Under label shift, the label distribution p(y) might change but the class-conditional distributions p(x|y) do not. There are two dominant approaches for estimating the label marginal. BBSE, a moment-matching approach based on confusion matrices, is provably consistent and provides interpretable error bounds. However, a maximum likelihood estimation approach, which we call MLLS, dominates empirically. In this paper, we present a unified view of the two methods and the first theoretical characterization of MLLS. Our contributions include (i) consistency conditions for MLLS, which include calibration of the classifier and a confusion matrix invertibility condition that BBSE also requires; (ii) a unified framework, casting BBSE as roughly equivalent to MLLS for a particular choice of calibration method; and (iii) a decomposition of MLLS's finite-sample error into terms reflecting miscalibration and estimation error. Our analysis attributes BBSE's statistical inefficiency to a loss of information due to coarse calibration. Experiments on synthetic data, MNIST, and CIFAR10 support our findings.
Trustworthy deployment of ML models requires a proper measure of uncertainty, especially in safety-critical applications. We focus on uncertainty quantification (UQ) for classification problems via two avenues -- prediction sets using conformal prediction and calibration of probabilistic predictors by post-hoc binning -- since these possess distribution-free guarantees for i.i.d. data. Two common ways of generalizing beyond the i.i.d. setting include handling covariate and label shift. Within the context of distribution-free UQ, the former has already received attention, but not the latter. It…
The quantification problem consists of determining the prevalence of a given label in a target population. However, one often has access to the labels in a sample from the training population but not in the target population. A common assumption in this situation is that of prior probability shift, that is, once the labels are known, the distribution of the features is the same in the training and target populations. In this paper, we derive a new lower bound for the risk of the quantification problem under the prior shift assumption. Complementing this lower bound, we present a new approximat…
Conformal Prediction for Federated Uncertainty Quantification Under Label Shift
Ecole Polytechnique（巴黎综合理工学院）；Lagrange Mathematics and Computing Research Center（拉格朗日数学与计算研究中心）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Technology Innovation Institute（技术创新研究院）
Classification under Nuisance Parameters and Generalized Label Shift in Likelihood-Free Inference
Carnegie Mellon University（卡内基梅隆大学）；Università di Padova（帕多瓦大学）；Istituto Nazionale di Fisica Nucleare（国家核物理研究所）；Lulea Techniska Universitet（吕勒奥理工大学）；Universal Scientific Education and Research Network（环球科学教育与研究网络）；Universidade Federal de São Carlos（圣卡洛斯联邦大学）
We study the minimax rates of the label shift problem in non-parametric classification. In addition to the unsupervised setting in which the learner only has access to unlabeled examples from the target domain, we also consider the setting in which a small number of labeled examples from the target domain is available to the learner. Our study reveals a difference in the difficulty of the label shift problem in the two settings, and we attribute this difference to the availability of data from the target domain to estimate the class conditional distributions in the latter setting. We also show…
Cornell University（康奈尔大学）；Facebook AI Research（Facebook 人工智能研究院）
Machine learning models often encounter distribution shifts when deployed in the real world. In this paper, we focus on adaptation to label distribution shift in the online setting, where the test-time label distribution is continually changing and the model must dynamically adapt to it without observing the true label. Leveraging a novel analysis, we show that the lack of true label does not hinder estimation of the expected test loss, which enables the reduction of online label shift adaptation to conventional online learning. Informed by this observation, we propose adaptation algorithms in…
Label shift refers to the phenomenon where the prior class probability p(y) changes between the training and test distributions, while the conditional probability p(x|y) stays fixed. Label shift arises in settings like medical diagnosis, where a classifier trained to predict disease given symptoms must be adapted to scenarios where the baseline prevalence of the disease is different. Given estimates of p(y|x) from a predictive model, Saerens et al. proposed an efficient maximum likelihood algorithm to correct for label shift that does not require model retraining, but a limiting assumption of …
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…
University of California, Irvine（加州大学尔湾分校）；California Institute of Technology（加州理工学院）；Institute of Theoretical Studies, ETH Zürich（苏黎世联邦理工学院理论研究所）
