Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, machine learning and computer vision, however, this perception has not yet received a theoretical justification. To fill this gap, we prove that computing the Wasserstein distance between a discrete probability measure supported on two points and the Lebesgue measure on the standard hypercube is already #P-hard. This insight prompts us to seek approximate solutions for semi-discrete optimal transport problems. We thus perturb the underlying transportation cost with an additive disturbance governed by an ambiguous probability distribution, and we introduce a distributionally robust dual optimal transport problem whose objective function is smoothed with the most adverse disturbance distributions from within a given ambiguity set. We further show that smoothing the dual objective function is equivalent to regularizing the primal objective function, and we identify several ambiguity sets that give rise to several known and new regularization schemes. As a byproduct, we discover an intimate relation between semi-discrete optimal transport problems and discrete choice models traditionally studied in psychology and economics. To solve the regularized optimal transport problems efficiently, we use a stochastic gradient descent algorithm with imprecise stochastic gradient oracles. A new convergence analysis reveals that this algorithm improves the best known convergence guarantee for semi-discrete optimal transport problems with entropic regularizers.
Institute for Infocomm Research, A*STAR（新加坡科技研究局资讯通信研究院）
Generative Adversarial Networks are powerful generative models that are able to model the manifold of natural images. We leverage this property to perform manifold regularization by approximating a variant of the Laplacian norm using a Monte Carlo approximation that is easily computed with the GAN. When incorporated into the semi-supervised feature-matching GAN we achieve state-of-the-art results for GAN-based semi-supervised learning on CIFAR-10 and SVHN benchmarks, with a method that is significantly easier to implement than competing methods. We also find that manifold regularization improv…
Consistency regularization on label predictions becomes a fundamental technique in semi-supervised learning, but it still requires a large number of training iterations for high performance. In this study, we analyze that the consistency regularization restricts the propagation of labeling information due to the exclusion of samples with unconfident pseudo-labels in the model updates. Then, we propose contrastive regularization to improve both efficiency and accuracy of the consistency regularization by well-clustered features of unlabeled data. In specific, after strongly augmented samples ar…
Thompson sampling (TS) has attracted a lot of interest in the bandit area. It was introduced in the 1930s but has not been theoretically proven until recent years. All of its analysis in the combinatorial multi-armed bandit (CMAB) setting requires an exact oracle to provide optimal solutions with any input. However, such an oracle is usually not feasible since many combinatorial optimization problems are NP-hard and only approximation oracles are available. An example (Wang and Chen, 2018) has shown the failure of TS to learn with an approximation oracle. However, this oracle is uncommon and i…
Télécom ParisTech（巴黎高等电信学院）；Institute for Infocomm Research（信息通信研究院）；CentraleSupélec（中央理工-高等电力学院）；Nanyang Technological University（南洋理工大学）
GANS are powerful generative models that are able to model the manifold of natural images. We leverage this property to perform manifold regularization by approximating the Laplacian norm using a Monte Carlo approximation that is easily computed with the GAN. When incorporated into the feature-matching GAN of Improved GAN, we achieve state-of-the-art results for GAN-based semi-supervised learning on the CIFAR-10 dataset, with a method that is significantly easier to implement than competing methods.
