In the problem of learning with label proportions, which we call LLP learning, the training data is unlabeled, and only the proportions of examples receiving each label are given. The goal is to learn a hypothesis that predicts the proportions of labels on the distribution underlying the sample. This model of learning is applicable to a wide variety of settings, including predicting the number of votes for candidates in political elections from polls.
In this paper, we formally define this class and resolve foundational questions regarding the computational complexity of LLP and characterize its relationship to PAC learning. Among our results, we show, perhaps surprisingly, that for finite VC classes what can be efficiently LLP learned is a strict subset of what can be leaned efficiently in PAC, under standard complexity assumptions. We also show that there exist classes of functions whose learnability in LLP is independent of ZFC, the standard set theoretic axioms. This implies that LLP learning cannot be easily characterized (like PAC by VC dimension).
Learning from Label Proportions (LLP) is a learning setting, where the training data is provided in groups, or "bags", and only the proportion of each class in each bag is known. The task is to learn a model to predict the class labels of the individual instances. LLP has broad applications in political science, marketing, healthcare, and computer vision. This work answers the fundamental question, when and why LLP is possible, by introducing a general framework, Empirical Proportion Risk Minimization (EPRM). EPRM learns an instance label classifier to match the given label proportions on the …
The problem of learning from label proportions (LLP) involves training classifiers with weak labels on bags of instances, rather than strong labels on individual instances. The weak labels only contain the label proportion of each bag. The LLP problem is important for many practical applications that only allow label proportions to be collected because of data privacy or annotation cost, and has recently received lots of research attention. Most existing works focus on extending supervised learning models to solve the LLP problem, but the weak learning nature makes it hard to further improve L…
Samsung Research China - Beijing（三星电子中国研究院（北京））；University of Chinese Academy of Sciences（中国科学院大学）；University of International Business and Economics（对外经济贸易大学）；The Chinese University of Hong Kong（香港中文大学）
Learning from label proportions (LLP) aims at learning an instance-level classifier with label proportions in grouped training data. Existing deep learning based LLP methods utilize end-to-end pipelines to obtain the proportional loss with Kullback-Leibler divergence between the bag-level prior and posterior class distributions. However, the unconstrained optimization on this objective can hardly reach a solution in accordance with the given proportions. Besides, concerning the probabilistic classifier, this strategy unavoidably results in high-entropy conditional class distributions at the in…
We study binary classification in the setting where the learner is presented with multiple corrupted training samples, with possibly different sample sizes and degrees of corruption, and introduce an approach based on minimizing a weighted combination of corruption-corrected empirical risks. We establish a generalization error bound, and further show that the bound is optimized when the weights are certain interpretable and intuitive functions of the sample sizes and degrees of corruptions. We then apply this setting to the problem of learning with label proportions (LLP), and propose an algor…
Learning from label proportions (LLP) is a weakly supervised setting for classification in which unlabeled training instances are grouped into bags, and each bag is annotated with the proportion of each class occurring in that bag. Prior work on LLP has yet to establish a consistent learning procedure, nor does there exist a theoretically justified, general purpose training criterion. In this work we address these two issues by posing LLP in terms of mutual contamination models (MCMs), which have recently been applied successfully to study various other weak supervision settings. In the proces…
We consider the problem of Learning from Label Proportions (LLP), a weakly supervised classification setup where instances are grouped into "bags", and only the frequency of class labels at each bag is available. Albeit, the objective of the learner is to achieve low task loss at an individual instance level. Here we propose Easyllp: a flexible and simple-to-implement debiasing approach based on aggregate labels, which operates on arbitrary loss functions. Our technique allows us to accurately estimate the expected loss of an arbitrary model at an individual level. We showcase the flexibility …
