A common approach in positive-unlabeled learning is to train a classification model between labeled and unlabeled data. This strategy is in fact known to give an optimal classifier under mild conditions; however, it results in biased empirical estimates of the classifier performance. In this work, we show that the typically used performance measures such as the receiver operating characteristic curve, or the precision-recall curve obtained on such data can be corrected with the knowledge of class priors; i.e., the proportions of the positive and negative examples in the unlabeled data. We extend the results to a noisy setting where some of the examples labeled positive are in fact negative and show that the correction also requires the knowledge of the proportion of noisy examples in the labeled positives. Using state-of-the-art algorithms to estimate the positive class prior and the proportion of noise, we experimentally evaluate two correction approaches and demonstrate their efficacy on real-life data.
We develop a worst-case analysis of aggregation of classifier ensembles for binary classification. The task of predicting to minimize error is formulated as a game played over a given set of unlabeled data (a transductive setting), where prior label information is encoded as constraints on the game. The minimax solution of this game identifies cases where a weighted combination of the classifiers can perform significantly better than any single classifier.
We consider a problem of learning a binary classifier only from positive data and unlabeled data (PU learning) and estimating the class-prior in unlabeled data under the case-control scenario. Most of the recent methods of PU learning require an estimate of the class-prior probability in unlabeled data, and it is estimated in advance with another method. However, such a two-step approach which first estimates the class prior and then trains a classifier may not be the optimal approach since the estimation error of the class-prior is not taken into account when a classifier is trained. In this …
Medical researchers have solved the problem of estimating the sensitivity and specificity of binary medical diagnostic tests without gold standard tests for comparison. That problem is the same as estimating confusion matrices for classifiers on unlabeled data. This article describes how to modify the diagnostic test solutions to estimate confusion matrices and accuracy statistics for supervised or unsupervised binary classifiers on unlabeled data.
Rakuten Institute of Technology（乐天技术研究所）；AIR Labs, Continental Automotive Group（大陆汽车集团AIR实验室）
Existing algorithms aiming to learn a binary classifier from positive (P) and unlabeled (U) data generally require estimating the class prior or label noises ahead of building a classification model. However, the estimation and classifier learning are normally conducted in a pipeline instead of being jointly optimized. In this paper, we propose to alternatively train the two steps using reinforcement learning. Our proposal adopts a policy network to adaptively make assumptions on the labels of unlabeled data, while a classifier is built upon the output of the policy network and provides reward…
The University of Tokyo（东京大学）；RIKEN（理化学研究所）；Google（谷歌）
Empirical risk minimization (ERM), with proper loss function and regularization, is the common practice of supervised classification. In this paper, we study training arbitrary (from linear to deep) binary classifier from only unlabeled (U) data by ERM. We prove that it is impossible to estimate the risk of an arbitrary binary classifier in an unbiased manner given a single set of U data, but it becomes possible given two sets of U data with different class priors. These two facts answer a fundamental question---what the minimal supervision is for training any binary classifier from only U dat…
Center for Advanced Intelligence Project, RIKEN（理化学研究所先进智能项目中心）；Graduate School of Frontier Sciences, The University of Tokyo（东京大学前沿科学研究生院）；Department of Statistics, Seoul National University（首尔国立大学统计系）
We consider the problem of learning a binary classifier from only positive and unlabeled observations (called PU learning). Recent studies in PU learning have shown superior performance theoretically and empirically. However, most existing algorithms may not be suitable for large-scale datasets because they face repeated computations of a large Gram matrix or require massive hyperparameter optimization. In this paper, we propose a computationally efficient and theoretically grounded PU learning algorithm. The proposed PU learning algorithm produces a closed-form classifier when the hypothesis …
