Embedding methods have shown promising performance in multi-label prediction, as they can discover the dependency of labels. Most embedding methods cannot well align the input and output, which leads to degradation in prediction performance. Besides, they suffer from expensive prediction computational costs when applied to large-scale datasets. To address the above issues, this paper proposes a Co-Hashing (CoH) method by formulating multi-label learning from the perspective of cross-view learning. CoH first regards the input and output as two views, and then aims to learn a common latent hamming space, where input and output pairs are compressed into compact binary embeddings. CoH enjoys two key benefits: 1) the input and output can be well aligned, and their correlations are explored; 2) the prediction is very efficient using fast cross-view kNN search in the hamming space. Moreover, we provide the generalization error bound for our method. Extensive experiments on eight real-world datasets demonstrate the superiority of the proposed CoH over the state-of-the-art methods in terms of both prediction accuracy and efficiency.

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.

Text data co-clustering is the process of partitioning the documents and words simultaneously. This approach has proven to be more useful than traditional one-sided clustering when dealing with sparsity. Among the wide range of co-clustering approaches, Non-Negative Matrix Tri-Factorization (NMTF) is recognized for its high performance, flexibility and theoretical foundations. One important aspect when dealing with text data, is to capture the semantic relationships between words since documents that are about the same topic may not necessarily use exactly the same vocabulary. However, this aspect has been overlooked by previous co-clustering models, including NMTF. To address this issue, we rely on the distributional hypothesis stating that words which co-occur frequently within the same context, e.g., a document or sentence, are likely to have similar meanings. We then propose a new NMTF model that maps frequently co-occurring words roughly to the same direction in the latent space to reflect the relationships between them. To infer the factor matrices, we derive a scalable alternating optimization algorithm, whose convergence is guaranteed. Extensive experiments, on several real-world datasets, provide strong evidence for the effectiveness of the proposed approach, in terms of co-clustering.

We study the problem of within network classification, where given a partially labeled network, we infer the labels of the remaining nodes based on the link structure. Conventional loss functions penalize a node based on a function of its predicted label and target label. Such loss functions under-perform while learning on a network having overlapping classes. In relational setting, even though the ground truth is not known for the unlabeled nodes, some evidence is present in the form of labeling acquired by the nodes in their neighborhood. We propose a structural loss function for learning in networks based on the hypothesis that loss is induced when a node fails to acquire a label that is consistent with the labels of the majority of the nodes in its neighborhood. We further combine this with a novel semantic regularizer, which we call homophily regularizer, to capture the smooth transition of discriminatory power and behavior of semantically similar nodes. The proposed structural loss along with the regularizer permits relaxation labeling. Through extensive comparative study on different real-world datasets, we found that our method improves over the state-of-the-art approaches.

Many applications infer the structure of a probabilistic graphical model from data to elucidate the relationships between variables. But how can we train graphical models on a massive data set? In this paper, we show how to construct coresets---compressed data sets which can be used as proxy for the original data and have provably bounded worst case error---for Gaussian dependency networks (DNs), i.e., cyclic directed graphical models over Gaussians, where the parents of each variable are its Markov blanket. Specifically, we prove that Gaussian DNs admit coresets of size independent of the size of the data set. Unfortunately, this does not extend to DNs over members of the exponential family in general. As we will prove, Poisson DNs do not admit small coresets. Despite this worst-case result, we will provide an argument why our coreset construction for DNs can still work well in practice on count data.To corroborate our theoretical results, we empirically evaluated the resulting Core DNs on real data sets. The results demonstrate significant gains over no or naive sub-sampling, even in the case of count data.

Just as semantic hashing can accelerate information retrieval, binary valued embeddings can significantly reduce latency in the retrieval of graphical data. We introduce a simple but effective model for learning such binary vectors for nodes in a graph. By imagining the embeddings as independent coin flips of varying bias, continuous optimization techniques can be applied to the approximate expected loss. Embeddings optimized in this fashion consistently outperform the quantization of both spectral graph embeddings and various learned real-valued embeddings, on both ranking and pre-ranking tasks for a variety of datasets.

Temporal point processes are a statistical framework for modelling the times at which events of interest occur. The Hawkes process is a well-studied instance of this framework that captures self-exciting behaviour, wherein the occurrence of one event increases the likelihood of future events. Such processes have been successfully applied to model phenomena ranging from earthquakes to behaviour in a social network. We propose a framework to design new loss functions to train linear and nonlinear Hawkes processes. This captures standard maximum likelihood as a special case, but allows for other losses that guarantee convex objective functions (for certain types of kernel), and admit simpler optimisation. We illustrate these points with three concrete examples: for linear Hawkes processes, we provide a least-squares style loss potentially admitting closed-form optimisation; for exponential Hawkes processes, we reduce training to a weighted logistic regression; and for sigmoidal Hawkes processes, we propose an asymmetric form of logistic regression.

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.

How can we classify multi-way data such as network traffic logs with multi-way relations between source IPs, destination IPs, and ports? Multi-way data can be represented as a tensor, and there have been several studies on classification of tensors to date. One critical issue in the classification of multi-way relations is how to extract important features for classification when objects in different multi-way data, i.e., in different tensors, are not necessarily in correspondence. In such situations, we aim to extract features that do not depend on how we allocate indices to an object such as a specific source IP; we are interested in only the structures of the multi-way relations. However, this issue has not been considered in previous studies on classification of multi-way data. We propose a novel method which can learn and classify multi-way data using neural networks. Our method leverages a novel type of tensor decomposition that utilizes a target core tensor expressing the important features whose indices are independent of those of the multi-way data. The target core tensor guides the tensor decomposition into more effective results and is optimized in a supervised manner. Our experiments on three different domains show that our method is highly accurate, especially on higher order data. It also enables us to interpret the classification results along with the matrices calculated with the novel tensor decomposition.

Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are batch methods designed mainly based on the convex optimization, say, the projected gradient descent method. However, they are generally time-consuming due to that the singular value decomposition (SVD) is commonly adopted during the update, especially when the data size is very large. To overcome this challenge, we propose a stochastic algorithm called SVRG-SBB, which has the following features: (a) SVD-free via dropping convexity, with good scalability by the use of stochastic algorithm, i.e., stochastic variance reduced gradient (SVRG), and (b) adaptive step size choice via introducing a new stabilized Barzilai-Borwein (SBB) method as the original version for convex problems might fail for the considered stochastic non-convex optimization problem. Moreover, we show that the proposed algorithm converges to a stationary point at a rate O (1/ T ) in our setting, where T is the number of total iterations. Numerous simulations and real-world data experiments are conducted to show the effectiveness of the proposed algorithm via comparing with the state-of-the-art methods, particularly, much lower computational cost with good prediction performance.