Learning from Label Proportions (LLP) is a weakly supervised learning method that aims to perform instance classification from training data consisting of pairs of bags containing multiple instances and the class label proportions within the bags. Previous studies on multiclass LLP can be divided into two categories according to the learning task: per-instance label classification and per-bag label proportion estimation. However, these methods often results in high variance estimates of the risk when applied to complex models, or lack statistical learning theory arguments. To address this issu…
This paper investigates the computational complexity of sparse label propagation which has been proposed recently for processing network structured data. Sparse label propagation amounts to a convex optimization problem and might be considered as an extension of basis pursuit from sparse vectors to network structured datasets. Using a standard first-order oracle model, we characterize the number of iterations for sparse label propagation to achieve a prescribed accuracy. In particular, we derive an upper bound on the number of iterations required to achieve a certain accuracy and show that thi…
Peking University（北京大学）；University of Technology, Sydney（悉尼科技大学）
We analyze the local Rademacher complexity of empirical risk minimization (ERM)-based multi-label learning algorithms, and in doing so propose a new algorithm for multi-label learning. Rather than using the trace norm to regularize the multi-label predictor, we instead minimize the tail sum of the singular values of the predictor in multi-label learning. Benefiting from the use of the local Rademacher complexity, our algorithm, therefore, has a sharper generalization error bound and a faster convergence rate. Compared to methods that minimize over all singular values, concentrating on the tail…
University of Arizona（亚利桑那大学）；Stevens Institute of Technology（史蒂文斯理工学院）；Google Research（谷歌研究院）；Rutgers University（罗格斯大学）
We study active learning of homogeneous $s$-sparse halfspaces in $\mathbb{R}^d$ under the setting where the unlabeled data distribution is isotropic log-concave and each label is flipped with probability at most $η$ for a parameter $η\in \big[0, \frac12\big)$, known as the bounded noise. Even in the presence of mild label noise, i.e. $η$ is a small constant, this is a challenging problem and only recently have label complexity bounds of the form $\tilde{O}\big(s \cdot \mathrm{polylog}(d, \frac{1}ε)\big)$ been established in [Zhang, 2018] for computationally efficient algorithms. In contrast, u…
We address the problem of active learning under label shift: when the class proportions of source and target domains differ. We introduce a "medial distribution" to incorporate a tradeoff between importance weighting and class-balanced sampling and propose their combined usage in active learning. Our method is known as Mediated Active Learning under Label Shift (MALLS). It balances the bias from class-balanced sampling and the variance from importance weighting. We prove sample complexity and generalization guarantees for MALLS which show active learning reduces asymptotic sample complexity ev…
Deep convolutional neural networks (CNNs) have been shown to be able to fit a random labeling over data while still being able to generalize well for normal labels. Describing CNN capacity through a posteriori measures of complexity has been recently proposed to tackle this apparent paradox. These complexity measures are usually validated by showing that they correlate empirically with GE; being empirically larger for networks trained on random vs normal labels. Focusing on the case of spectral complexity we investigate theoretically and empirically the insensitivity of the complexity measure …
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Univ. Grenoble Alpes（格勒诺布尔-阿尔卑斯大学）；CNRS（法国国家科学研究中心）；Grenoble INP（格勒诺布尔理工学院）；University of Washington（华盛顿大学）
We propose Rademacher complexity bounds for multiclass classifiers trained with a two-step semi-supervised model. In the first step, the algorithm partitions the partially labeled data and then identifies dense clusters containing $κ$ predominant classes using the labeled training examples such that the proportion of their non-predominant classes is below a fixed threshold. In the second step, a classifier is trained by minimizing a margin empirical loss over the labeled training set and a penalization term measuring the disability of the learner to predict the $κ$ predominant classes of the i…
We study the theoretical advantages of active learning over passive learning. Specifically, we prove that, in noise-free classifier learning for VC classes, any passive learning algorithm can be transformed into an active learning algorithm with asymptotically strictly superior label complexity for all nontrivial target functions and distributions. We further provide a general characterization of the magnitudes of these improvements in terms of a novel generalization of the disagreement coefficient. We also extend these results to active learning in the presence of label noise, and find that e…