We propose Regularized Learning under Label shifts (RLLS), a principled and a practical domain-adaptation algorithm to correct for shifts in the label distribution between a source and a target domain. We first estimate importance weights using labeled source data and unlabeled target data, and then train a classifier on the weighted source samples. We derive a generalization bound for the classifier on the target domain which is independent of the (ambient) data dimensions, and instead only depends on the complexity of the function class. To the best of our knowledge, this is the first genera…
Columbia University（哥伦比亚大学）；Princeton University（普林斯顿大学）
We present new minimax results that concisely capture the relative benefits of source and target labeled data, under covariate-shift. Namely, we show that the benefits of target labels are controlled by a transfer-exponent $γ$ that encodes how singular Q is locally w.r.t. P, and interestingly allows situations where transfer did not seem possible under previous insights. In fact, our new minimax analysis - in terms of $γ$ - reveals a continuum of regimes ranging from situations where target labels have little benefit, to regimes where target labels dramatically improve classification. We then …
In safety-critical applications of machine learning, it is often important to abstain from making predictions on low confidence examples. Standard abstention methods tend to be focused on optimizing top-k accuracy, but in many applications, accuracy is not the metric of interest. Further, label shift (a shift in class proportions between training time and prediction time) is ubiquitous in practical settings, and existing abstention methods do not handle label shift well. In this work, we present a general framework for abstention that can be applied to optimize any metric of interest, that is …
Theory-inspired Label Shift Adaptation via Aligned Distribution Mixture
College of Science, National University of Defense Technology（国防科技大学理学院）；Institute of Big Data Science and Industry, Shanxi University（山西大学大数据科学与产业研究院）
Discrepancy between training and testing domains is a fundamental problem in the generalization of machine learning techniques. Recently, several approaches have been proposed to learn domain invariant feature representations through adversarial deep learning. However, label shift, where the percentage of data in each class is different between domains, has received less attention. Label shift naturally arises in many contexts, especially in behavioral studies where the behaviors are freely chosen. In this work, we propose a method called Domain Adversarial nets for Target Shift (DATS) to addr…
LIME is a popular approach for explaining a black-box prediction through an interpretable model that is trained on instances in the vicinity of the predicted instance. To generate these instances, LIME randomly selects a subset of the non-zero features of the predicted instance. After that, the perturbed instances are fed into the black-box model to obtain labels for these, which are then used for training the interpretable model. In this study, we present a systematic evaluation of the interpretable models that are output by LIME on the two use-cases that were considered in the original paper…
We study generalization under labeled shift for categorical and general normed label spaces. We propose a series of methods to estimate the importance weights from labeled source to unlabeled target domain and provide confidence bounds for these estimators. We deploy these estimators and provide generalization bounds in the unlabeled target domain.
Monash University（莫纳什大学）；VinAI Research（VinAI研究院）；University of Michigan, Ann Arbor（密歇根大学安娜堡分校）；University of Texas, Austin（德克萨斯大学奥斯汀分校）
We study the label shift problem between the source and target domains in general domain adaptation (DA) settings. We consider transformations transporting the target to source domains, which enable us to align the source and target examples. Through those transformations, we define the label shift between two domains via optimal transport and develop theory to investigate the properties of DA under various DA settings (e.g., closed-set, partial-set, open-set, and universal settings). Inspired from the developed theory, we propose Label and Data Shift Reduction via Optimal Transport (LDROT) wh…
A generalized approach to label shift: the Conditional Probability Shift Model
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）
Nanjing University（南京大学）；The University of Tokyo（东京大学）；RIKEN AIP（理化学研究所人工智能研究中心）
The standard supervised learning paradigm works effectively when training data shares the same distribution as the upcoming testing samples. However, this stationary assumption is often violated in real-world applications, especially when testing data appear in an online fashion. In this paper, we formulate and investigate the problem of \emph{online label shift} (OLaS): the learner trains an initial model from the labeled offline data and then deploys it to an unlabeled online environment where the underlying label distribution changes over time but the label-conditional density does not. The…