Assessing the performance of a learned model is a crucial part of machine learning. However, in some domains only positive and unlabeled examples are available, which prohibits the use of most standard evaluation metrics. We propose an approach to estimate any metric based on contingency tables, including ROC and PR curves, using only positive and unlabeled data. Estimating these performance metrics is essentially reduced to estimating the fraction of (latent) positives in the unlabeled set, assuming known positives are a random sample of all positives. We provide theoretical bounds on the qua…
We propose an efficient method to estimate the accuracy of classifiers using only unlabeled data. We consider a setting with multiple classification problems where the target classes may be tied together through logical constraints. For example, a set of classes may be mutually exclusive, meaning that a data instance can belong to at most one of them. The proposed method is based on the intuition that: (i) when classifiers agree, they are more likely to be correct, and (ii) when the classifiers make a prediction that violates the constraints, at least one classifier must be making an error. Ex…
National Research University Higher School of Economics（国立研究型大学高等经济学院）；JetBrains Research（JetBrains研究院）
Positive-Unlabeled (PU) learning is an analog to supervised binary classification for the case when only the positive sample is clean, while the negative sample is contaminated with latent instances of positive class and hence can be considered as an unlabeled mixture. The objectives are to classify the unlabeled sample and train an unbiased PN classifier, which generally requires to identify the mixing proportions of positives and negatives first. Recently, unbiased risk estimation framework has achieved state-of-the-art performance in PU learning. This approach, however, exhibits two major b…
On Leveraging Unlabeled Data for Concurrent Positive-Unlabeled Classification and Robust Generation
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；State Key Lab of General AI, School of Intelligence Science and Technology, Peking University（人工智能国家重点实验室，北京大学智能科学与技术学院）；Institute for Artificial Intelligence, Peking University（北京大学人工智能研究院）；Pazhou Laboratory (Huangpu), Guangzhou, Guangdong, China（黄埔实验室）；Department of Computer Science, University College London（伦敦大学学院计算机科学系）；School of Electrical and Computer Science, University of Southampton（南安普顿大学电子与计算机科学学院）
To cope with high annotation costs, training a classifier only from weakly supervised data has attracted a great deal of attention these days. Among various approaches, strengthening supervision from completely unsupervised classification is a promising direction, which typically employs class priors as the only supervision and trains a binary classifier from unlabeled (U) datasets. While existing risk-consistent methods are theoretically grounded with high flexibility, they can learn only from two U sets. In this paper, we propose a new approach for binary classification from $m$ U-sets for $…
Continual learning usually assumes the incoming data are fully labeled, which might not be applicable in real applications. In this work, we consider semi-supervised continual learning (SSCL) that incrementally learns from partially labeled data. Observing that existing continual learning methods lack the ability to continually exploit the unlabeled data, we propose deep Online Replay with Discriminator Consistency (ORDisCo) to interdependently learn a classifier with a conditional generative adversarial network (GAN), which continually passes the learned data distribution to the classifier. I…
Learning binary classifiers only from positive and unlabeled (PU) data is an important and challenging task in many real-world applications, including web text classification, disease gene identification and fraud detection, where negative samples are difficult to verify experimentally. Most recent PU learning methods are developed based on the conventional misclassification risk of the supervised learning type, and they require to solve the intractable risk estimation problem by approximating the negative data distribution or the class prior. In this paper, we introduce a variational principl…
We study a robust alternative to empirical risk minimization called distributionally robust learning (DRL), in which one learns to perform against an adversary who can choose the data distribution from a specified set of distributions. We illustrate a problem with current DRL formulations, which rely on an overly broad definition of allowed distributions for the adversary, leading to learned classifiers that are unable to predict with any confidence. We propose a solution that incorporates unlabeled data into the DRL problem to further constrain the adversary. We show that this new formulation…
Often domain adaptation is performed using a discriminator (domain classifier) to learn domain-invariant feature representations so that a classifier trained on labeled source data will generalize well to unlabeled target data. A line of research stemming from semi-supervised learning uses pseudo labeling to directly generate "pseudo labels" for the unlabeled target data and trains a classifier on the now-labeled target data, where the samples are selected or weighted based on some measure of confidence. In this paper, we propose multi-purposing the discriminator to not only aid in producing d…