KU Leuven（鲁汶大学）；imec（校际微电子中心）；Yonsei University（延世大学）
Deep neural networks (DNNs) have become increasingly important due to their excellent empirical performance on a wide range of problems. However, regularization is generally achieved by indirect means, largely due to the complex set of functions defined by a network and the difficulty in measuring function complexity. There exists no method in the literature for additive regularization based on a norm of the function, as is classically considered in statistical learning theory. In this work, we propose sampling-based approximations to weighted function norms as regularizers for deep neural net…
As annotations of data can be scarce in large-scale practical problems, leveraging unlabelled examples is one of the most important aspects of machine learning. This is the aim of semi-supervised learning. To benefit from the access to unlabelled data, it is natural to diffuse smoothly knowledge of labelled data to unlabelled one. This induces to the use of Laplacian regularization. Yet, current implementations of Laplacian regularization suffer from several drawbacks, notably the well-known curse of dimensionality. In this paper, we provide a statistical analysis to overcome those issues, and…
Delft University of Technology（代尔夫特理工大学）；University of Copenhagen（哥本哈根大学）
Manifold regularization is a commonly used technique in semi-supervised learning. It enforces the classification rule to be smooth with respect to the data-manifold. Here, we derive sample complexity bounds based on pseudo-dimension for models that add a convex data dependent regularization term to a supervised learning process, as is in particular done in Manifold regularization. We then compare the bound for those semi-supervised methods to purely supervised methods, and discuss a setting in which the semi-supervised method can only have a constant improvement, ignoring logarithmic terms. By…
Generative Adversarial Networks (GANs) based semi-supervised learning (SSL) approaches are shown to improve classification performance by utilizing a large number of unlabeled samples in conjunction with limited labeled samples. However, their performance still lags behind the state-of-the-art non-GAN based SSL approaches. We identify that the main reason for this is the lack of consistency in class probability predictions on the same image under local perturbations. Following the general literature, we address this issue via label consistency regularization, which enforces the class probabili…
Recent advances in semi-supervised learning have shown tremendous potential in overcoming a major barrier to the success of modern machine learning algorithms: access to vast amounts of human-labeled training data. Previous algorithms based on consistency regularization can harness the abundance of unlabeled data to produce impressive results on a number of semi-supervised benchmarks, approaching the performance of strong supervised baselines using only a fraction of the available labeled data. In this work, we challenge the long-standing success of consistency regularization by introducing se…
Compared with standard supervised learning, the key difficulty in semi-supervised learning is how to make full use of the unlabeled data. A recently proposed method, virtual adversarial training (VAT), smartly performs adversarial training without label information to impose a local smoothness on the classifier, which is especially beneficial to semi-supervised learning. In this work, we propose tangent-normal adversarial regularization (TNAR) as an extension of VAT by taking the data manifold into consideration. The proposed TNAR is composed by two complementary parts, the tangent adversarial…
U.S. Naval Academy（美国海军学院）；Naval Research Laboratory（海军研究实验室）
Many classification problems involve data instances that are interlinked with each other, such as webpages connected by hyperlinks. Techniques for "collective classification" (CC) often increase accuracy for such data graphs, but usually require a fully-labeled training graph. In contrast, we examine how to improve the semi-supervised learning of CC models when given only a sparsely-labeled graph, a common situation. We first describe how to use novel combinations of classifiers to exploit the different characteristics of the relational features vs. the non-relational features. We also extend …
Sookmyung Women’s University（淑明女子大学）；UNIST（蔚山科学技术院）；University of California Berkeley（加州大学伯克利分校）；Seoul National University（首尔国立大学）
Non-stationarity is ubiquitous in human behavior and addressing it in the contextual bandits is challenging. Several works have addressed the problem by investigating semi-parametric contextual bandits and warned that ignoring non-stationarity could harm performances. Another prevalent human behavior is social interaction which has become available in a form of a social network or graph structure. As a result, graph-based contextual bandits have received much attention. In this paper, we propose "SemiGraphTS," a novel contextual Thompson-sampling algorithm for a graph-based semi-parametric rew…
We propose a new regularization method based on virtual adversarial loss: a new measure of local smoothness of the conditional label distribution given input. Virtual adversarial loss is defined as the robustness of the conditional label distribution around each input data point against local perturbation. Unlike adversarial training, our method defines the adversarial direction without label information and is hence applicable to semi-supervised learning. Because the directions in which we smooth the model are only "virtually" adversarial, we call our method virtual adversarial training (VAT)…
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Washington（华盛顿大学）