Criteo AI Lab（Criteo人工智能实验室）；Ecole Polytechnique（巴黎综合理工学院）；INSA de Rouen Normandie（鲁昂国立应用科学学院）；Université Technologique de Compiègne（贡比涅技术大学）；Université de Rouen Normandie（鲁昂诺曼底大学）；Université de Bretagne Sud（南布列塔尼大学）
We address the problem of unsupervised domain adaptation under the setting of generalized target shift (joint class-conditional and label shifts). For this framework, we theoretically show that, for good generalization, it is necessary to learn a latent representation in which both marginals and class-conditional distributions are aligned across domains. For this sake, we propose a learning problem that minimizes importance weighted loss in the source domain and a Wasserstein distance between weighted marginals. For a proper weighting, we provide an estimator of target label proportion by blen…
Southwest University（西南大学）；China University of Geosciences（中国地质大学）；George Mason University（乔治梅森大学）；Deakin University（迪肯大学）；Beijing University of Civil Engineering and Architecture（北京建筑大学）
Multi-view Multi-instance Multi-label Learning(M3L) deals with complex objects encompassing diverse instances, represented with different feature views, and annotated with multiple labels. Existing M3L solutions only partially explore the inter or intra relations between objects (or bags), instances, and labels, which can convey important contextual information for M3L. As such, they may have a compromised performance. In this paper, we propose a collaborative matrix factorization based solution called M3Lcmf. M3Lcmf first uses a heterogeneous network composed of nodes of bags, instances, and …
Deployed machine learning (ML) models often encounter new user data that differs from their training data. Therefore, estimating how well a given model might perform on the new data is an important step toward reliable ML applications. This is very challenging, however, as the data distribution can change in flexible ways, and we may not have any labels on the new data, which is often the case in monitoring settings. In this paper, we propose a new distribution shift model, Sparse Joint Shift (SJS), which considers the joint shift of both labels and a few features. This unifies and generalizes…
Southwest University（西南大学）；Shandong University（山东大学）；Joint SDU-NTU Centre for Artificial Intelligence Research（山东大学-南洋理工大学人工智能联合研究中心）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；George Mason University（乔治梅森大学）
Multi-typed objects Multi-view Multi-instance Multi-label Learning (M4L) deals with interconnected multi-typed objects (or bags) that are made of diverse instances, represented with heterogeneous feature views and annotated with a set of non-exclusive but semantically related labels. M4L is more general and powerful than the typical Multi-view Multi-instance Multi-label Learning (M3L), which only accommodates single-typed bags and lacks the power to jointly model the naturally interconnected multi-typed objects in the physical world. To combat with this novel and challenging learning task, we …
What sorts of structure might enable a learner to discover classes from unlabeled data? Traditional approaches rely on feature-space similarity and heroic assumptions on the data. In this paper, we introduce unsupervised learning under Latent Label Shift (LLS), where we have access to unlabeled data from multiple domains such that the label marginals $p_d(y)$ can shift across domains but the class conditionals $p(\mathbf{x}|y)$ do not. This work instantiates a new principle for identifying classes: elements that shift together group together. For finite input spaces, we establish an isomorphis…
Covariate shift relaxes the widely-employed independent and identically distributed (IID) assumption by allowing different training and testing input distributions. Unfortunately, common methods for addressing covariate shift by trying to remove the bias between training and testing distributions using importance weighting often provide poor performance guarantees in theory and unreliable predictions with high variance in practice. Recently developed methods that construct a predictor that is inherently robust to the difficulties of learning under covariate shift are restricted to minimizing l…
YerevaNN；Yerevan State University（埃里温国立大学）；University of Southern California（南加州大学）
Investigation of machine learning algorithms robust to changes between the training and test distributions is an active area of research. In this paper we explore a special type of dataset shift which we call class-dependent domain shift. It is characterized by the following features: the input data causally depends on the label, the shift in the data is fully explained by a known variable, the variable which controls the shift can depend on the label, there is no shift in the label distribution. We define a simple optimization problem with an information theoretic constraint and attempt to so…
Shenzhen Key Laboratory of Visual Object Detection and Recognition, Harbin Institute of Technology, Shenzhen, China（哈尔滨工业大学（深圳））；Pengcheng Laboratory, Shenzhen, China（鹏城实验室）