Augmented prediction of a true class for Positive Unlabeled data under selection bias
Institute of Computer Science, Polish Academy of Sciences（波兰科学院计算机科学研究所）；Faculty of Mathematics and Information Science, Warsaw University of Technology（华沙理工大学数学与信息科学学院）
Semi-supervised learning methods are motivated by the availability of large datasets with unlabeled features in addition to labeled data. Unlabeled data is, however, not guaranteed to improve classification performance and has in fact been reported to impair the performance in certain cases. A fundamental source of error arises from restrictive assumptions about the unlabeled features, which result in unreliable classifiers that underestimate their prediction error probabilities. In this paper, we develop a semi-supervised learning approach that relaxes such assumptions and is capable of provi…
Positive-unlabeled (PU) learning trains a binary classifier using only positive and unlabeled data. A common simplifying assumption is that the positive data is representative of the target positive class. This assumption rarely holds in practice due to temporal drift, domain shift, and/or adversarial manipulation. This paper shows that PU learning is possible even with arbitrarily non-representative positive data given unlabeled data from the source and target distributions. Our key insight is that only the negative class's distribution need be fixed. We integrate this into two statistically …
Radboud University（拉德堡德大学）；Delft University of Technology（代尔夫特理工大学）；University of Copenhagen（哥本哈根大学）
Consider a classification problem where we have both labeled and unlabeled data available. We show that for linear classifiers defined by convex margin-based surrogate losses that are decreasing, it is impossible to construct any semi-supervised approach that is able to guarantee an improvement over the supervised classifier measured by this surrogate loss on the labeled and unlabeled data. For convex margin-based loss functions that also increase, we demonstrate safe improvements are possible.
In this paper we explore the role of sample mean in building a neural network for classification. This role is surprisingly extensive and includes: direct computation of weights without training, performance monitoring for samples without known classification, and self-training for unlabeled data. Experimental computation on a CIFAR-10 data set provides promising empirical evidence on the efficacy of a simple and widely applicable approach to some difficult problems.
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Unsupervised classification methods learn a discriminative classifier from unlabeled data, which has been proven to be an effective way of simultaneously clustering the data and training a classifier from the data. Various unsupervised classification methods obtain appealing results by the classifiers learned in an unsupervised manner. However, existing methods do not consider the misclassification error of the unsupervised classifiers except unsupervised SVM, so the performance of the unsupervised classifiers is not fully evaluated. In this work, we study the misclassification error of two po…
Vrije Universiteit Brussel（布鲁塞尔自由大学）；Queens University Belfast（英国女王大学贝尔法斯特分校）
In the context of some machine learning applications, obtaining data instances is a relatively easy process but labeling them could become quite expensive or tedious. Such scenarios lead to datasets with few labeled instances and a larger number of unlabeled ones. Semi-supervised classification techniques combine labeled and unlabeled data during the learning phase in order to increase the classifier's generalization capability. Regrettably, most successful semi-supervised classifiers do not allow explaining their outcome, thus behaving like black boxes. However, there is an increasing number …
Bottlenecks of binary classification from positive and unlabeled data (PU classification) are the requirements that given unlabeled patterns are drawn from the test marginal distribution, and the penalty of the false positive error is identical to the false negative error. However, such requirements are often not fulfilled in practice. In this paper, we generalize PU classification to the class prior shift and asymmetric error scenarios. Based on the analysis of the Bayes optimal classifier, we show that given a test class prior, PU classification under class prior shift is equivalent to PU cl…
Computer Science Laboratory (LIG)（计算机科学实验室（LIG））；Department of Statistics (LJK)（统计系（LJK））；Departement of Physics (SIMaP)（物理系（SIMaP））；University of Grenoble Alpes（格勒诺布尔阿尔卑斯大学）
