How does Disagreement Help Generalization against Label Corruption?

Learning with noisy labels is one of the hottest problems in weakly-supervised learning. Based on memorization effects of deep neural networks, training on small-loss instances becomes very promising for handling noisy labels. This fosters the state-of-the-art approach "Co-teaching" that cross-trains two deep neural networks using the small-loss trick. However, with the increase of epochs, two networks converge to a consensus and Co-teaching reduces to the self-training MentorNet. To tackle this issue, we propose a robust learning paradigm called Co-teaching+, which bridges the "Update by Disagreement" strategy with the original Co-teaching. First, two networks feed forward and predict all data, but keep prediction disagreement data only. Then, among such disagreement data, each network selects its small-loss data, but back propagates the small-loss data from its peer network and updates its own parameters. Empirical results on benchmark datasets demonstrate that Co-teaching+ is much superior to many state-of-the-art methods in the robustness of trained models.

How Does Disagreement Benefit Co-teaching?

Learning with noisy labels is one of the most important question in weakly-supervised learning domain. Classical approaches focus on adding the regularization or estimating the noise transition matrix. However, either a regularization bias is permanently introduced, or the noise transition matrix is hard to be estimated accurately. In this paper, following a novel path to train on small-loss samples, we propose a robust learning paradigm called Co-teaching+. This paradigm naturally bridges "Update by Disagreement" strategy with Co-teaching that trains two deep neural networks, thus consists of disagreement-update step and cross-update step. In disagreement-update step, two networks predicts all data first, and feeds forward prediction disagreement data only. Then, in cross-update step, each network selects its small-loss data from such disagreement data, but back propagates the small-loss data by its peer network and updates itself parameters. Empirical results on noisy versions of MNIST, CIFAR-10 and NEWS demonstrate that Co-teaching+ is much superior to the state-of-the-art methods in the robustness of trained deep models.

A Survey on Multi-output Learning

Multi-output learning aims to simultaneously predict multiple outputs given an input. It is an important learning problem due to the pressing need for sophisticated decision making in real-world applications. Inspired by big data, the 4Vs characteristics of multi-output imposes a set of challenges to multi-output learning, in terms of the volume, velocity, variety and veracity of the outputs. Increasing number of works in the literature have been devoted to the study of multi-output learning and the development of novel approaches for addressing the challenges encountered. However, it lacks a comprehensive overview on different types of challenges of multi-output learning brought by the characteristics of the multiple outputs and the techniques proposed to overcome the challenges. This paper thus attempts to fill in this gap to provide a comprehensive review on this area. We first introduce different stages of the life cycle of the output labels. Then we present the paradigm on multi-output learning, including its myriads of output structures, definitions of its different sub-problems, model evaluation metrics and popular data repositories used in the study. Subsequently, we review a number of state-of-the-art multi-output learning methods, which are categorized based on the challenges.

VR-SGD: A Simple Stochastic Variance Reduction Method for Machine Learning

In this paper, we propose a simple variant of the original SVRG, called variance reduced stochastic gradient descent (VR-SGD). Unlike the choices of snapshot and starting points in SVRG and its proximal variant, Prox-SVRG, the two vectors of VR-SGD are set to the average and last iterate of the previous epoch, respectively. The settings allow us to use much larger learning rates, and also make our convergence analysis more challenging. We also design two different update rules for smooth and non-smooth objective functions, respectively, which means that VR-SGD can tackle non-smooth and/or non-strongly convex problems directly without any reduction techniques. Moreover, we analyze the convergence properties of VR-SGD for strongly convex problems, which show that VR-SGD attains linear convergence. Different from its counterparts that have no convergence guarantees for non-strongly convex problems, we also provide the convergence guarantees of VR-SGD for this case, and empirically verify that VR-SGD with varying learning rates achieves similar performance to its momentum accelerated variant that has the optimal convergence rate $\mathcal{O}(1/T^2)$. Finally, we apply VR-SGD to solve various machine learning problems, such as convex and non-convex empirical risk minimization, and leading eigenvalue computation. Experimental results show that VR-SGD converges significantly faster than SVRG and Prox-SVRG, and usually outperforms state-of-the-art accelerated methods, e.g., Katyusha.

Privacy-preserving Stochastic Gradual Learning

It is challenging for stochastic optimizations to handle large-scale sensitive data safely. Recently, Duchi et al. proposed private sampling strategy to solve privacy leakage in stochastic optimizations. However, this strategy leads to robustness degeneration, since this strategy is equal to the noise injection on each gradient, which adversely affects updates of the primal variable. To address this challenge, we introduce a robust stochastic optimization under the framework of local privacy, which is called Privacy-pREserving StochasTIc Gradual lEarning (PRESTIGE). PRESTIGE bridges private updates of the primal variable (by private sampling) with the gradual curriculum learning (CL). Specifically, the noise injection leads to the issue of label noise, but the robust learning process of CL can combat with label noise. Thus, PRESTIGE yields "private but robust" updates of the primal variable on the private curriculum, namely an reordered label sequence provided by CL. In theory, we reveal the convergence rate and maximum complexity of PRESTIGE. Empirical results on six datasets show that, PRESTIGE achieves a good tradeoff between privacy preservation and robustness over baselines.

