In multi-label learning, each training example is represented by a single instance (feature vector) while associated with multiple class labels simultaneously. The task is to learn a predictive model from the training examples which can assign a set of proper labels for the unseen instance. Most existing approaches make use of multi-label training examples by exploiting their labeling information in a crisp manner, i.e. one class label is either fully relevant or irrelevant to the instance. In this paper, a novel multi-label learning approach is proposed which aims to enrich the labeling information by leveraging the structural information in feature space. Firstly, the underlying structure of feature space is characterized by conducting sparse reconstruction among the training examples. Secondly, the reconstruction information is conveyed from feature space to label space so as to enrich the original categorical labels into numerical ones. Thirdly, the multi-label predictive model is induced by learning from training examples with enriched labeling information. Extensive experiments on fifteen benchmark data sets clearly validate the effectiveness of the proposed feature-induced strategy for enhancing labeling information of multi-label examples.

It is expensive and difficult to precisely annotate objects with multiple labels. Instead, in many real tasks, annotators may roughly assign each object with a set of candidate labels. The candidate set contains at least one but unknown number of ground-truth labels, and is usually adulterated with some irrelevant labels. In this paper, we formalize such problems as a new learning framework called partial multi-label learning (PML). To solve the PML problem, a confidence value is maintained for each candidate label to estimate how likely it is a ground-truth label of the instance. On one hand, the relevance ordering of labels on each instance is optimized by minimizing a rank loss weighted by the confidences; on the other hand, the confidence values are optimized by further exploiting structure information in feature and label spaces.Experimental results on various datasets show that the proposed approach is effective for solving PML problems.

Networked data, in which every training example involves two objects and may share some common objects with others, is used in many machine learning tasks such as learning to rank and link prediction. A challenge of learning from networked examples is that target values are not known for some pairs of objects. In this case, neither the classical i.i.d. assumption nor techniques based on complete U-statistics can be used. Most existing theoretical results of this problem only deal with the classical empirical risk minimization (ERM) principle that always weights every example equally, but this strategy leads to unsatisfactory bounds. We consider general weighted ERM and show new universal risk bounds for this problem. These new bounds naturally define an optimization problem which leads to appropriate weights for networked examples. Though this optimization problem is not convex in general, we devise a new fully polynomial-time approximation scheme (FPTAS) to solve it.

To deal with the low qualities of web workers in crowdsourcing, many unsupervised label aggregation methods have been investigated but most of them provide inconsistent performance. In this paper, we explore the learning from crowds with selective verification problem. In addition to the noisy responses from the crowds, it also collects the ground truths for a well-chosen subset of tasks as the reference, then aggregates the redundant responses based on the patterns provided by both the supervised and unsupervised signal. To improve the labeling efficiency, we propose the EBM selecting strategy for choosing the verification subset, which is based on the loss error minimization. Specifically, we first establish the expected loss error given the semi-supervised learning estimate, then find the subset that minimizes this selecting criterion. We do extensive empirical comparisons on both synthetic and real-world datasets to show the benefits of this new learning setting as well as our proposal.

The randomized-feature approach has been successfully employed in large-scale kernel approximation and supervised learning. The distribution from which the random features are drawn impacts the number of features required to efficiently perform a learning task. Recently, it has been shown that employing data-dependent randomization improves the performance in terms of the required number of random features. In this paper, we are concerned with the randomized-feature approach in supervised learning for good generalizability. We propose the Energy-based Exploration of Random Features (EERF) algorithm based on a data-dependent score function that explores the set of possible features and exploits the promising regions. We prove that the proposed score function with high probability recovers the spectrum of the best fit within the model class. Our empirical results on several benchmark datasets further verify that our method requires smaller number of random features to achieve a certain generalization error compared to the state-of-the-art while introducing negligible pre-processing overhead. EERF can be implemented in a few lines of code and requires no additional tuning parameters.

The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to the hypergraph setting, and propose a novel hypergraph p-Laplacian. Unlike the existing two-node graph Laplacians, this generalization makes it possible to analyze hypergraphs, where the edges are allowed to connect any number of nodes. Moreover, we propose a semi-supervised learning method based on the proposed hypergraph p-Laplacian, and formalize them as the analogue to the Dirichlet problem, which often appears in physics. We further explore theoretical connections to normalized hypergraph cut on a hypergraph, and propose normalized cut corresponding to hypergraph p-Laplacian. The proposed p-Laplacian is shown to outperform standard hypergraph Laplacians in the experiment on a hypergraph semi-supervised learning and normalized cut setting.

In this paper, we consider the interpretability of the foundational Laplacian-based semi-supervised learning approaches on graphs. We introduce a novel flow-based learning framework that subsumes the foundational approaches and additionally provides a detailed, transparent, and easily understood expression of the learning process in terms of graph flows. As a result, one can visualize and interactively explore the precise subgraph along which the information from labeled nodes flows to an unlabeled node of interest. Surprisingly, the proposed framework avoids trading accuracy for interpretability, but in fact leads to improved prediction accuracy, which is supported both by theoretical considerations and empirical results. The flow-based framework guarantees the maximum principle by construction and can handle directed graphs in an out-of-the-box manner.

In this work we generalize traditional node/link prediction tasks in dynamic heterogeneous networks, to consider joint prediction over larger k-node induced subgraphs. Our key insight is to incorporate the unavoidable dependencies in the training observations of induced subgraphs into both the input features and the model architecture itself via high-order dependencies. The strength of the representation is its invariance to isomorphisms and varying local neighborhood sizes, while still being able to take node/edge labels into account, and facilitating inductive reasoning (i.e., generalization to unseen portions of the network). Empirical results show that our proposed method significantly outperforms other state-of-the-art methods designed for static and/or single node/link prediction tasks. In addition, we show that our method is scalable and learns interpretable parameters.

Many interesting problems in machine learning are being revisited with new deep learning tools. For graph-based semi-supervised learning, a recent important development is graph convolutional networks (GCNs), which nicely integrate local vertex features and graph topology in the convolutional layers. Although the GCN model compares favorably with other state-of-the-art methods, its mechanisms are not clear and it still requires considerable amount of labeled data for validation and model selection. In this paper, we develop deeper insights into the GCN model and address its fundamental limits. First, we show that the graph convolution of the GCN model is actually a special form of Laplacian smoothing, which is the key reason why GCNs work, but it also brings potential concerns of over-smoothing with many convolutional layers. Second, to overcome the limits of the GCN model with shallow architectures, we propose both co-training and self-training approaches to train GCNs. Our approaches significantly improve GCNs in learning with very few labels, and exempt them from requiring additional labels for validation. Extensive experiments on benchmarks have verified our theory and proposals.

This paper considers the task of learning the preferences of users on a combinatorial set of alternatives, as it can be the case for example with online configurators. In many settings, what is available to the learner is a set of positive examples of alternatives that have been selected during past interactions. We propose to learn a model of the users' preferences that ranks previously chosen alternatives as high as possible. In this paper, we study the particular task of learning conditional lexicographic preferences. We present an algorithm to learn several classes of lexicographic preference trees, prove convergence properties of the algorithm, and experiment on both synthetic data and on a real-world bench in the domain of recommendation in interactive configuration.