Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating mechanism. In this paper we work under the model assumption that the data is made of random perturbations of feature vectors lying on a low-dimensional manifold. We study two questions: how to define the similarity relationship over noisy data points, and what is the resulting impact of the choice of similarity in the extraction of global geometric information from the underlying manifold. We provide concrete mathematical evidence that using a local regularization of the noisy data to define the similarity improves the approximation of the hidden Euclidean distance between unperturbed points. Furthermore, graph-based objects constructed with the locally regularized similarity function satisfy better error bounds in their recovery of global geometric ones. Our theory is supported by numerical experiments that demonstrate that the gain in geometric understanding facilitated by local regularization translates into a gain in classification accuracy in simulated and real data.
The University of Tokyo（东京大学）；RIKEN AIP（理化学研究所先进智能项目中心）
Many weakly supervised classification methods employ a noise transition matrix to capture the class-conditional label corruption. To estimate the transition matrix from noisy data, existing methods often need to estimate the noisy class-posterior, which could be unreliable due to the overconfidence of neural networks. In this work, we propose a theoretically grounded method that can estimate the noise transition matrix and learn a classifier simultaneously, without relying on the error-prone noisy class-posterior estimation. Concretely, inspired by the characteristics of the stochastic label c…
Deep neural networks (DNNs) exhibit great success on many tasks with the help of large-scale well annotated datasets. However, labeling large-scale data can be very costly and error-prone so that it is difficult to guarantee the annotation quality (i.e., having noisy labels). Training on these noisy labeled datasets may adversely deteriorate their generalization performance. Existing methods either rely on complex training stage division or bring too much computation for marginal performance improvement. In this paper, we propose a Temporal Calibrated Regularization (TCR), in which we utilize …
We propose a hierarchical learning strategy aimed at generating sparse representations and associated models for large noisy datasets. The hierarchy follows from approximation spaces identified at successively finer scales. For promoting model generalization at each scale, we also introduce a novel, projection based penalty operator across multiple dimension, using permutation operators for incorporating proximity and ordering information. The paper presents a detailed analysis of approximation properties in the reconstruction Reproducing Kernel Hilbert Spaces (RKHS) with emphasis on optimalit…
Deep Learning with noisy labels is a practically challenging problem in weakly supervised learning. The state-of-the-art approaches "Decoupling" and "Co-teaching+" claim that the "disagreement" strategy is crucial for alleviating the problem of learning with noisy labels. In this paper, we start from a different perspective and propose a robust learning paradigm called JoCoR, which aims to reduce the diversity of two networks during training. Specifically, we first use two networks to make predictions on the same mini-batch data and calculate a joint loss with Co-Regularization for each traini…
New York University（纽约大学）；NYU School of Medicine（纽约大学医学院）
We propose a novel framework to perform classification via deep learning in the presence of noisy annotations. When trained on noisy labels, deep neural networks have been observed to first fit the training data with clean labels during an "early learning" phase, before eventually memorizing the examples with false labels. We prove that early learning and memorization are fundamental phenomena in high-dimensional classification tasks, even in simple linear models, and give a theoretical explanation in this setting. Motivated by these findings, we develop a new technique for noisy classificatio…
Large datasets often have unreliable labels-such as those obtained from Amazon's Mechanical Turk or social media platforms-and classifiers trained on mislabeled datasets often exhibit poor performance. We present a simple, effective technique for accounting for label noise when training deep neural networks. We augment a standard deep network with a softmax layer that models the label noise statistics. Then, we train the deep network and noise model jointly via end-to-end stochastic gradient descent on the (perhaps mislabeled) dataset. The augmented model is overdetermined, so in order to enco…
Harbin Institute of Technology（哈尔滨工业大学）；Peng Cheng Laboratory（鹏城实验室）；Tsinghua University（清华大学）
Learning with noisy labels is an important and challenging task for training accurate deep neural networks. Some commonly-used loss functions, such as Cross Entropy (CE), suffer from severe overfitting to noisy labels. Robust loss functions that satisfy the symmetric condition were tailored to remedy this problem, which however encounter the underfitting effect. In this paper, we theoretically prove that \textbf{any loss can be made robust to noisy labels} by restricting the network output to the set of permutations over a fixed vector. When the fixed vector is one-hot, we only need to constra…
Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；McGill University（麦吉尔大学）；Université de Montréal（蒙特利尔大学）
It is common in computer vision to be confronted with domain shift: images which have the same class but different acquisition conditions. In domain adaptation (DA), one wants to classify unlabeled target images using source labeled images. Unfortunately, deep neural networks trained on a source training set perform poorly on target images which do not belong to the training domain. One strategy to improve these performances is to align the source and target image distributions in an embedded space using optimal transport (OT). However OT can cause negative transfer, i.e. aligning samples with…