We study {\em online} active learning of homogeneous halfspaces in $\mathbb{R}^d$ with adversarial noise where the overall probability of a noisy label is constrained to be at most $ν$. Our main contribution is a Perceptron-like online active learning algorithm that runs in polynomial time, and under the conditions that the marginal distribution is isotropic log-concave and $ν= Ω(ε)$, where $ε\in (0, 1)$ is the target error rate, our algorithm PAC learns the underlying halfspace with near-optimal label complexity of $\tilde{O}\big(d \cdot polylog(\frac{1}ε)\big)$ and sample complexity of $\til…
IBM Research（IBM研究院）；Indian Institute of Science（印度科学学院）；University of Michigan（密歇根大学）
Mixture proportion estimation (MPE) is the problem of estimating the weight of a component distribution in a mixture, given samples from the mixture and component. This problem constitutes a key part in many "weakly supervised learning" problems like learning with positive and unlabelled samples, learning with label noise, anomaly detection and crowdsourcing. While there have been several methods proposed to solve this problem, to the best of our knowledge no efficient algorithm with a proven convergence rate towards the true proportion exists for this problem. We fill this gap by constructing…
We adapt the idea of random projections applied to the output space, so as to enhance tree-based ensemble methods in the context of multi-label classification. We show how learning time complexity can be reduced without affecting computational complexity and accuracy of predictions. We also show that random output space projections may be used in order to reach different bias-variance tradeoffs, over a broad panel of benchmark problems, and that this may lead to improved accuracy while reducing significantly the computational burden of the learning stage.
A private learner is an algorithm that given a sample of labeled individual examples outputs a generalizing hypothesis while preserving the privacy of each individual. In 2008, Kasiviswanathan et al. (FOCS 2008) gave a generic construction of private learners, in which the sample complexity is (generally) higher than what is needed for non-private learners. This gap in the sample complexity was then further studied in several followup papers, showing that (at least in some cases) this gap is unavoidable. Moreover, those papers considered ways to overcome the gap, by relaxing either the privacy…
Stevens Institute of Technology（史蒂文斯理工学院）；University of Arizona（亚利桑那大学）
This paper is concerned with computationally efficient learning of homogeneous sparse halfspaces in $\mathbb{R}^d$ under noise. Though recent works have established attribute-efficient learning algorithms under various types of label noise (e.g. bounded noise), it remains an open question when and how $s$-sparse halfspaces can be efficiently learned under the challenging malicious noise model, where an adversary may corrupt both the unlabeled examples and the labels. We answer this question in the affirmative by designing a computationally efficient active learning algorithm with near-optimal …
Objective: Using traditional approaches, a Brain-Computer Interface (BCI) requires the collection of calibration data for new subjects prior to online use. Calibration time can be reduced or eliminated e.g.~by transfer of a pre-trained classifier or unsupervised adaptive classification methods which learn from scratch and adapt over time. While such heuristics work well in practice, none of them can provide theoretical guarantees. Our objective is to modify an event-related potential (ERP) paradigm to work in unison with the machine learning decoder to achieve a reliable calibration-less decod…
This work establishes distribution-free upper and lower bounds on the minimax label complexity of active learning with general hypothesis classes, under various noise models. The results reveal a number of surprising facts. In particular, under the noise model of Tsybakov (2004), the minimax label complexity of active learning with a VC class is always asymptotically smaller than that of passive learning, and is typically significantly smaller than the best previously-published upper bounds in the active learning literature. In high-noise regimes, it turns out that all active learning problems…
We study the problem of learning a hierarchical tree representation of data from labeled samples, taken from an arbitrary (and possibly adversarial) distribution. Consider a collection of data tuples labeled according to their hierarchical structure. The smallest number of such tuples required in order to be able to accurately label subsequent tuples is of interest for data collection in machine learning. We present optimal sample complexity bounds for this problem in several learning settings, including (agnostic) PAC learning and online learning. Our results are based on tight bounds of the …
Learning with Label Proportions (LLP) is the problem of recovering the underlying true labels given a dataset when the data is presented in the form of bags. This paradigm is particularly suitable in contexts where providing individual labels is expensive and label aggregates are more easily obtained. In the healthcare domain, it is a burden for a patient to keep a detailed diary of their daily routines, but often they will be amenable to provide higher level summaries of daily behavior. We present a novel and efficient graph-based algorithm that encourages local smoothness and exploits the gl…