Target-Independent Active Learning via Distribution-Splitting

To reduce the label complexity in Agnostic Active Learning (A^2 algorithm), volume-splitting splits the hypothesis edges to reduce the Vapnik-Chervonenkis (VC) dimension in version space. However, the effectiveness of volume-splitting critically depends on the initial hypothesis and this problem is also known as target-dependent label complexity gap. This paper attempts to minimize this gap by introducing a novel notion of number density which provides a more natural and direct way to describe the hypothesis distribution than volume. By discovering the connections between hypothesis and input distribution, we map the volume of version space into the number density and propose a target-independent distribution-splitting strategy with the following advantages: 1) provide theoretical guarantees on reducing label complexity and error rate as volume-splitting; 2) break the curse of initial hypothesis; 3) provide model guidance for a target-independent AL algorithm in real AL tasks. With these guarantees, for AL application, we then split the input distribution into more near-optimal spheres and develop an application algorithm called Distribution-based A^2 (DA^2). Experiments further verify the effectiveness of the halving and querying abilities of DA^2. Contributions of this paper are as follows.

Understanding VAEs in Fisher-Shannon Plane

In information theory, Fisher information and Shannon information (entropy) are respectively used to quantify the uncertainty associated with the distribution modeling and the uncertainty in specifying the outcome of given variables. These two quantities are complementary and are jointly applied to information behavior analysis in most cases. The uncertainty property in information asserts a fundamental trade-off between Fisher information and Shannon information, which enlightens us the relationship between the encoder and the decoder in variational auto-encoders (VAEs). In this paper, we investigate VAEs in the Fisher-Shannon plane and demonstrate that the representation learning and the log-likelihood estimation are intrinsically related to these two information quantities. Through extensive qualitative and quantitative experiments, we provide with a better comprehension of VAEs in tasks such as high-resolution reconstruction, and representation learning in the perspective of Fisher information and Shannon information. We further propose a variant of VAEs, termed as Fisher auto-encoder (FAE), for practical needs to balance Fisher information and Shannon information. Our experimental results have demonstrated its promise in improving the reconstruction accuracy and avoiding the non-informative latent code as occurred in previous works.

Degeneration in VAE: in the Light of Fisher Information Loss

While enormous progress has been made to Variational Autoencoder (VAE) in recent years, similar to other deep networks, VAE with deep networks suffers from the problem of degeneration, which seriously weakens the correlation between the input and the corresponding latent codes, deviating from the goal of the representation learning. To investigate how degeneration affects VAE from a theoretical perspective, we illustrate the information transmission in VAE and analyze the intermediate layers of the encoders/decoders. Specifically, we propose a Fisher Information measure for the layer-wise analysis. With such measure, we demonstrate that information loss is ineluctable in feed-forward networks and causes the degeneration in VAE. We show that skip connections in VAE enable the preservation of information without changing the model architecture. We call this class of VAE equipped with skip connections as SCVAE and perform a range of experiments to show its advantages in information preservation and degeneration mitigation.

A Structured Perspective of Volumes on Active Learning

Active Learning (AL) is a learning task that requires learners interactively query the labels of the sampled unlabeled instances to minimize the training outputs with human supervisions. In theoretical study, learners approximate the version space which covers all possible classification hypothesis into a bounded convex body and try to shrink the volume of it into a half-space by a given cut size. However, only the hypersphere with finite VC dimensions has obtained formal approximation guarantees that hold when the classes of Euclidean space are separable with a margin. In this paper, we approximate the version space to a structured {hypersphere} that covers most of the hypotheses, and then divide the available AL sampling approaches into two kinds of strategies: Outer Volume Sampling and Inner Volume Sampling. After providing provable guarantees for the performance of AL in version space, we aggregate the two kinds of volumes to eliminate their sampling biases via finding the optimal inscribed hyperspheres in the enclosing space of outer volume. To touch the version space from Euclidean space, we propose a theoretical bridge called Volume-based Model that increases the `sampling target-independent'. In non-linear feature space, spanned by kernel, we use sequential optimization to globally optimize the original space to a sparse space by halving the size of the kernel space. Then, the EM (Expectation Maximization) model which returns the local center helps us to find a local representation. To describe this process, we propose an easy-to-implement algorithm called Volume-based AL (VAL).

Geometric Active Learning via Enclosing Ball Boundary

Active Learning (AL) requires learners to retrain the classifier with the minimum human supervisions or labeling in the unlabeled data pool when the current training set is not enough. However, general AL sampling strategies with a few label support inevitably suffer from performance decrease. To identify which samples determine the performance of the classification hyperplane, Core Vector Machine (CVM) and Ball Vector Machine (BVM) use the geometry boundary points of each Minimum Enclosing Ball (MEB) to train the classification hypothesis. Their theoretical analysis and experimental results show that the improved classifiers not only converge faster but also obtain higher accuracies compared with Support Vector Machine (SVM). Inspired by this, we formulate the cluster boundary point detection issue as the MEB boundary problem after presenting a convincing proof of this observation. Because the enclosing ball boundary may have a high fitting ratio when it can not enclose the class tightly, we split the global ball problem into two kinds of small Local Minimum Enclosing Ball (LMEB): Boundary ball (B-ball) and Core ball (C-ball) to tackle its over-fitting problem. Through calculating the update of radius and center when extending the local ball space, we adopt the minimum update ball to obtain the geometric update optimization scheme of B-ball and C-ball. After proving their update relationship, we design the LEB (Local Enclosing Ball) algorithm using centers of B-ball of each class to detect the enclosing ball boundary points for AL sampling. Experimental and theoretical studies have shown that the classification accuracy, time, and space performance of our proposed method significantly are superior than the state-of-the-art algorithms.