In few-shot classification, the aim is to learn models able to discriminate classes using only a small number of labeled examples. In this context, works have proposed to introduce Graph Neural Networks (GNNs) aiming at exploiting the information contained in other samples treated concurrently, what is commonly referred to as the transductive setting in the literature. These GNNs are trained all together with a backbone feature extractor. In this paper, we propose a new method that relies on graphs only to interpolate feature vectors instead, resulting in a transductive learning setting with no additional parameters to train. Our proposed method thus exploits two levels of information: a) transfer features obtained on generic datasets, b) transductive information obtained from other samples to be classified. Using standard few-shot vision classification datasets, we demonstrate its ability to bring significant gains compared to other works.
Graph Neural Networks (GNNs) have received a lot of interest in the recent times. From the early spectral architectures that could only operate on undirected graphs per a transductive learning paradigm to the current state of the art spatial ones that can apply inductively to arbitrary graphs, GNNs have seen significant contributions from the research community. In this paper, we utilize some theoretical tools to better visualize the operations performed by state of the art spatial GNNs. We analyze the inner workings of these architectures and introduce a simple concept, Node Masking, that allows them to generalize and scale better. To empirically validate the concept, we perform several experiments on some widely-used datasets for node classification in both the transductive and inductive settings, hence laying down strong benchmarks for future research.
In a standard multi-output classification scenario, both features and labels of training data are partially observed. This challenging issue is widely witnessed due to sensor or database failures, crowd-sourcing and noisy communication channels in industrial data analytic services. Classic methods for handling multi-output classification with incomplete supervision information usually decompose the problem into an imputation stage that reconstructs the missing training information, and a learning stage that builds a classifier based on the imputed training set. These methods fail to fully leverage the dependencies between features and labels. In order to take full advantage of these dependencies we consider a purely probabilistic setting in which the features imputation and multi-label classification problems are jointly solved. Indeed, we show that a simple Restricted Boltzmann Machine can be trained with an adapted algorithm based on mean-field equations to efficiently solve problems of inductive and transductive learning in which both features and labels are missing at random. The effectiveness of the approach is demonstrated empirically on various datasets, with particular focus on a real-world Internet-of-Things security dataset.
In this paper, we propose an end-to-end graph learning framework, namely Deep Iterative and Adaptive Learning for Graph Neural Networks (DIAL-GNN), for jointly learning the graph structure and graph embeddings simultaneously. We first cast the graph structure learning problem as a similarity metric learning problem and leverage an adapted graph regularization for controlling smoothness, connectivity and sparsity of the generated graph. We further propose a novel iterative method for searching for a hidden graph structure that augments the initial graph structure. Our iterative method dynamically stops when the learned graph structure approaches close enough to the optimal graph. Our extensive experiments demonstrate that the proposed DIAL-GNN model can consistently outperform or match state-of-the-art baselines in terms of both downstream task performance and computational time. The proposed approach can cope with both transductive learning and inductive learning.
This paper develops new methods to recover the missing entries of a high-rank or even full-rank matrix when the intrinsic dimension of the data is low compared to the ambient dimension. Specifically, we assume that the columns of a matrix are generated by polynomials acting on a low-dimensional intrinsic variable, and wish to recover the missing entries under this assumption. We show that we can identify the complete matrix of minimum intrinsic dimension by minimizing the rank of the matrix in a high dimensional feature space. We develop a new formulation of the resulting problem using the kernel trick together with a new relaxation of the rank objective, and propose an efficient optimization method. We also show how to use our methods to complete data drawn from multiple nonlinear manifolds. Comparative studies on synthetic data, subspace clustering with missing data, motion capture data recovery, and transductive learning verify the superiority of our methods over the state-of-the-art.