As we all know, multi-view data is more expressive than single-view data and multi-label annotation enjoys richer supervision information than single-label, which makes multi-view multi-label learning widely applicable for various pattern recognition tasks. In this complex representation learning problem, three main challenges can be characterized as follows: i) How to learn consistent representations of samples across all views? ii) How to exploit and utilize category correlations of multi-label to guide inference? iii) How to avoid the negative impact resulting from the incompleteness of vie…
Carnegie Mellon University（卡内基梅隆大学）；Amazon AI（亚马逊人工智能）；UC Santa Barbara（加州大学圣巴巴拉分校）
Faced with distribution shift between training and test set, we wish to detect and quantify the shift, and to correct our classifiers without test set labels. Motivated by medical diagnosis, where diseases (targets) cause symptoms (observations), we focus on label shift, where the label marginal $p(y)$ changes but the conditional $p(x| y)$ does not. We propose Black Box Shift Estimation (BBSE) to estimate the test distribution $p(y)$. BBSE exploits arbitrary black box predictors to reduce dimensionality prior to shift correction. While better predictors give tighter estimates, BBSE works even …
We introduce the problem of domain adaptation under Open Set Label Shift (OSLS) where the label distribution can change arbitrarily and a new class may arrive during deployment, but the class-conditional distributions p(x|y) are domain-invariant. OSLS subsumes domain adaptation under label shift and Positive-Unlabeled (PU) learning. The learner's goals here are two-fold: (a) estimate the target label distribution, including the novel class; and (b) learn a target classifier. First, we establish necessary and sufficient conditions for identifying these quantities. Second, motivated by advances …
University of Amsterdam（阿姆斯特丹大学）；University of Exeter（埃克塞特大学）；Microsoft Research（微软研究院）；University of Tuebingen（蒂宾根大学）
The information bottleneck principle provides an information-theoretic method for representation learning, by training an encoder to retain all information which is relevant for predicting the label while minimizing the amount of other, excess information in the representation. The original formulation, however, requires labeled data to identify the superfluous information. In this work, we extend this ability to the multi-view unsupervised setting, where two views of the same underlying entity are provided but the label is unknown. This enables us to identify superfluous information as that n…
Peking University（北京大学）；University of Technology, Sydney（悉尼科技大学）
There is growing interest in multi-label image classification due to its critical role in web-based image analytics-based applications, such as large-scale image retrieval and browsing. Matrix completion has recently been introduced as a method for transductive (semi-supervised) multi-label classification, and has several distinct advantages, including robustness to missing data and background noise in both feature and label space. However, it is limited by only considering data represented by a single-view feature, which cannot precisely characterize images containing several semantic concept…
Multi-label classification deals with the problem where each instance is associated with multiple class labels. Because evaluation in multi-label classification is more complicated than single-label setting, a number of performance measures have been proposed. It is noticed that an algorithm usually performs differently on different measures. Therefore, it is important to understand which algorithms perform well on which measure(s) and why. In this paper, we propose a unified margin view to revisit eleven performance measures in multi-label classification. In particular, we define label-wise m…
Microsoft Research Montreal（微软研究院蒙特利尔）；D. E. Shaw & Co.（D. E. Shaw公司）；UC Santa Barbara（加州大学圣巴巴拉分校）
Adversarial learning has demonstrated good performance in the unsupervised domain adaptation setting, by learning domain-invariant representations. However, recent work has shown limitations of this approach when label distributions differ between the source and target domains. In this paper, we propose a new assumption, generalized label shift ($GLS$), to improve robustness against mismatched label distributions. $GLS$ states that, conditioned on the label, there exists a representation of the input that is invariant between the source and target domains. Under $GLS$, we provide theoretical g…
Label-shift robust federated feature screening for high-dimensional classification
Center for Applied Statistics and School of Statistics Renmin University of China（应用统计中心和中国人民大学统计学院）；School of Mathematics and Statistics Xi’an Jiaotong University（西安交通大学数学与统计学院）；Department of Mathematics and Fundamental Research Peng Cheng Laboratory School of Mathematics and Statistics Xi’an Jiaotong University（数学与基础研究部鹏城实验室数学与统计学院）
