitrary probabilistic label noise models; and (c) promote the accurate prediction of infrequently occurring, hard to predict, but rewarding tail labels. Another contribution is the development of algorithms which efficiently scale to extremely large datasets with up to 9 million labels, 70 million points and 2 million dimensions and which give significant improvements over the state-of-the-art. This paper's results also apply to tagging, recommendation and ranking which are the motivating applications for extreme multi-label learning. They generalize previous attempts at deriving unbiased losses under the restrictive assumption that labels go missing uniformly at random from the ground truth. Furthermore, they provide a sound theoretical justification for popular label weighting heuristics used to recommend rare items. Finally, they demonstrate that the proposed contributions align with real world applications by achieving superior clickthrough rates on sponsored search advertising in Bing. Multiclass classification problems such as image annotation can involve a large number of classes. In this context, confusion between classes can occur, and single label classification may be misleading. We provide in the present paper a general device that, given an unlabeled dataset and a score function defined as the minimizer of some empirical and convex risk, outputs a set of class labels, instead of a single one. Interestingly, this procedure does not require that the unlabeled dataset explores the whole classes. Even more, the method is calibrated to control the expected size of the output set while minimizing the classification risk. We show the statistical optimality of the procedure and establish rates of convergence under the Tsybakov margin condition. It turns out that these rates are linear on the number of labels. We apply our methodology to convex aggregation of confidence sets based on the V-fold cross validation principle also known as the superlearning principle. We illustrate the numerical performance of the procedure on real data and demonstrate in particular that with moderate expected size, w.r.t. the number of labels, the procedure provides significant improvement of the classification risk.