You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Learning with label proportions (LLP), which is a learning task that only provides unlabeled data in bags and each bag's label proportion, has widespread successful applications in practice. However, most of the existing LLP methods don't consider the knowledge transfer for uncertain data. This paper presents a transfer learning-based approach for the problem of learning with label proportions(TL-LLP) to transfer knowledge from source task to target task where both the source and target tasks contain uncertain data. Our approach first formulates objective model for the uncertain data and deals with transfer learning at the same time, and then proposes an iterative framework to build an accurate classifier for the target task. Extensive experiments have shown that the proposed TL-LLP method can obtain the better accuracies and is less sensitive to noise compared with the existing LLP methods.

Cited Abstract(s):
[1]: We study the problem of learning with label proportions in which the training data is provided in groups and only the proportion of each class in each group is known. We propose a new method called proportion-SVM, or @math SVM, which explicitly models the latent unknown instance labels together with the known group label proportions in a large-margin framework. Unlike the existing works, our approach avoids making restrictive assumptions about the data. The @math SVM model leads to a non-convex integer programming problem. In order to solve it efficiently, we propose two algorithms: one based on simple alternating optimization and the other based on a convex relaxation. Extensive experiments on standard datasets show that @math SVM outperforms the state-of-the-art, especially for larger group sizes.

[2]: Recently, learning from label proportions (LLPs), which seeks generalized instance-level predictors merely based on bag-level label proportions, has attracted widespread interest. However, due to its weak label scenario, LLP usually falls into a transductive learning framework accounting for an intractable combinatorial optimization issue. In this paper, we propose a brand new algorithm, called LLPs via nonparallel support vector machine (LLP-NPSVM), to facilitate this dilemma. To harness satisfactory data adaption, instead of transductive learning fashion, our scheme determined instance labels according to two nonparallel hyper-planes under the supervision of label proportion information. In a geometrical view, our approach can be interpreted as an alternative competitive method benefiting from large margin clustering. In practice, LLP-NPSVM can be efficiently addressed by applying two fast sequential minimal optimization paths iteratively. To rationally support the effectiveness of our method, finite termination and monotonic decrease of the proposed LLP-NPSVM procedure were essentially analyzed. Various experiments demonstrated our algorithm enjoys rapid convergence and robust numerical stability, along with best accuracies among several recently developed methods in most cases.

[3]: Learning a classifier from groups of unlabeled data, only knowing, for each group, the proportions of data with particular labels, is an important branch of classification tasks that are conceivable in many practical applications. In this paper, we proposed a novel solution for the problem of learning with label proportions (LLP) based on nonparallel support vector machines, termed as proportion-NPSVM, which can improve the classifiers to be a pair of nonparallel classification hyperplanes. The unique property of our method is that it only needs to solve a pair of smaller quadratic programming problems. Moreover, it can efficiently incorporate the known group label proportions with the latent unknown observation labels into one optimization model under a large-margin framework. Compared to the existing approaches, there are several advantages shown as follows: 1) it does not need to make restrictive assumptions on the training data; 2) nonparallel classifiers can be achieved without computing the large inverse matrices; 3) the optimization model can be effectively solved by using the alternative strategy with SMO technique or SOR method; 4) proportion-NPSVM has better generalization ability. Sufficient experimental results on both binary-classes and multi-classes data sets show the efficiency of our proposed method in classification accuracy, which prove the state-of-the-art method for LLP problems compared with competing algorithms.

[4]: In this paper, we study the problem of learning from label proportions in which label information of data is provided in bag level. In this kind of problem, training data is grouped into various bags and only the proportions of positive instances is known. Inspired by proportion-SVM, we propose a new classification model based on twin SVM, which is also in a large-margin framework and only needs to solve two smaller problems. Avoiding making restrictive assumptions of the data, our model can learn the labels of every single instance based on group proportions information. In order to solve the non-convex problem in our new model, we propose an alternative algorithm to obtain the optimal solution efficiently. Also, we prove the effectiveness of our method in theoretical and experimental way.

[5]: 

[6]: Proportion-SVM has been deeply studied due to its broad application prospects, such as modeling voting behaviors and spam filtering. However, the geometric information has been widely ignored. Thus, current methods usually show sensitivity to noises. To address these problems, in this paper, we combine the proportion learning framework with Laplacian term. We exploit the advantages of Laplacian term. Extensive experiments show the effectiveness of our method.
Some methods are proposed to deal with LLP problem based on SVM technology. [5] treat the mean of each bag as a super-instance and estimate a classifier based on support vector regression. [1] introduce a large-margin framework called proportion-SVM which jointly optimizes over the unknown instances labels and the known label proportions. For the above framework, the two methods, called alter- @math SVM, conv- @math SVM, have been proposed for LLP problem. Following the idea in [1] , the method in [4] is based on twin SVM and needs to solve two smaller binary classification problems. [6] discuss how to combine the proportion learning framework with Laplacian term and analyze the structured information in proportion learning problem. The method introduces the Laplacian term to exploit the geometric information of data points. [3] try to address the LLP problem via nonparallel support vector machines, where the method can improve the classifiers to be a pair of nonparallel classification hyperplanes. [2] build a LLP-NPSVM method by a generalized classifier that determines instance labels according to two nonparallel hyper-planes under the supervision of label proportion information.