We propose an AdaPtive Noise Augmentation (PANDA) technique to regularize the estimation and construction of undirected graphical models. PANDA iteratively optimizes the objective function given the noise augmented data until convergence to achieve regularization on model parameters. The augmented noises can be designed to achieve various regularization effects on graph estimation, such as the bridge (including lasso and ridge), elastic net, adaptive lasso, and SCAD penalization; it also realizes the group lasso and fused ridge. We examine the tail bound of the noise-augmented loss function an…
Consistency regularization is a commonly-used technique for semi-supervised and self-supervised learning. It is an auxiliary objective function that encourages the prediction of the network to be similar in the vicinity of the observed training samples. Hendrycks et al. (2020) have recently shown such regularization naturally brings test-time robustness to corrupted data and helps with calibration. This paper empirically studies the relevance of consistency regularization for training-time robustness to noisy labels. First, we make two interesting and useful observations regarding the consiste…
University Bretagne Sud（布列塔尼南部大学）；CNRS（法国国家科学研究中心）；INRIA（法国国家信息与自动化研究所）；IRISA（法国信息与自动化系统研究所）；InterDigital R&D（InterDigital研发中心）；Université de Paris（巴黎大学）；Wageningen University（瓦赫宁根大学）；École Polytechnique（巴黎综合理工学院）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Noisy labels often occur in vision datasets, especially when they are obtained from crowdsourcing or Web scraping. We propose a new regularization method, which enables learning robust classifiers in presence of noisy data. To achieve this goal, we propose a new adversarial regularization scheme based on the Wasserstein distance. Using this distance allows taking into account specific relations between classes by leveraging the geometric properties of the labels space. Our Wasserstein Adversarial Regularization (WAR) encodes a selective regularization, which promotes smoothness of the classifi…
KU Leuven（鲁汶大学）；Samsung AI Center（三星人工智能中心）；Tencent AI lab（腾讯人工智能实验室）；Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Supervised learning can be viewed as distilling relevant information from input data into feature representations. This process becomes difficult when supervision is noisy as the distilled information might not be relevant. In fact, recent research shows that networks can easily overfit all labels including those that are corrupted, and hence can hardly generalize to clean datasets. In this paper, we focus on the problem of learning with noisy labels and introduce compression inductive bias to network architectures to alleviate this over-fitting problem. More precisely, we revisit one classica…
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；CEA（法国原子能和替代能源委员会）；Institut de physique théorique（理论物理研究所）；Laboratoire de Physique de l’Ecole normale supérieure（巴黎高等师范学院物理实验室）；ENS（巴黎高等师范学院）；Université PSL（巴黎文理研究大学）；Sorbonne Université（索邦大学）；Université de Paris（巴黎大学）；John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）
We consider a high-dimensional mixture of two Gaussians in the noisy regime where even an oracle knowing the centers of the clusters misclassifies a small but finite fraction of the points. We provide a rigorous analysis of the generalization error of regularized convex classifiers, including ridge, hinge and logistic regression, in the high-dimensional limit where the number $n$ of samples and their dimension $d$ go to infinity while their ratio is fixed to $α= n/d$. We discuss surprising effects of the regularization that in some cases allows to reach the Bayes-optimal performances. We also …
In machine learning, data augmentation (DA) is a technique for improving the generalization performance. In this paper, we mainly considered gradient descent of linear regression under DA using noisy copies of datasets, in which noise is injected into inputs. We analyzed the situation where random noisy copies are newly generated and used at each epoch; i.e., the case of using on-line noisy copies. Therefore, it is viewed as an analysis on a method using noise injection into training process by DA manner; i.e., on-line version of DA. We derived the averaged behavior of training process under t…
Recently deep neural networks have shown their capacity to memorize training data, even with noisy labels, which hurts generalization performance. To mitigate this issue, we provide a simple but effective baseline method that is robust to noisy labels, even with severe noise. Our objective involves a variance regularization term that implicitly penalizes the Jacobian norm of the neural network on the whole training set (including the noisy-labeled data), which encourages generalization and prevents overfitting to the corrupted labels. Experiments on both synthetically generated incorrect label…
Nordita, KTH Royal Institute of Technology（北欧理论物理研究所，瑞典皇家理工学院）；Stockholm University（斯德哥尔摩大学）；University of Pittsburgh（匹兹堡大学）；ICSI（国际计算机科学研究所）；UC Berkeley（加州大学伯克利分校）
We provide a general framework for studying recurrent neural networks (RNNs) trained by injecting noise into hidden states. Specifically, we consider RNNs that can be viewed as discretizations of stochastic differential equations driven by input data. This framework allows us to study the implicit regularization effect of general noise injection schemes by deriving an approximate explicit regularizer in the small noise regime. We find that, under reasonable assumptions, this implicit regularization promotes flatter minima; it biases towards models with more stable dynamics; and, in classificat…
Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape representations; or (ii) loss functions explicitly defined over the neural level sets. In this paper we offer a new paradigm for computing high fidelity implicit neural representations directly from raw data (i.e., point clouds, with or without normal information). We observe that a rather simple loss function, encouraging the neural network to vanish on the inpu…
