Positive and unlabeled learning in categorical data

International audienceIn common binary classification scenarios, the presence of both positive and negative examples in training datais needed to build an efficient classifier. Unfortunately, in many domains, this requirement is not satisfied andonly one class of examples is available. To cope with this setting, classification algorithms have been introducedthat learn from Positive and Unlabeled (PU) data. Originally, these approaches were exploited in the context ofdocument classification. Only few works address the PU problem for categorical datasets. Nevertheless, theavailable algorithms are mainly based on Naive Bayes classifiers. In this work we present a new distance basedPU learning approach for categorical data: Pulce. Our framework takes advantage of the intrinsic relationshipsbetween attribute values and exceeds the independence assumption made by Naive Bayes. Pulce, in fact,leverages on the statistical properties of the data to learn a distance metric employed during the classificationtask. We extensively validate our approach over real world datasets and demonstrate that our strategy obtainsstatistically significant improvements w.r.t. state-of-the-art competitors

Positive unlabeled learning with tensor networks

Positive unlabeled learning is a binary classification problem with positive and unlabeled data. It is common in domains where negative labels are costly or impossible to obtain, e.g., medicine and personalized advertising. We apply the locally purified state tensor network to the positive unlabeled learning problem and test our model on the MNIST image and 15 categorical/mixed datasets. On the MNIST dataset, we achieve state-of-the-art results even with very few labeled positive samples. Similarly, we significantly improve the state-of-the-art on categorical datasets. Further, we show that the agreement fraction between outputs of different models on unlabeled samples is a good indicator of the model's performance. Finally, our method can generate new positive and negative instances, which we demonstrate on simple synthetic datasets.Comment: 12 pages, 5 figures, 4 table

Diffusion Mechanism in Residual Neural Network: Theory and Applications

Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data points and is a critical component for achieving high classification accuracy. Many existing deep learning approaches directly impose the fusion loss when training neural networks. In this work, inspired by the convection-diffusion ordinary differential equations (ODEs), we propose a novel diffusion residual network (Diff-ResNet), internally introduces diffusion into the architectures of neural networks. Under the structured data assumption, it is proved that the proposed diffusion block can increase the distance-diameter ratio that improves the separability of inter-class points and reduces the distance among local intra-class points. Moreover, this property can be easily adopted by the residual networks for constructing the separable hyperplanes. Extensive experiments of synthetic binary classification, semi-supervised graph node classification and few-shot image classification in various datasets validate the effectiveness of the proposed method

Learning with Multiple Similarities

The notion of similarities between data points is central to many classification and clustering algorithms. We often encounter situations when there are more than one set of pairwise similarity graphs between objects, either arising from different measures of similarity between objects or from a single similarity measure defined on multiple data representations, or a combination of these. Such examples can be found in various applications in computer vision, natural language processing and computational biology. Combining information from these multiple sources is often beneficial in learning meaningful concepts from data. This dissertation proposes novel methods to effectively fuse information from these multiple similarity graphs, targeted towards two fundamental tasks in machine learning - classification and clustering. In particular, I propose two models for learning spectral embedding from multiple similarity graphs using ideas from co-training and co-regularization. Further, I propose a novel approach to the problem of multiple kernel learning (MKL), converting it to a more familiar problem of binary classification in a transformed space. The proposed MKL approach learns a ``good'' linear combination of base kernels by optimizing a quality criterion that is justified both empirically and theoretically. The ideas of the proposed MKL method are also extended to learning nonlinear combinations of kernels, in particular, polynomial kernel combination and more general nonlinear kernel combination using random forests

Minimum Density Hyperplanes

Associating distinct groups of objects (clusters) with contiguous regions of high probability density (high-density clusters), is central to many statistical and machine learning approaches to the classification of unlabelled data. We propose a novel hyperplane classifier for clustering and semi-supervised classification which is motivated by this objective. The proposed minimum density hyperplane minimises the integral of the empirical probability density function along it, thereby avoiding intersection with high density clusters. We show that the minimum density and the maximum margin hyperplanes are asymptotically equivalent, thus linking this approach to maximum margin clustering and semi-supervised support vector classifiers. We propose a projection pursuit formulation of the associated optimisation problem which allows us to find minimum density hyperplanes efficiently in practice, and evaluate its performance on a range of benchmark datasets. The proposed approach is found to be very competitive with state of the art methods for clustering and semi-supervised classification

Exact heat kernel on a hypersphere and its applications in kernel SVM

Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector machine compared to other competing similarity measures. Specifically, the idea of using heat diffusion on a hypersphere to measure similarity has been previously proposed, demonstrating promising results based on a heuristic heat kernel obtained from the zeroth order parametrix expansion; however, how well this heuristic kernel agrees with the exact hyperspherical heat kernel remains unknown. This paper presents a higher order parametrix expansion of the heat kernel on a unit hypersphere and discusses several problems associated with this expansion method. We then compare the heuristic kernel with an exact form of the heat kernel expressed in terms of a uniformly and absolutely convergent series in high-dimensional angular momentum eigenmodes. Being a natural measure of similarity between sample points dwelling on a hypersphere, the exact kernel often shows superior performance in kernel SVM classifications applied to text mining, tumor somatic mutation imputation, and stock market analysis

Learning with Low-Quality Data: Multi-View Semi-Supervised Learning with Missing Views

The focus of this thesis is on learning approaches for what we call ``low-quality data'' and in particular data in which only small amounts of labeled target data is available. The first part provides background discussion on low-quality data issues, followed by preliminary study in this area. The remainder of the thesis focuses on a particular scenario: multi-view semi-supervised learning. Multi-view learning generally refers to the case of learning with data that has multiple natural views, or sets of features, associated with it. Multi-view semi-supervised learning methods try to exploit the combination of multiple views along with large amounts of unlabeled data in order to learn better predictive functions when limited labeled data is available. However, lack of complete view data limits the applicability of multi-view semi-supervised learning to real world data. Commonly, one data view is readily and cheaply available, but additionally views may be costly or only available in some cases. This thesis work aims to make multi-view semi-supervised learning approaches more applicable to real world data specifically by addressing the issue of missing views through both feature generation and active learning, and addressing the issue of model selection for semi-supervised learning with limited labeled data. This thesis introduces a unified approach for handling missing view data in multi-view semi-supervised learning tasks, which applies to both data with completely missing additional views and data only missing views in some instances. The idea is to learn a feature generation function mapping one view to another with the mapping biased to encourage the features generated to be useful for multi-view semi-supervised learning algorithms. The mapping is then used to fill in views as pre-processing. Unlike previously proposed single-view multi-view learning approaches, the proposed approach is able to take advantage of additional view data when available, and for the case of partial view presence is the first feature-generation approach specifically designed to take into account the multi-view semi-supervised learning aspect. The next component of this thesis is the analysis of an active view completion scenario. In some tasks, it is possible to obtain missing view data for a particular instance, but with some associated cost. Recent work has shown an active selection strategy can be more effective than a random one. In this thesis, a better understanding of active approaches is sought, and it is demonstrated that the effectiveness of an active selection strategy over a random one can depend on the relationship between the views. Finally, an important component of making multi-view semi-supervised learning applicable to real world data is the task of model selection, an open problem which is often avoided entirely in previous work. For cases of very limited labeled training data the commonly used cross-validation approach can become ineffective. This thesis introduces a re-training alternative to the method-dependent approaches similar in motivation to cross-validation, that involves generating new training and test data by sampling from the large amount of unlabeled data and estimated conditional probabilities for the labels. The proposed approaches are evaluated on a variety of multi-view semi-supervised learning data sets, and the experimental results demonstrate their efficacy