We investigate the generalization properties of a self-training algorithm with halfspaces. The approach learns a list of halfspaces iteratively from labeled and unlabeled training data, in which each iteration consists of two steps: exploration and pruning. In the exploration phase, the halfspace is found sequentially by maximizing the unsigned-margin among unlabeled examples and then assigning pseudo-labels to those that have a distance higher than the current threshold. The pseudo-labeled examples are then added to the training set, and a new classifier is learned. This process is repeated u…
To assess generalization, machine learning scientists typically either (i) bound the generalization gap and then (after training) plug in the empirical risk to obtain a bound on the true risk; or (ii) validate empirically on holdout data. However, (i) typically yields vacuous guarantees for overparameterized models. Furthermore, (ii) shrinks the training set and its guarantee erodes with each re-use of the holdout set. In this paper, we introduce a method that leverages unlabeled data to produce generalization bounds. After augmenting our (labeled) training set with randomly labeled fresh exam…
Classifiers deployed in the real world operate in a dynamic environment, where the data distribution can change over time. These changes, referred to as concept drift, can cause the predictive performance of the classifier to drop over time, thereby making it obsolete. To be of any real use, these classifiers need to detect drifts and be able to adapt to them, over time. Detecting drifts has traditionally been approached as a supervised task, with labeled data constantly being used for validating the learned model. Although effective in detecting drifts, these techniques are impractical, as la…
We develop a classification algorithm for estimating posterior distributions from positive-unlabeled data, that is robust to noise in the positive labels and effective for high-dimensional data. In recent years, several algorithms have been proposed to learn from positive-unlabeled data; however, many of these contributions remain theoretical, performing poorly on real high-dimensional data that is typically contaminated with noise. We build on this previous work to develop two practical classification algorithms that explicitly model the noise in the positive labels and utilize univariate tra…
In many real-world applications, data is not collected as one batch, but sequentially over time, and often it is not possible or desirable to wait until the data is completely gathered before analyzing it. Thus, we propose a framework to sequentially update a maximum margin classifier by taking advantage of the Maximum Entropy Discrimination principle. Our maximum margin classifier allows for a kernel representation to represent large numbers of features and can also be regularized with respect to a smooth sub-manifold, allowing it to incorporate unlabeled observations. We compare the performa…
Peking University（北京大学）；The University of Sydney（悉尼大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Peng Cheng Laboratory（鹏城实验室）
This paper defines a positive and unlabeled classification problem for standard GANs, which then leads to a novel technique to stabilize the training of the discriminator in GANs. Traditionally, real data are taken as positive while generated data are negative. This positive-negative classification criterion was kept fixed all through the learning process of the discriminator without considering the gradually improved quality of generated data, even if they could be more realistic than real data at times. In contrast, it is more reasonable to treat the generated data as unlabeled, which could …
Most positive and unlabeled data is subject to selection biases. The labeled examples can, for example, be selected from the positive set because they are easier to obtain or more obviously positive. This paper investigates how learning can be ena BHbled in this setting. We propose and theoretically analyze an empirical-risk-based method for incorporating the labeling mechanism. Additionally, we investigate under which assumptions learning is possible when the labeling mechanism is not fully understood and propose a practical method to enable this. Our empirical analysis supports the theoretic…
Data augmentation by incorporating cheap unlabeled data from multiple domains is a powerful way to improve prediction especially when there is limited labeled data. In this work, we investigate how adversarial robustness can be enhanced by leveraging out-of-domain unlabeled data. We demonstrate that for broad classes of distributions and classifiers, there exists a sample complexity gap between standard and robust classification. We quantify to what degree this gap can be bridged via leveraging unlabeled samples from a shifted domain by providing both upper and lower bounds. Moreover, we show …
IMT Atlantique（大西洋高等电信学校）；Lab-STICC（布列塔尼电子与电信通信科学实验室）；MILA, Université de Montréal（蒙特利尔大学MILA人工智能研究所）；Université Cote d’Azur（蔚蓝海岸大学）；École Normale Supérieure de Lyon（里昂高等师范学院）