We describe a graph-based semi-supervised learning framework in the context of deep neural networks that uses a graph-based entropic regularizer to favor smooth solutions over a graph induced by the data. The main contribution of this work is a computationally efficient, stochastic graph-regularization technique that uses mini-batches that are consistent with the graph structure, but also provides enough stochasticity (in terms of mini-batch data diversity) for convergence of stochastic gradient descent methods to good solutions. For this work, we focus on results of frame-level phone classifi…
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Washington（华盛顿大学）
We describe a computationally efficient, stochastic graph-regularization technique that can be utilized for the semi-supervised training of deep neural networks in a parallel or distributed setting. We utilize a technique, first described in [13] for the construction of mini-batches for stochastic gradient descent (SGD) based on synthesized partitions of an affinity graph that are consistent with the graph structure, but also preserve enough stochasticity for convergence of SGD to good local minima. We show how our technique allows a graph-based semi-supervised loss function to be decomposed i…
IBM Research AI（IBM研究院人工智能部门）；Thomas J. Watson Research Center（托马斯·J·沃森研究中心）
Active graph-based semi-supervised learning (AG-SSL) aims to select a small set of labeled examples and utilize their graph-based relation to other unlabeled examples to aid in machine learning tasks. It is also closely related to the sampling theory in graph signal processing. In this paper, we revisit the original formulation of graph-based SSL and prove the supermodularity of an AG-SSL objective function under a broad class of regularization functions parameterized by Stieltjes matrices. Under this setting, supermodularity yields a novel greedy label sampling algorithm with guaranteed perfo…
The success of deep learning relies on the availability of large-scale annotated data sets, the acquisition of which can be costly, requiring expert domain knowledge. Semi-supervised learning (SSL) mitigates this challenge by exploiting the behavior of the neural function on large unlabeled data. The smoothness of the neural function is a commonly used assumption exploited in SSL. A successful example is the adoption of mixup strategy in SSL that enforces the global smoothness of the neural function by encouraging it to behave linearly when interpolating between training examples. Despite its …
Incorporating spatial information into hyperspectral unmixing procedures has been shown to have positive effects, due to the inherent spatial-spectral duality in hyperspectral scenes. Current research works that consider spatial information are mainly focused on the linear mixing model. In this paper, we investigate a variational approach to incorporating spatial correlation into a nonlinear unmixing procedure. A nonlinear algorithm operating in reproducing kernel Hilbert spaces, associated with an $\ell_1$ local variation norm as the spatial regularizer, is derived. Experimental results, with…
Institute of Information Engineering, Chinese Academy of Sciences（中国科学院信息工程研究所）；Inception Institute of Artificial Intelligence (IIAI)（阿布扎比人工智能孵化研究所）；School of Cyber Security, University of Chinese Academy of Sciences（中国科学院大学网络空间安全学院）；National Engineering Research Center for Information Security（国家信息安全工程技术研究中心）；National Engineering Laboratory for Information Security Technology（国家信息安全技术工程实验室）
Manifold regularization, such as laplacian regularized least squares (LapRLS) and laplacian support vector machine (LapSVM), has been widely used in semi-supervised learning, and its performance greatly depends on the choice of some hyper-parameters. Cross-validation (CV) is the most popular approach for selecting the optimal hyper-parameters, but it has high complexity due to multiple times of learner training. In this paper, we provide a method to approximate the CV for manifold regularization based on a notion of robust statistics, called Bouligand influence function (BIF). We first provide…
The problem of learning from label proportions (LLP) involves training classifiers with weak labels on bags of instances, rather than strong labels on individual instances. The weak labels only contain the label proportion of each bag. The LLP problem is important for many practical applications that only allow label proportions to be collected because of data privacy or annotation cost, and has recently received lots of research attention. Most existing works focus on extending supervised learning models to solve the LLP problem, but the weak learning nature makes it hard to further improve L…
Trace norm regularization is a popular method of multitask learning. We give excess risk bounds with explicit dependence on the number of tasks, the number of examples per task and properties of the data distribution. The bounds are independent of the dimension of the input space, which may be infinite as in the case of reproducing kernel Hilbert spaces. A byproduct of the proof are bounds on the expected norm of sums of random positive semidefinite matrices with subexponential moments.
Carnegie Mellon University（卡内基梅隆大学）；University of Cambridge（剑桥大学）
We investigate a family of regression problems in a semi-supervised setting. The task is to assign real-valued labels to a set of $n$ sample points, provided a small training subset of $N$ labeled points. A goal of semi-supervised learning is to take advantage of the (geometric) structure provided by the large number of unlabeled data when assigning labels. We consider random geometric graphs, with connection radius $ε(n)$, to represent the geometry of the data set. Functionals which model the task reward the regularity of the estimator function and impose or reward the agreement with the trai…
Idiap Research Institute（伊迪亚普研究所）；Adobe Research（奥多比研究院）
