Given the real-world deployments of attacker-defender Stackelberg security games, robustness to deviations from expected attacker behaviors has now emerged as a critically important issue. This paper provides four key contributions in this context. First, it identifies a fundamentally problematic aspect of current algorithms for security games. It shows that there are many situations where these algorithms face multiple equilibria, and they arbitrarily select one that may hand the defender a significant disadvantage, particularly if the attacker deviates from its equilibrium strategies due to unknown constraints. Second, for important subclasses of security games, it identifies situations where we will face such multiple equilibria. Third, to address these problematic situations, it presents two equilibrium refinement algorithms that can optimize the defender's utility if the attacker deviates from equilibrium strategies. Finally, it experimentally illustrates that the refinement approach achieved significant robustness in consideration of attackers' deviation due to unknown constraints.

In the existing methods for solving matrix completion, such as singular value thresholding (SVT), soft-impute and fixed point continuation (FPCA) algorithms, it is typically required to repeatedly implement singular value decompositions (SVD) of matrices.When the size of the matrix in question is large, the computational complexity of finding a solution is costly. To reduce this expensive computational complexity, we apply Kronecker products to handle the matrix completion problem. In particular, we propose using Kronecker factorization, which approximates a matrix by the Kronecker product of several matrices of smaller sizes. Weintroduce Kronecker factorization into the soft-impute framework and devise an effective matrix completion algorithm.Especially when the factorized matrices have about the samesizes, the computational complexity of our algorithm is improved substantially.

Multi-task learning aims at improving the generalization performance of a learning task with the help of some other related tasks. Although many multi-task learning methods have been proposed, they are all based on the assumption that all tasks share the same data representation. This assumption is too restrictive for general applications. In this paper, we propose a multi-task extension of linear discriminant analysis (LDA), called multi-task discriminant analysis (MTDA), which can deal with learning tasks with different data representations. For each task, MTDA learns a separate transformation which consists of two parts, one specific to the task and one common to all tasks. A by-product of MTDA is that it can alleviate the labeled data deficiency problem of LDA. Moreover, unlike many existing multi-task learning methods, MTDA can handle binary and multi-class problems for each task in a generic way. Experimental results on face recognition show that MTDA consistently outperforms related methods.

Automated feature discovery is a fundamental problem in machine learning. Although classical feature discovery methods do not guarantee optimal solutions in general, it has been recently noted that certain subspace learning and sparse coding problems can be solved efficiently, provided the number of features is not restricted a priori. We provide an extended characterization of this optimality result and describe the nature of the solutions under an expanded set of practical contexts. In particular, we apply the framework to a semi-supervised learning problem, and demonstrate that feature discovery can co-occur with input reconstruction and supervised training while still admitting globally optimal solutions. A comparison to existing semi-supervised feature discovery methods shows improved generalization and efficiency.

The increasing volume of information generated on micro-blogging sites such as Twitter raises several challenges to traditional text mining techniques. First, most texts from those sites are abbreviated due to the constraints of limited characters in one post; second, the input usually comes in streams of large-volumes. Therefore, it is of significant importance to develop effective and efficient representations of abbreviated texts for better filtering and mining. In this paper, we introduce a novel transfer learning approach, namely transfer latent semantic learning, that utilizes a large number of related tagged documents with rich information from other sources (source domain) to help build a robust latent semantic space for the abbreviated texts (target domain). This is achieved by simultaneously minimizing the document reconstruction error and the classification error of the labeled examples from the source domain by building a classifier with hinge loss in the latent semantic space. We demonstrate the effectiveness of our method by applying them to the task of classifying and tagging abbreviated texts. Experimental results on both synthetic datasets and real application datasets, including Reuters-21578 and Twitter data, suggest substantial improvements using our approach over existing ones.

Clustering is a fundamental research topic in the field of data mining. Optimizing the objective functions of clustering algorithms, e.g. normalized cut and k-means, is an NP-hard optimization problem. Existing algorithms usually relax the elements of cluster indicator matrix from discrete values to continuous ones. Eigenvalue decomposition is then performed to obtain a relaxed continuous solution, which must be discretized. The main problem is that the signs of the relaxed continuous solution are mixed. Such results may deviate severely from the true solution, making it a nontrivial task to get the cluster labels. To address the problem, we impose an explicit nonnegative constraint for a more accurate solution during the relaxation. Besides, we additionally introduce a discriminative regularization into the objective to avoid overfitting. A new iterative approach is proposed to optimize the objective. We show that the algorithm is a general one which naturally leads to other extensions. Experiments demonstrate the effectiveness of our algorithm.

Methods for estimating the ratio of two probability density functions have been actively explored recently since they can be used for various data processing tasks such as non-stationarity adaptation, outlier detection, feature selection, and conditional probability estimation. In this paper, we propose a new density-ratio estimator which incorporates dimensionality reduction into the density-ratio estimation procedure. Through experiments, the proposed method is shown to compare favorably with existing density-ratio estimators in terms of both accuracy and computational costs.

Several kernel based methods for multi-task learning have been proposed, which leverage relations among tasks as regularization to enhance the overall learning accuracies. These methods assume that the tasks share the same kernel, which could limit their applications because in practice different tasks may need different kernels. The main challenge of introducing multiple kernels into multiple tasks is that models from different Reproducing Kernel Hilbert Spaces (RKHSs) are not comparable, making it difficult to exploit relations among tasks. This paper addresses the challenge by formalizing the problem in the Square Integrable Space (SIS). Specially, it proposes a kernel based method which makes use of a regularization term defined in the SIS to represent task relations. We prove a new representer theorem for the proposed approach in SIS. We further derive a practical method for solving the learning problem and conduct consistency analysis of the method. We discuss the relations between our method and an existing method. We also give an SVM based implementation of our method for multi-label classification. Experiments on two real-world data sets show that the proposed method performs better than the existing method.

A common approach in machine learning is to use a large amount of labeled data to train a model. Usually this model can then only be used to classify data in the same feature space. However, labeled data is often expensive to obtain. A number of strategies have been developed by the machine learning community in recent years to address this problem, including: semi-supervised learning,domain adaptation,multi-task learning,and self-taught learning. While training data and test may have different distributions, they must remain in the same feature set. Furthermore, all the above methods work in the same feature space. In this paper, we consider an extreme case of transfer learning called heterogeneous transfer learning — where the feature spaces of the source task and the target tasks are disjoint. Previous approaches mostly fall in the multi-view learning category, where co-occurrence data from both feature spaces is required. We generalize the previous work on cross-lingual adaptation and propose a multi-task strategy for the task. We also propose the use of a restricted Boltzmann machine (RBM), a special type of probabilistic graphical models, as an implementation. We present experiments on two tasks: action recognition and cross-lingual sentiment classification.

K-flats is a model-based linear manifold clustering algorithm which has been successfully applied in many real-world scenarios. Though some previous works have shown that K-flats doesn’t always provide good performance, little effort has been devoted to analyze its inherent deficiency. In this paper, we address this challenge by showing that the deteriorative performance of K-flats can be attributed to the usual reconstruction error measure and the infinitely extending representations of linear models. Then we propose Localized K-flats algorithm (LKF), which introduces localized representations of linear models and a new distortion measure, to remove confusion among different clusters. Experiments on both synthetic and real-world data sets demonstrate the efficiency of the proposed algorithm. Moreover, preliminary experiments show that LKF has the potential to group manifolds with nonlinear structure.