In the context of few-shot learning, one cannot measure the generalization ability of a trained classifier using validation sets, due to the small number of labeled samples. In this paper, we are interested in finding alternatives to answer the question: is my classifier generalizing well to previously unseen data? We first analyze the reasons for the variability of generalization performances. We then investigate the case of using transfer-based solutions, and consider three settings: i) supervised where we only have access to a few labeled samples, ii) semi-supervised where we have access to…
High-dimensional Semi-supervised Classification via the Fermat Distance
School of Mathematical Sciences and School of Economics and Management, Tongji University（同济大学数学科学学院和经济管理学院）；Department of Sciences, North China University of Technology（华北理工大学理学院）
An interactive image retrieval system learns which images in the database belong to a user's query concept, by analyzing the example images and feedback provided by the user. The challenge is to retrieve the relevant images with minimal user interaction. In this work, we propose to solve this problem by posing it as a binary classification task of classifying all images in the database as being relevant or irrelevant to the user's query concept. Our method combines active learning with graph-based semi-supervised learning (GSSL) to tackle this problem. Active learning reduces the number of use…
A theoretical study is presented for a simple linear classifier called reference distance estimator (RDE), which assigns the weight of each feature j as P(r|j)-P(r), where r is a reference feature relevant to the target class y. The analysis shows that if r performs better than random guess in predicting y and is conditionally independent with each feature j, the RDE will have the same classification performance as that from P(y|j)-P(y), a classifier trained with the gold standard y. Since the estimation of P(r|j)-P(r) does not require labeled data, under the assumption above, RDE trained with…
Recent advances in weakly supervised classification allow us to train a classifier only from positive and unlabeled (PU) data. However, existing PU classification methods typically require an accurate estimate of the class-prior probability, which is a critical bottleneck particularly for high-dimensional data. This problem has been commonly addressed by applying principal component analysis in advance, but such unsupervised dimension reduction can collapse underlying class structure. In this paper, we propose a novel representation learning method from PU data based on the information-maximiz…
Positive Unlabeled (PU) learning is widely used in many applications, where a binary classifier is trained on the datasets consisting of only positive and unlabeled samples. In this paper, we improve PU learning over state-of-the-art from two aspects. Firstly, existing model evaluation methods for PU learning requires ground truth of unlabeled samples, which is unlikely to be obtained in practice. In order to release this restriction, we propose an asymptotic unbiased practical AUL (area under the lift) estimation method, which makes use of raw PU data without prior knowledge of unlabeled samp…
From only positive (P) and unlabeled (U) data, a binary classifier could be trained with PU learning, in which the state of the art is unbiased PU learning. However, if its model is very flexible, empirical risks on training data will go negative, and we will suffer from serious overfitting. In this paper, we propose a non-negative risk estimator for PU learning: when getting minimized, it is more robust against overfitting, and thus we are able to use very flexible models (such as deep neural networks) given limited P data. Moreover, we analyze the bias, consistency, and mean-squared-error re…
Washington University in St. Louis（圣路易斯华盛顿大学）；Microsoft Research（微软研究院）
As machine learning transitions increasingly towards real world applications controlling the test-time cost of algorithms becomes more and more crucial. Recent work, such as the Greedy Miser and Speedboost, incorporate test-time budget constraints into the training procedure and learn classifiers that provably stay within budget (in expectation). However, so far, these algorithms are limited to the supervised learning scenario where sufficient amounts of labeled data are available. In this paper we investigate the common scenario where labeled data is scarce but unlabeled data is available in …
Carnegie Mellon University（卡内基梅隆大学）；Amazon Web Services（亚马逊云科技）