Rectified Linear Units (ReLUs) are among the most widely used activation function in a broad variety of tasks in vision. Recent theoretical results suggest that despite their excellent practical performance, in various cases, a substitution with basis expansions (e.g., polynomials) can yield significant benefits from both the optimization and generalization perspective. Unfortunately, the existing results remain limited to networks with a couple of layers, and the practical viability of these results is not yet known. Motivated by some of these results, we explore the use of Hermite polynomial expansions as a substitute for ReLUs in deep networks. While our experiments with supervised learning do not provide a clear verdict, we find that this strategy offers considerable benefits in semi-supervised learning (SSL) / transductive learning settings. We carefully develop this idea and show how the use of Hermite polynomials based activations can yield improvements in pseudo-label accuracies and sizable financial savings (due to concurrent runtime benefits). Further, we show via theoretical analysis, that the networks (with Hermite activations) offer robustness to noise and other attractive mathematical properties.
Representation learning on networks offers a powerful alternative to the oft painstaking process of manual feature engineering, and as a result, has enjoyed considerable success in recent years. However, all the existing representation learning methods are based on the first-order network (FON), that is, the network that only captures the pairwise interactions between the nodes. As a result, these methods may fail to incorporate non-Markovian higher-order dependencies in the network. Thus, the embeddings that are generated may not accurately represent of the underlying phenomena in a network, resulting in inferior performance in different inductive or transductive learning tasks. To address this challenge, this paper presents HONEM, a higher-order network embedding method that captures the non-Markovian higher-order dependencies in a network. HONEM is specifically designed for the higher-order network structure (HON) and outperforms other state-of-the-art methods in node classification, network re-construction, link prediction, and visualization for networks that contain non-Markovian higher-order dependencies.
In few-shot learning, a machine learning system learns from a small set of labelled examples relating to a specific task, such that it can generalize to new examples of the same task. Given the limited availability of labelled examples in such tasks, we wish to make use of all the information we can. Usually a model learns task-specific information from a small training-set (support-set) to predict on an unlabelled validation set (target-set). The target-set contains additional task-specific information which is not utilized by existing few-shot learning methods. Making use of the target-set examples via transductive learning requires approaches beyond the current methods; at inference time, the target-set contains only unlabelled input data-points, and so discriminative learning cannot be used. In this paper, we propose a framework called Self-Critique and Adapt or SCA, which learns to learn a label-free loss function, parameterized as a neural network. A base-model learns on a support-set using existing methods (e.g. stochastic gradient descent combined with the cross-entropy loss), and then is updated for the incoming target-task using the learnt loss function. This label-free loss function is itself optimized such that the learnt model achieves higher generalization performance. Experiments demonstrate that SCA offers substantially reduced error-rates compared to baselines which only adapt on the support-set, and results in state of the art benchmark performance on Mini-ImageNet and Caltech-UCSD Birds 200.
Semi-supervised learning is becoming increasingly important because it can combine data carefully labeled by humans with abundant unlabeled data to train deep neural networks. Classic methods on semi-supervised learning that have focused on transductive learning have not been fully exploited in the inductive framework followed by modern deep learning. The same holds for the manifold assumption---that similar examples should get the same prediction. In this work, we employ a transductive label propagation method that is based on the manifold assumption to make predictions on the entire dataset and use these predictions to generate pseudo-labels for the unlabeled data and train a deep neural network. At the core of the transductive method lies a nearest neighbor graph of the dataset that we create based on the embeddings of the same network.Therefore our learning process iterates between these two steps. We improve performance on several datasets especially in the few labels regime and show that our work is complementary to current state of the art.
When labeled training data is scarce, a promising data augmentation approach is to generate visual features of unknown classes using their attributes. To learn the class conditional distribution of CNN features, these models rely on pairs of image features and class attributes. Hence, they can not make use of the abundance of unlabeled data samples. In this paper, we tackle any-shot learning problems i.e. zero-shot and few-shot, in a unified feature generating framework that operates in both inductive and transductive learning settings. We develop a conditional generative model that combines the strength of VAE and GANs and in addition, via an unconditional discriminator, learns the marginal feature distribution of unlabeled images. We empirically show that our model learns highly discriminative CNN features for five datasets, i.e. CUB, SUN, AWA and ImageNet, and establish a new state-of-the-art in any-shot learning, i.e. inductive and transductive (generalized) zero- and few-shot learning settings. We also demonstrate that our learned features are interpretable: we visualize them by inverting them back to the pixel space and we explain them by generating textual arguments of why they are associated with a certain label.
