Today's available datasets in the wild, e.g., from social media and open platforms, present tremendous opportunities and challenges for deep learning, as there is a significant portion of tagged images, but often with noisy, i.e. erroneous, labels. Recent studies improve the robustness of deep models against noisy labels without the knowledge of true labels. In this paper, we advocate to derive a stronger classifier which proactively makes use of the noisy labels in addition to the original images - turning noisy labels into learning features. To such an end, we propose a novel framework, ExpertNet, composed of Amateur and Expert, which iteratively learn from each other. Amateur is a regular image classifier trained by the feedback of Expert, which imitates how human experts would correct the predicted labels from Amateur using the noise pattern learnt from the knowledge of both the noisy and ground truth labels. The trained Amateur and Expert proactively leverage the images and their noisy labels to infer image classes. Our empirical evaluations on noisy versions of CIFAR-10, CIFAR-100 and real-world data of Clothing1M show that the proposed model can achieve robust classification against a wide range of noise ratios and with as little as 20-50% training data, compared to state-of-the-art deep models that solely focus on distilling the impact of noisy labels.
Several works have shown that perturbation stable instances of the MAP inference problem in Potts models can be solved exactly using a natural linear programming (LP) relaxation. However, most of these works give few (or no) guarantees for the LP solutions on instances that do not satisfy the relatively strict perturbation stability definitions. In this work, we go beyond these stability results by showing that the LP approximately recovers the MAP solution of a stable instance even after the instance is corrupted by noise. This "noisy stable" model realistically fits with practical MAP infere…
We study a practical algorithm for sparse principal component analysis (PCA) of incomplete and noisy data. Our algorithm is based on the semidefinite program (SDP) relaxation of the non-convex $l_1$-regularized PCA problem. We provide theoretical and experimental evidence that SDP enables us to exactly recover the true support of the sparse leading eigenvector of the unknown true matrix, despite only observing an incomplete (missing uniformly at random) and noisy version of it. We derive sufficient conditions for exact recovery, which involve matrix incoherence, the spectral gap between the la…
We consider learning Ising tree models when the observations from the nodes are corrupted by independent but non-identically distributed noise with unknown statistics. Katiyar et al. (2020) showed that although the exact tree structure cannot be recovered, one can recover a partial tree structure; that is, a structure belonging to the equivalence class containing the true tree. This paper presents a systematic improvement of Katiyar et al. (2020). First, we present a novel impossibility result by deriving a bound on the necessary number of samples for partial recovery. Second, we derive a sign…
We propose a new framework -- Square Root Principal Component Pursuit -- for low-rank matrix recovery from observations corrupted with noise and outliers. Inspired by the square root Lasso, this new formulation does not require prior knowledge of the noise level. We show that a single, universal choice of the regularization parameter suffices to achieve reconstruction error proportional to the (a priori unknown) noise level. In comparison, previous formulations such as stable PCP rely on noise-dependent parameters to achieve similar performance, and are therefore challenging to deploy in appli…
Thresholded Basis Pursuit: An LP Algorithm for Achieving Optimal Support Recovery for Sparse and Approximately Sparse Signals from Noisy Random Measurements
Exploring the Limitations of kNN Noisy Feature Detection and Recovery for Self-Driving Labs
University of Toronto（多伦多大学）；Artificial, Inc.（Artificial公司）；National Research Council Canada（加拿大国家研究委员会）；Natural Resources Canada（加拿大自然资源部）；Vector Institute for Artificial Intelligence（Vector人工智能研究所）；Schwartz Reisman Institute for Technology and Society（Schwartz Reisman技术与社会研究所）