Google Research（谷歌研究院）；CREST ENSAE（法国国家统计与经济管理学院经济与统计研究中心）；MINES ParisTech, PSL University（巴黎文理研究大学巴黎国立高等矿业学院）
We propose a learning algorithm capable of learning from label proportions instead of direct data labels. In this scenario, our data are arranged into various bags of a certain size, and only the proportions of each label within a given bag are known. This is a common situation in cases where per-data labeling is lengthy, but a more general label is easily accessible. Several approaches have been proposed to learn in this setting with linear models in the multiclass setting, or with nonlinear models in the binary classification setting. Here we investigate the more general nonlinear multiclass…
Columbia University（哥伦比亚大学）；Google Research（谷歌研究院）
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 $\propto$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 $\propto$SVM model leads to a non-convex integer programming problem. In order to solve it efficiently, we propose two algorithms: one …
In this work we show that iterative thresholding and K-means (ITKM) algorithms can recover a generating dictionary with K atoms from noisy $S$ sparse signals up to an error $\tilde \varepsilon$ as long as the initialisation is within a convergence radius, that is up to a $\log K$ factor inversely proportional to the dynamic range of the signals, and the sample size is proportional to $K \log K \tilde \varepsilon^{-2}$. The results are valid for arbitrary target errors if the sparsity level is of the order of the square root of the signal dimension $d$ and for target errors down to $K^{-\ell}$ …
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…
University of Chinese Academy of Sciences（中国科学院大学）；University of International Business and Economics（对外经济贸易大学）
In this paper, we leverage generative adversarial networks (GANs) to derive an effective algorithm LLP-GAN for learning from label proportions (LLP), where only the bag-level proportional information in labels is available. Endowed with end-to-end structure, LLP-GAN performs approximation in the light of an adversarial learning mechanism, without imposing restricted assumptions on distribution. Accordingly, we can directly induce the final instance-level classifier upon the discriminator. Under mild assumptions, we give the explicit generative representation and prove the global optimality for…
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）
In classical statistical learning theory, one of the most well studied problems is that of binary classification. The information-theoretic sample complexity of this task is tightly characterized by the Vapnik-Chervonenkis (VC) dimension. A quantum analog of this task, with training data given as a quantum state has also been intensely studied and is now known to have the same sample complexity as its classical counterpart. We propose a novel quantum version of the classical binary classification task by considering maps with classical input and quantum output and corresponding classical-quant…
Learning from Label Proportions with Dual-proportion Constraints
The University of Tokyo, Japan（东京大学，日本）；College of Computer Science and Technology, Jilin University, China（吉林大学计算机科学与技术学院，中国）；Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, China（教育部符号计算与知识工程重点实验室，吉林大学，中国）；RIKEN Center for Advanced Intelligence Project, Japan（日本RIKEN先进人工智能项目中心）
In learning from label proportions (LLP), the instances are grouped into bags, and the task is to learn an instance classifier given relative class proportions in training bags. LLP is useful when obtaining individual instance labels is impossible or costly. In this work, we focus on the case of small bags, which allows to design an algorithm that explicitly considers all consistent instance label combinations. In particular, we propose an EM algorithm alternating between optimizing a general neural network instance classifier and incorporating bag-level annotations. Using two different image …
We are interested in estimating individual labels given only coarse, aggregated signal over the data points. In our setting, we receive sets ("bags") of unlabeled instances with constraints on label proportions. We relax the unrealistic assumption of known label proportions, made in previous work; instead, we assume only to have upper and lower bounds, and constraints on bag differences. We motivate the problem, propose an intuitive formulation and algorithm, and apply our methods to real-world scenarios. Across several domains, we show how using only proportion constraints and no labeled exam…
Universität Potsdam（波茨坦大学）；University of Michigan（密歇根大学）