Data selection techniques applied to neural machine translation (NMT) aim to increase the performance of a model by retrieving a subset of sentences for use as training data. One of the possible data selection techniques are transductive learning methods, which select the data based on the test set, i.e. the document to be translated. A limitation of these methods to date is that using the source-side test set does not by itself guarantee that sentences are selected with correct translations, or translations that are suitable given the test-set domain. Some corpora, such as subtitle corpora, may contain parallel sentences with inaccurate translations caused by localization or length restrictions. In order to try to fix this problem, in this paper we propose to use an approximated target-side in addition to the source-side when selecting suitable sentence-pairs for training a model. This approximated target-side is built by pre-translating the source-side. In this work, we explore the performance of this general idea for one specific data selection approach called Feature Decay Algorithms (FDA). We train German-English NMT models on data selected by using the test set (source), the approximated target side, and a mixture of both. Our findings reveal that models built using a combination of outputs of FDA (using the test set and an approximated target side) perform better than those solely using the test set. We obtain a statistically significant improvement of more than 1.5 BLEU points over a model trained with all data, and more than 0.5 BLEU points over a strong FDA baseline that uses source-side information only.
For many text classification tasks, there is a major problem posed by the lack of labeled data in a target domain. Although classifiers for a target domain can be trained on labeled text data from a related source domain, the accuracy of such classifiers is usually lower in the cross-domain setting. Recently, string kernels have obtained state-of-the-art results in various text classification tasks such as native language identification or automatic essay scoring. Moreover, classifiers based on string kernels have been found to be robust to the distribution gap between different domains. In this paper, we formally describe an algorithm composed of two simple yet effective transductive learning approaches to further improve the results of string kernels in cross-domain settings. By adapting string kernels to the test set without using the ground-truth test labels, we report significantly better accuracy rates in cross-domain English polarity classification.
Neural state-of-the-art sequence-to-sequence (seq2seq) models often do not perform well for small training sets. We address paradigm completion, the morphological task of, given a partial paradigm, generating all missing forms. We propose two new methods for the minimal-resource setting: (i) Paradigm transduction: Since we assume only few paradigms available for training, neural seq2seq models are able to capture relationships between paradigm cells, but are tied to the idiosyncracies of the training set. Paradigm transduction mitigates this problem by exploiting the input subset of inflected forms at test time. (ii) Source selection with high precision (SHIP): Multi-source models which learn to automatically select one or multiple sources to predict a target inflection do not perform well in the minimal-resource setting. SHIP is an alternative to identify a reliable source if training data is limited. On a 52-language benchmark dataset, we outperform the previous state of the art by up to 9.71% absolute accuracy.
The goal behind Domain Adaptation (DA) is to leverage the labeled examples from a source domain so as to infer an accurate model in a target domain where labels are not available or in scarce at the best. A state-of-the-art approach for the DA is due to (Ganin et al. 2016), known as DANN, where they attempt to induce a common representation of source and target domains via adversarial training. This approach requires a large number of labeled examples from the source domain to be able to infer a good model for the target domain. However, in many situations obtaining labels in the source domain is expensive which results in deteriorated performance of DANN and limits its applicability in such scenarios. In this paper, we propose a novel approach to overcome this limitation. In our work, we first establish that DANN reduces the original DA problem into a semi-supervised learning problem over the space of common representation. Next, we propose a learning approach, namely TransDANN, that amalgamates adversarial learning and transductive learning to mitigate the detrimental impact of limited source labels and yields improved performance. Experimental results (both on text and images) show a significant boost in the performance of TransDANN over DANN under such scenarios. We also provide theoretical justification for the performance boost.
