The decision to take vaccinations and other protective interventions for avoiding an infection is a natural game-theoretic setting. Most of the work on vaccination games has focused on decisions at the start of an epidemic. However, a lot of people defer their vaccination decisions, in practice. For example, in the case of the seasonal flu, vaccination rates gradually increase, as the epidemic rate increases. This motivates the study of temporal vaccination games, in which vaccination decisions can be made more than once. An important issue in the context of temporal decisions is that of resource limitations, which may arise due to production and distribution constraints. While there has been some work on temporal vaccination games, resource constraints have not been considered. In this paper, we study temporal vaccination games for epidemics in the SI (susceptible-infectious) model, with resource constraints in the form of a repeated game in complex social networks, with budgets on the number of vaccines that can be taken at any time. We find that the resource constraints and the vaccination and infection costs have a significant impact on the structure of Nash equilibria (NE). In general, the budget constraints can cause NE to become very inefficient, and finding efficient NE as well as the social optimum are NP-hard problems. We develop algorithms for finding NE and approximating the social optimum. We evaluate our results using simulations on different kinds of networks.

Unsupervised feature selection (UFS) aims to reduce the time complexity and storage burden, as well as improve the generalization performance. Most existing methods convert UFS to supervised learning problem by generating labels with specific techniques (e.g., spectral analysis, matrix factorization and linear predictor). Instead, we proposed a novel coupled analysis-synthesis dictionary learning method, which is free of generating labels. The representation coefficients are used to model the cluster structure and data distribution. Specifically, the synthesis dictionary is used to reconstruct samples, while the analysis dictionary analytically codes the samples and assigns probabilities to the samples. Afterwards, the analysis dictionary is used to select features that can well preserve the data distribution. The effective L2p-norm (0 < p <1) regularization is imposed on the analysis dictionary to get much sparse solution and is more effective in feature selection.We proposed an iterative reweighted least squares algorithm to solve the L2p-norm optimization problem and proved it can converge to a fixed point. Experiments on benchmark datasets validated the effectiveness of the proposed method

Due to the storage and retrieval efficiency, hashing has been widely deployed to approximate nearest neighbor search for large-scale multimedia retrieval. Supervised hashing, which improves the quality of hash coding by exploiting the semantic similarity on data pairs, has received increasing attention recently. For most existing supervised hashing methods for image retrieval, an image is first represented as a vector of hand-crafted or machine-learned features, followed by another separate quantization step that generates binary codes. However, suboptimal hash coding may be produced, because the quantization error is not statistically minimized and the feature representation is not optimally compatible with the binary coding. In this paper, we propose a novel Deep Hashing Network (DHN) architecture for supervised hashing, in which we jointly learn good image representation tailored to hash coding and formally control the quantization error. The DHN model constitutes four key components: (1) a sub-network with multiple convolution-pooling layers to capture image representations; (2) a fully-connected hashing layer to generate compact binary hash codes; (3) a pairwise cross-entropy loss layer for similarity-preserving learning; and (4) a pairwise quantization loss for controlling hashing quality. Extensive experiments on standard image retrieval datasets show the proposed DHN model yields substantial boosts over latest state-of-the-art hashing methods.

We propose Veto-Consensus Multiple Kernel Learning (VCMKL), a novel way of combining multiple kernels such that one class of samples is described by the logical intersection (consensus) of base kernelized decision rules, whereas the other classes by the union (veto) of their complements. The proposed configuration is a natural fit for domain description and learning with hidden subgroups. We first provide generalization risk bound in terms of the Rademacher complexity of the classifier, and then a large margin multi-ν learning objective with tunable training error bound is formulated. Seeing that the corresponding optimization is non-convex and existing methods severely suffer from local minima, we establish a new algorithm, namely Parametric Dual Descent Procedure (PDDP) that can approach global optimum with guarantees. The bases of PDDP are two theorems that reveal the global convexity and local explicitness of the parameterized dual optimum, for which a series of new techniques for parametric program have been developed. The proposed method is evaluated on extensive set of experiments, and the results show significant improvement over the state-of-the-art approaches.