In this paper, we explore various approaches for semi supervised learning in an end to end automatic speech recognition (ASR) framework. The first step in our approach involves training a seed model on the limited amount of labelled data. Additional unlabelled speech data is employed through a data selection mechanism to obtain the best hypothesized output, further used to retrain the seed model. However, uncertainties of the model may not be well captured with a single hypothesis. As opposed to this technique, we apply a dropout mechanism to capture the uncertainty by obtaining multiple hypot…
Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）；Center for Data Science, New York University（纽约大学数据科学中心）
We show a simple reduction which demonstrates the cryptographic hardness of learning a single periodic neuron over isotropic Gaussian distributions in the presence of noise. More precisely, our reduction shows that any polynomial-time algorithm (not necessarily gradient-based) for learning such functions under small noise implies a polynomial-time quantum algorithm for solving worst-case lattice problems, whose hardness form the foundation of lattice-based cryptography. Our core hard family of functions, which are well-approximated by one-layer neural networks, take the general form of a univa…
Semi-supervised Laplacian regularization, a standard graph-based approach for learning from both labelled and unlabelled data, was recently demonstrated to have an insignificant high dimensional learning efficiency with respect to unlabelled data (Mai and Couillet 2018), causing it to be outperformed by its unsupervised counterpart, spectral clustering, given sufficient unlabelled data. Following a detailed discussion on the origin of this inconsistency problem, a novel regularization approach involving centering operation is proposed as solution, supported by both theoretical analysis and emp…
Tokyo Institute of Technology（东京工业大学）；Purdue University（普渡大学）
We propose a general information-theoretic approach called Seraph (SEmi-supervised metRic leArning Paradigm with Hyper-sparsity) for metric learning that does not rely upon the manifold assumption. Given the probability parameterized by a Mahalanobis distance, we maximize the entropy of that probability on labeled data and minimize it on unlabeled data following entropy regularization, which allows the supervised and unsupervised parts to be integrated in a natural and meaningful way. Furthermore, Seraph is regularized by encouraging a low-rank projection induced from the metric. The optimizat…
Tel Aviv University（特拉维夫大学）；University College London（伦敦大学学院）
Transfer learning is a very important tool in deep learning as it allows propagating information from one "source dataset" to another "target dataset", especially in the case of a small number of training examples in the latter. Yet, discrepancies between the underlying distributions of the source and target data are commonplace and are known to have a substantial impact on algorithm performance. In this work we suggest a novel information theoretic approach for the analysis of the performance of deep neural networks in the context of transfer learning. We focus on the task of semi-supervised …
In recent years, semi-supervised multi-view nonnegative matrix factorization (MVNMF) algorithms have achieved promising performances for multi-view clustering. While most of semi-supervised MVNMFs have failed to effectively consider discriminative information among clusters and feature alignment from multiple views simultaneously. In this paper, a novel Discriminatively Constrained Semi-Supervised Multi-View Nonnegative Matrix Factorization (DCS^2MVNMF) is proposed. Specifically, a discriminative weighting matrix is introduced for the auxiliary matrix of each view, which enhances the inter-cla…
Applied Artificial Intelligence Institute (A2I2), Deakin University（应用人工智能研究所（A2I2），迪肯大学）
We propose two generic methods for improving semi-supervised learning (SSL). The first integrates weight perturbation (WP) into existing "consistency regularization" (CR) based methods. We implement WP by leveraging variational Bayesian inference (VBI). The second method proposes a novel consistency loss called "maximum uncertainty regularization" (MUR). While most consistency losses act on perturbations in the vicinity of each data point, MUR actively searches for "virtual" points situated beyond this region that cause the most uncertain class predictions. This allows MUR to impose smoothness…
Baidu Research（百度研究院）；University of Oregon（俄勒冈大学）；University of Macau（澳门大学）
While recent studies on semi-supervised learning have shown remarkable progress in leveraging both labeled and unlabeled data, most of them presume a basic setting of the model is randomly initialized. In this work, we consider semi-supervised learning and transfer learning jointly, leading to a more practical and competitive paradigm that can utilize both powerful pre-trained models from source domain as well as labeled/unlabeled data in the target domain. To better exploit the value of both pre-trained weights and unlabeled target examples, we introduce adaptive consistency regularization th…
In this paper, we propose a novel graph-based approach for semi-supervised learning problems, which considers an adaptive adjacency of the examples throughout the unsupervised portion of the training. Adjacency of the examples is inferred using the predictions of a neural network model which is first initialized by a supervised pretraining. These predictions are then updated according to a novel unsupervised objective which regularizes another adjacency, now linking the output nodes. Regularizing the adjacency of the output nodes, inferred from the predictions of the network, creates an easier…
Lancaster University（兰卡斯特大学）；Harvard SEAS（哈佛大学工程与应用科学学院）；MPI for Informatics（马克斯·普朗克信息学研究所）
In many learning tasks, the structure of the target space of a function holds rich information about the relationships between evaluations of functions on different data points. Existing approaches attempt to exploit this relationship information implicitly by enforcing smoothness on function evaluations only. However, what happens if we explicitly regularize the relationships between function evaluations? Inspired by homophily, we regularize based on a smooth relationship function, either defined from the data or with labels. In experiments, we demonstrate that this significantly improves the…