We propose a novel deep neural network, coined DeepFPC-$\ell_2$, for solving the 1-bit compressed sensing problem. The network is designed by unfolding the iterations of the fixed-point continuation (FPC) algorithm with one-sided $\ell_2$-norm (FPC-$\ell_2$). The DeepFPC-$\ell_2$ method shows higher signal reconstruction accuracy and convergence speed than the traditional FPC-$\ell_2$ algorithm. Furthermore, we compare its robustness to noise with the previously proposed DeepFPC network---which stemmed from unfolding the FPC-$\ell_1$ algorithm---for different signal to noise ratio (SNR) and si…
In this work, we study the performance of sub-gradient method (SubGM) on a natural nonconvex and nonsmooth formulation of low-rank matrix recovery with $\ell_1$-loss, where the goal is to recover a low-rank matrix from a limited number of measurements, a subset of which may be grossly corrupted with noise. We study a scenario where the rank of the true solution is unknown and over-estimated instead. The over-estimation of the rank gives rise to an over-parameterized model in which there are more degrees of freedom than needed. Such over-parameterization may lead to overfitting, or adversely af…
The power of small initialization in noisy low-tubal-rank tensor recovery
State Key Laboratory of Robotics and Intelligent Systems, Shenyang Institute of Automation, Chinese Academy of Sciences, China（机器人与智能系统国家重点实验室，沈阳自动化研究所，中国科学院，中国）；University of Chinese Academy of Sciences, China（中国科学院大学，中国）；School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore（南洋理工大学电子与电气工程学院，新加坡）；The Center for Intelligent Decision-making and Machine Learning, School of Management, Xi’an Jiaotong University, China（智能决策与机器学习中心，西安交通大学管理学院，中国）
Learning from unlabeled and noisy data is one of the grand challenges of machine learning. As such, it has seen a flurry of research with new ideas proposed continuously. In this work, we revisit a classical idea: Stein's Unbiased Risk Estimator (SURE). We show that, in the context of image recovery, SURE and its generalizations can be used to train convolutional neural networks (CNNs) for a range of image denoising and recovery problems without any ground truth data. Specifically, our goal is to reconstruct an image $x$ from a noisy linear transformation (measurement) of the image. We conside…
Geometric Data Perturbation with Noisy-Anchor Alignment for Privacy-Preserving Collaborative Learning
University of Tsukuba（筑波大学）；Graduate School of Science and Technology, University of Tsukuba（筑波大学大学院理工学研究科）；Institute of Systems and Information Engineering, University of Tsukuba（筑波大学系统情报工程学系）；Center for Artificial Intelligence Research, Tsukuba Institute for Advanced Research (TIAR), University of Tsukuba（筑波大学筑波高等研究院人工智能研究中心）
Chinese Academy of Sciences（中国科学院）；National University of Singapore（新加坡国立大学）
In this paper, we aim to estimate the direction of an underlying signal from its nonlinear observations following the semi-parametric single index model (SIM). Unlike conventional compressed sensing where the signal is assumed to be sparse, we assume that the signal lies in the range of an $L$-Lipschitz continuous generative model with bounded $k$-dimensional inputs. This is mainly motivated by the tremendous success of deep generative models in various real applications. Our reconstruction method is non-iterative (though approximating the projection step may use an iterative procedure) and hi…
In this paper, we consider the graph alignment problem, which is the problem of recovering, given two graphs, a one-to-one mapping between nodes that maximizes edge overlap. This problem can be viewed as a noisy version of the well-known graph isomorphism problem and appears in many applications, including social network deanonymization and cellular biology. Our focus here is on partial recovery, i.e., we look for a one-to-one mapping which is correct on a fraction of the nodes of the graph rather than on all of them, and we assume that the two input graphs to the problem are correlated Erdős-…
One-bit compressive sensing is concerned with the accurate recovery of an underlying sparse signal of interest from its one-bit noisy measurements. The conventional signal recovery approaches for this problem are mainly developed based on the assumption that an exact knowledge of the sensing matrix is available. In this work, however, we present a novel data-driven and model-based methodology that achieves blind recovery; i.e., signal recovery without requiring the knowledge of the sensing matrix. To this end, we make use of the deep unfolding technique and develop a model-driven deep neural a…