Stochastic gradient descent (SGD) and its variants have become more and more popular in machine learning due to their efficiency and effectiveness. To handle large-scale problems, researchers have recently proposed several parallel SGD methods for multicore systems. However, existing parallel SGD methods cannot achieve satisfactory performance in real applications. In this paper, we propose a fast asynchronous parallel SGD method, called AsySVRG, by designing an asynchronous strategy to parallelize the recently proposed SGD variant called stochastic variance reduced gradient (SVRG). AsySVRG adopts a lock-free strategy which is more efficient than other strategies with locks. Furthermore, we theoretically prove that AsySVRG is convergent with a linear convergence rate. Both theoretical and empirical results show that AsySVRG can outperform existing state-of-the-art parallel SGD methods like Hogwild! in terms of convergence rate and computation cost.

In many learning tasks, structural models usually lead to better interpretability and higher generalization performance. In recent years, however, the simple structural models such as lasso are frequently proved to be insufficient. Accordingly, there has been a lot of work on "superposition-structured" models where multiple structural constraints are imposed. To efficiently solve these "superposition-structured" statistical models, we develop a framework based on a proximal Newton-type method. Employing the smoothed conic dual approach with the LBFGS updating formula, we propose a scalable and extensible proximal quasi-Newton (SEP-QN) framework. Empirical analysis on various datasets shows that our framework is potentially powerful, and achieves super-linear convergence rate for optimizing some popular "superposition-structured" statistical models such as the fused sparse group lasso.

We study how to communicate findings of Bayesian inference to third parties, while preserving the strong guarantee of differential privacy. Our main contributions are four different algorithms for private Bayesian inference on probabilistic graphical models. These include two mechanisms for adding noise to the Bayesian updates, either directly to the posterior parameters, or to their Fourier transform so as to preserve update consistency. We also utilise a recently introduced posterior sampling mechanism, for which we prove bounds for the specific but general case of discrete Bayesian networks; and we introduce a maximum-a-posteriori private mechanism. Our analysis includes utility and privacy bounds, with a novel focus on the influence of graph structure on privacy. Worked examples and experiments with Bayesian naive Bayes and Bayesian linear regression illustrate the application of our mechanisms.

Recently, active learning has been applied to recommendation to deal with data sparsity on a single domain. In this paper, we propose an active learning strategy for recommendation to alleviate the data sparsity in a multi-domain scenario. Specifically, our proposed active learning strategy simultaneously consider both specific and independent knowledge over all domains. We use the expected entropy to measure the generalization error of the domain-specific knowledge and propose a variance-based strategy to measure the generalization error of the domain-independent knowledge. The proposed active learning strategy use a unified function to effectively combine these two measurements. We compare our strategy with five state-of-the-art baselines on five different multi-domain recommendation tasks, which are constituted by three real-world data sets. The experimental results show that our strategy performs significantly better than all the baselines and reduces human labeling efforts by at least 5.6%, 8.3%, 11.8%, 12.5% and 15.4% on the five tasks, respectively.

Graph-based Semi-Supervised learning is one of the most popular and successful semi-supervised learning methods. Typically, it predicts the labels of unlabeled data by minimizing a quadratic objective induced by the graph, which is unfortunately a procedure of polynomial complexity in the sample size $n$. In this paper, we address this scalability issue by proposing a method that approximately solves the quadratic objective in nearly linear time. The method consists of two steps: it first approximates a graph by a minimum spanning tree, and then solves the tree-induced quadratic objective function in O(n) time which is the main contribution of this work. Extensive experiments show the significant scalability improvement over existing scalable semi-supervised learning methods.

In this paper, we present an accelerated numerical method based on random projection for sparse linear regression. Previous studies have shown that under appropriate conditions, gradient-based methods enjoy a geometric convergence rate when applied to this problem. However, the time complexity of evaluating the gradient is as large as $\mathcal{O}(nd)$, where $n$ is the number of data points and $d$ is the dimensionality, making those methods inefficient for large-scale and high-dimensional dataset. To address this limitation, we first utilize random projection to find a rank-$k$ approximator for the data matrix, and reduce the cost of gradient evaluation to $\mathcal{O}(nk+dk)$, a significant improvement when $k$ is much smaller than $d$ and $n$. Then, we solve the sparse linear regression problem via a proximal gradient method with a homotopy strategy to generate sparse intermediate solutions. Theoretical analysis shows that our method also achieves a global geometric convergence rate, and moreover the sparsity of all the intermediate solutions are well-bounded over the iterations. Finally, we conduct experiments to demonstrate the efficiency of the proposed method.