Given only positive examples and unlabeled examples (from both positive and negative classes), we might hope nevertheless to estimate an accurate positive-versus-negative classifier. Formally, this task is broken down into two subtasks: (i) Mixture Proportion Estimation (MPE) -- determining the fraction of positive examples in the unlabeled data; and (ii) PU-learning -- given such an estimate, learning the desired positive-versus-negative classifier. Unfortunately, classical methods for both problems break down in high-dimensional settings. Meanwhile, recently proposed heuristics lack theoreti…
Bielefeld University（比勒费尔德大学）；University of Waterloo（滑铁卢大学）；Google Brain（谷歌大脑）；York University（约克大学）
In semi-supervised classification, one is given access both to labeled and unlabeled data. As unlabeled data is typically cheaper to acquire than labeled data, this setup becomes advantageous as soon as one can exploit the unlabeled data in order to produce a better classifier than with labeled data alone. However, the conditions under which such an improvement is possible are not fully understood yet. Our analysis focuses on improvements in the minimax learning rate in terms of the number of labeled examples (with the number of unlabeled examples being allowed to depend on the number of label…
Given $k$ pre-trained classifiers and a stream of unlabeled data examples, how can we actively decide when to query a label so that we can distinguish the best model from the rest while making a small number of queries? Answering this question has a profound impact on a range of practical scenarios. In this work, we design an online selective sampling approach that actively selects informative examples to label and outputs the best model with high probability at any round. Our algorithm can be used for online prediction tasks for both adversarial and stochastic streams. We establish several th…
Weizmann Institute of Science（魏茨曼科学研究所）；Yale University, School of Medicine（耶鲁大学医学院）；New York University, Langone Medical Center（纽约大学朗格尼医学中心）
In various situations one is given only the predictions of multiple classifiers over a large unlabeled test data. This scenario raises the following questions: Without any labeled data and without any a-priori knowledge about the reliability of these different classifiers, is it possible to consistently and computationally efficiently estimate their accuracies? Furthermore, also in a completely unsupervised manner, can one construct a more accurate unsupervised ensemble classifier? In this paper, focusing on the binary case, we present simple, computationally efficient algorithms to solve thes…
The University of Tokyo（东京大学）；Boston University（波士顿大学）；RIKEN（日本理化学研究所）
In PU learning, a binary classifier is trained from positive (P) and unlabeled (U) data without negative (N) data. Although N data is missing, it sometimes outperforms PN learning (i.e., ordinary supervised learning). Hitherto, neither theoretical nor experimental analysis has been given to explain this phenomenon. In this paper, we theoretically compare PU (and NU) learning against PN learning based on the upper bounds on estimation errors. We find simple conditions when PU and NU learning are likely to outperform PN learning, and we prove that, in terms of the upper bounds, either PU or NU l…
We present a novel approach to learn binary classifiers when only positive and unlabeled instances are available (PU learning). This problem is routinely cast as a supervised task with label noise in the negative set. We use an ensemble of SVM models trained on bootstrap resamples of the training data for increased robustness against label noise. The approach can be considered in a bagging framework which provides an intuitive explanation for its mechanics in a semi-supervised setting. We compared our method to state-of-the-art approaches in simulations using multiple public benchmark data set…
Active learning aims to train a classifier as fast as possible with as few labels as possible. The core element in virtually any active learning strategy is the criterion that measures the usefulness of the unlabeled data based on which new points to be labeled are picked. We propose a novel approach which we refer to as maximizing variance for active learning or MVAL for short. MVAL measures the value of unlabeled instances by evaluating the rate of change of output variables caused by changes in the next sample to be queried and its potential labelling. In a sense, this criterion measures ho…
University of Technology Sydney（悉尼科技大学）；RIKEN（理化学研究所）；Hong Kong Baptist University（香港浸会大学）；University of Tokyo（东京大学）
In unsupervised domain adaptation (UDA), classifiers for the target domain (TD) are trained with clean labeled data from the source domain (SD) and unlabeled data from TD. However, in the wild, it is difficult to acquire a large amount of perfectly clean labeled data in SD given limited budget. Hence, we consider a new, more realistic and more challenging problem setting, where classifiers have to be trained with noisy labeled data from SD and unlabeled data from TD -- we name it wildly UDA (WUDA). We show that WUDA ruins all UDA methods if taking no care of label noise in SD, and to this end,…