Image classification is a challenging problem for computer in reality. Large numbers of methods can achieve satisfying performances with sufficient labeled images. However, labeled images are still highly limited for certain image classification tasks. Instead, lots of unlabeled images are available and easy to be obtained. Therefore, making full use of the available unlabeled data can be a potential way to further improve the performance of current image classification methods. In this paper, we propose a discriminative semi-supervised sparse representation algorithm for image classification.…
University of Oulu（奥卢大学）；Oulu University Hospital（奥卢大学医院）；KU Leuven（鲁汶大学）；Ailean Technologies Oy
Knee osteoarthritis (OA) is one of the highest disability factors in the world. This musculoskeletal disorder is assessed from clinical symptoms, and typically confirmed via radiographic assessment. This visual assessment done by a radiologist requires experience, and suffers from moderate to high inter-observer variability. The recent literature has shown that deep learning methods can reliably perform the OA severity assessment according to the gold standard Kellgren-Lawrence (KL) grading system. However, these methods require large amounts of labeled data, which are costly to obtain. In thi…
University of Technology Sydney（悉尼科技大学）；University of Tasmania（塔斯马尼亚大学）；Indian Institute of Technology Indore（印度理工学院印多尔分校）
Recently, distributed semi-supervised learning (DSSL) algorithms have shown their effectiveness in leveraging unlabeled samples over interconnected networks, where agents cannot share their original data with each other and can only communicate non-sensitive information with their neighbors. However, existing DSSL algorithms cannot cope with data uncertainties and may suffer from high computation and communication overhead problems. To handle these issues, we propose a distributed semi-supervised fuzzy regression (DSFR) model with fuzzy if-then rules and interpolation consistency regularizatio…
Semi-supervised learning has been an effective paradigm for leveraging unlabeled data to reduce the reliance on labeled data. We propose CoMatch, a new semi-supervised learning method that unifies dominant approaches and addresses their limitations. CoMatch jointly learns two representations of the training data, their class probabilities and low-dimensional embeddings. The two representations interact with each other to jointly evolve. The embeddings impose a smoothness constraint on the class probabilities to improve the pseudo-labels, whereas the pseudo-labels regularize the structure of th…
Network quantization, which aims to reduce the bit-lengths of the network weights and activations, has emerged as one of the key ingredients to reduce the size of neural networks for their deployments to resource-limited devices. In order to overcome the nature of transforming continuous activations and weights to discrete ones, recent study called Relaxed Quantization (RQ) [Louizos et al. 2019] successfully employ the popular Gumbel-Softmax that allows this transformation with efficient gradient-based optimization. However, RQ with this Gumbel-Softmax relaxation still suffers from bias-varian…
Nanjing University（南京大学）；The University of Sydney（悉尼大学）；Southeast University（东南大学）；University of Wollongong（伍伦贡大学）
The core issue in semi-supervised learning (SSL) lies in how to effectively leverage unlabeled data, whereas most existing methods tend to put a great emphasis on the utilization of high-confidence samples yet seldom fully explore the usage of low-confidence samples. In this paper, we aim to utilize low-confidence samples in a novel way with our proposed mutex-based consistency regularization, namely MutexMatch. Specifically, the high-confidence samples are required to exactly predict "what it is" by conventional True-Positive Classifier, while the low-confidence samples are employed to achiev…
Many real-world phenomena are observed at multiple resolutions. Predictive models designed to predict these phenomena typically consider different resolutions separately. This approach might be limiting in applications where predictions are desired at fine resolutions but available training data is scarce. In this paper, we propose classification algorithms that leverage supervision from coarser resolutions to help train models on finer resolutions. The different resolutions are modeled as different views of the data in a multi-view framework that exploits the complementarity of features acros…
Consistency regularization describes a class of approaches that have yielded state-of-the-art results for semi-supervised classification. While semi-supervised semantic segmentation proved to be more challenging, a number of successful approaches have been recently proposed. Recent work explored the challenges involved in using consistency regularization for segmentation problems. In their self-supervised work Chen et al. found that colour augmentation prevents a classification network from using image colour statistics as a short-cut for self-supervised learning via instance discrimination. D…
Remote-sensing (RS) Change Detection (CD) aims to detect "changes of interest" from co-registered bi-temporal images. The performance of existing deep supervised CD methods is attributed to the large amounts of annotated data used to train the networks. However, annotating large amounts of remote sensing images is labor-intensive and expensive, particularly with bi-temporal images, as it requires pixel-wise comparisons by a human expert. On the other hand, we often have access to unlimited unlabeled multi-temporal RS imagery thanks to ever-increasing earth observation programs. In this paper, …