Recently, string kernels have obtained state-of-the-art results in various text classification tasks such as Arabic dialect identification or native language identification. In this paper, we apply two simple yet effective transductive learning approaches to further improve the results of string kernels. The first approach is based on interpreting the pairwise string kernel similarities between samples in the training set and samples in the test set as features. Our second approach is a simple self-training method based on two learning iterations. In the first iteration, a classifier is trained on the training set and tested on the test set, as usual. In the second iteration, a number of test samples (to which the classifier associated higher confidence scores) are added to the training set for another round of training. However, the ground-truth labels of the added test samples are not necessary. Instead, we use the labels predicted by the classifier in the first training iteration. By adapting string kernels to the test set, we report significantly better accuracy rates in English polarity classification and Arabic dialect identification.
We develop a technique for deriving data-dependent error bounds for transductive learning algorithms based on transductive Rademacher complexity. Our technique is based on a novel general error bound for transduction in terms of transductive Rademacher complexity, together with a novel bounding technique for Rademacher averages for particular algorithms, in terms of their "unlabeled-labeled" representation. This technique is relevant to many advanced graph-based transductive algorithms and we demonstrate its effectiveness by deriving error bounds to three well known algorithms. Finally, we present a new PAC-Bayesian bound for mixtures of transductive algorithms based on our Rademacher bounds.
Given a hypothesis space, the large volume principle by Vladimir Vapnik prioritizes equivalence classes according to their volume in the hypothesis space. The volume approximation has hitherto been successfully applied to binary learning problems. In this paper, we extend it naturally to a more general definition which can be applied to several transductive problem settings, such as multi-class, multi-label and serendipitous learning. Even though the resultant learning method involves a non-convex optimization problem, the globally optimal solution is almost surely unique and can be obtained in O(n^3) time. We theoretically provide stability and error analyses for the proposed method, and then experimentally show that it is promising.
Although the parallel corpus has an irreplaceable role in machine translation, its scale and coverage is still beyond the actual needs. Non-parallel corpus resources on the web have an inestimable potential value in machine translation and other natural language processing tasks. This article proposes a semi-supervised transductive learning method for expanding the training corpus in statistical machine translation system by extracting parallel sentences from the non-parallel corpus. This method only requires a small amount of labeled corpus and a large unlabeled corpus to build a high-performance classifier, especially for when there is short of labeled corpus. The experimental results show that by combining the non-parallel corpus alignment and the semi-supervised transductive learning method, we can more effectively use their respective strengths to improve the performance of machine translation system.
We tackle the problem of multi-task learning with copula process. Multivariable prediction in spatial and spatial-temporal processes such as natural resource estimation and pollution monitoring have been typically addressed using techniques based on Gaussian processes and co-Kriging. While the Gaussian prior assumption is convenient from analytical and computational perspectives, nature is dominated by non-Gaussian likelihoods. Copula processes are an elegant and flexible solution to handle various non-Gaussian likelihoods by capturing the dependence structure of random variables with cumulative distribution functions rather than their marginals. We show how multi-task learning for copula processes can be used to improve multivariable prediction for problems where the simple Gaussianity prior assumption does not hold. Then, we present a transductive approximation for multi-task learning and derive analytical expressions for the copula process model. The approach is evaluated and compared to other techniques in one artificial dataset and two publicly available datasets for natural resource estimation and concrete slump prediction.
We show two novel concentration inequalities for suprema of empirical processes when sampling without replacement, which both take the variance of the functions into account. While these inequalities may potentially have broad applications in learning theory in general, we exemplify their significance by studying the transductive setting of learning theory. For which we provide the first excess risk bounds based on the localized complexity of the hypothesis class, which can yield fast rates of convergence also in the transductive learning setting. We give a preliminary analysis of the localized complexities for the prominent case of kernel classes.