In many real-world classification problems, the labels of training examples are randomly corrupted. Most previous theoretical work on classification with label noise assumes that the two classes are separable, that the label noise is independent of the true class label, or that the noise proportions for each class are known. In this work, we give conditions that are necessary and sufficient for the true class-conditional distributions to be identifiable. These conditions are weaker than those analyzed previously, and allow for the classes to be nonseparable and the noise levels to be asymmetri…
Class-aware and Augmentation-free Contrastive Learning from Label Proportion
The Hong Kong University of Science and Technology（香港科技大学）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；Tencent America（腾讯美国公司）；Tencent Europe B.V.（腾讯欧洲有限责任公司）
Bar-Ilan University（巴伊兰大学）；Intel（英特尔）；Allen Institute for Artificial Intelligence（艾伦人工智能研究所）
Deep learning systems thrive on abundance of labeled training data but such data is not always available, calling for alternative methods of supervision. One such method is expectation regularization (XR) (Mann and McCallum, 2007), where models are trained based on expected label proportions. We propose a novel application of the XR framework for transfer learning between related tasks, where knowing the labels of task A provides an estimation of the label proportion of task B. We then use a model trained for A to label a large corpus, and use this corpus with an XR loss to train a model for t…
Signal Analysis and Interpretation Lab（信号分析与解释实验室）；University of Southern California（南加州大学）；Department of Psychiatry and Behavioral Sciences（精神病学与行为科学系）；University of Washington（华盛顿大学）；Department Educational Psychology（教育心理学系）；University of Utah（犹他大学）
Many text classification tasks are domain-dependent, and various domain adaptation approaches have been proposed to predict unlabeled data in a new domain. Domain-adversarial neural networks (DANN) and their variants have been used widely recently and have achieved promising results for this problem. However, most of these approaches assume that the label proportions of the source and target domains are similar, which rarely holds in most real-world scenarios. Sometimes the label shift can be large and the DANN fails to learn domain-invariant features. In this study, we focus on unsupervised d…
The University of Melbourne（墨尔本大学）；Tsinghua University（清华大学）；National Institute of Informatics（国立信息学研究所）
Datasets with significant proportions of noisy (incorrect) class labels present challenges for training accurate Deep Neural Networks (DNNs). We propose a new perspective for understanding DNN generalization for such datasets, by investigating the dimensionality of the deep representation subspace of training samples. We show that from a dimensionality perspective, DNNs exhibit quite distinctive learning styles when trained with clean labels versus when trained with a proportion of noisy labels. Based on this finding, we develop a new dimensionality-driven learning strategy, which monitors the…
Enhancing Clinical Predictive Modeling through Model Complexity-Driven Class Proportion Tuning for Class Imbalanced Data: An Empirical Study on Opioid Overdose Prediction
Federated learning (FL) has recently emerged as a new form of collaborative machine learning, where a common model can be learned while keeping all the training data on local devices. Although it is designed for enhancing the data privacy, we demonstrated in this paper a new direction in inference attacks in the context of FL, where valuable information about training data can be obtained by adversaries with very limited power. In particular, we proposed three new types of attacks to exploit this vulnerability. The first type of attack, Class Sniffing, can detect whether a certain label appear…
Multi-label text classification is a popular machine learning task where each document is assigned with multiple relevant labels. This task is challenging due to high dimensional features and correlated labels. Multi-label text classifiers need to be carefully regularized to prevent the severe over-fitting in the high dimensional space, and also need to take into account label dependencies in order to make accurate predictions under uncertainty. We demonstrate significant and practical improvement by carefully regularizing the model complexity during training phase, and also regularizing the l…
Forming Auxiliary High-confident Instance-level Loss to Promote Learning from Label Proportions
College of Computer Science and Technology, Jilin University（吉林大学计算机科学与技术学院）；Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University（吉林大学符号计算与知识工程教育部重点实验室）
Data privacy and decentralised data collection has become more and more popular in recent years. In order to solve issues with privacy, communication bandwidth and learning from spatio-temporal data, we will propose two efficient models which use Differential Privacy and decentralized LSTM-Learning: One, in which a Long Short Term Memory (LSTM) model is learned for extracting local temporal node constraints and feeding them into a Dense-Layer (LabelProportionToLocal). The other approach extends the first one by fetching histogram data from the neighbors and joining the information with the LST…
