Tensor completion is an important topic in the area of image processing and computer vision research, which is generally built on extraction of the intrinsic structure of the tensor data. Drawing on this fact, action classification, relying heavily on the extracted features of high-dimensional tensors, may indeed benefit from tensor completion techniques. In this paper, we propose a low-rank tensor completion method for action classification, as well as image recovery. Since there may exist distortion and corruption in the tensor representations of video sequences, we project the tensors into a subspace, which contains the invariant structure of the tensors. In order to integrate useful supervisory information for classification, we adopt a discriminant analysis criterion to learn the projection matrices. The resulting multi-variate optimization problem can be effectively solved using the augmented Lagrange multiplier (ALM) algorithm. Experiments demonstrate that our method results with better accuracy compared with some other state-of-the-art low-rank tensor representation learning approaches on the MSR Hand Gesture 3D database and the MSR Action 3D database. By denoising the Multi-PIE face database, our experimental setup testifies the proposed method can also be employed to recover images.

Gambles in casinos are usually set up so that the casino makes a profit in expectation -- as long as gamblers play honestly. However, some gamblers are able to cheat, reducing the casino’s profit. How should the casino address this? A common strategy is to selectively kick gamblers out, possibly even without being sure that they were cheating. In this paper, we address the following question: Based solely on a gambler’s track record,when is it optimal for the casino to kick the gambler out? Because cheaters will adapt to the casino’s policy, this is a game-theoretic question. Specifically, we model the problem as a Bayesian game in which the casino is a Stackelberg leader that can commit to a (possibly randomized) policy for when to kick gamblers out, and we provide efficient algorithms for computing the optimal policy. Besides being potentially useful to casinos, we imagine that similar techniques could be useful for addressing related problems -- for example, illegal trades in financial markets.

This paper proposes the Proximal Iteratively REweighted (PIRE) algorithm for solving a general problem, which involves a large body of nonconvex sparse and structured sparse related problems. Comparing with previous iterative solvers for nonconvex sparse problem, PIRE is much more general and efficient. The computational cost of PIRE in each iteration is usually as low as the state-of-the-art convex solvers. We further propose the PIRE algorithm with Parallel Splitting (PIRE-PS) and PIRE algorithm with Alternative Updating (PIRE-AU) to handle the multi-variable problems. In theory, we prove that our proposed methods converge and any limit solution is a stationary point. Extensive experiments on both synthesis and real data sets demonstrate that our methods achieve comparative learning performance, but are much more efficient, by comparing with previous nonconvex solvers.

In portfolio selection, it often might be preferable to focus on a few top performing industries/sectors to beat the market. These top performing sectors however might change over time. In this paper, we propose an online portfolio selection algorithm that can take advantage of sector information through the use of a group sparsity inducing regularizer while making lazy updates to the portfolio. The lazy updates prevent changing ones portfolio too often which otherwise might incur huge transaction costs. The proposed formulation leads to a non-smooth constrained optimization problem at every step, with the constraint that the solution has to lie in a probability simplex. We propose an efficient primal-dual based alternating direction method of multipliers algorithm and demonstrate its effectiveness for the problem of online portfolio selection with sector information. We show that our algorithm OLU-GS has sub-linear regret w.r.t. the best fixed and best shifting solution in hindsight. We successfully establish the robustness and scalability of OLU-GS by performing extensive experiments on two real-world datasets.

Stackelberg security games (SSGs) have been deployed in a number of real-world domains. One key challenge in these applications is the assessment of attacker payoffs, which may not be perfectly known. Previous work has studied SSGs with uncertain payoffs modeled by interval uncertainty and provided maximin-based robust solutions. In contrast, in this work we propose the use of the less conservative minimax regret decision criterion for such payoff-uncertain SSGs and present the first algorithms for computing minimax regret for SSGs. We also address the challenge of preference elicitation, using minimax regret to develop the first elicitation strategies for SSGs. Experimental results validate the effectiveness of our approaches.

Vendors of all types face the problem of selecting a slate of product offerings—their assortment or catalog—that will maximize their profits. The profitability of a catalog is determined by both customer preferences and the offerings of their competitors. We develop a game-theoretic model for analyzing the vendor catalog optimization problem in the face of competing vendors. We show that computing a best response is intractable in general, but can be solved by dynamic programming given certain informational or structural assumptions about consumer preferences. We also analyze conditions under which pure Nash equilibria exist and provide several price of anarchy/stability results

As an effective technology for navigating a large number of images, image summarization is becoming a promising task with the rapid development of image sharing sites and social networks. Most existing summarization approaches use the visual-based features for image representation without considering tag information.In this paper, we propose a novel framework, named JOINT, which employs both image content and tag information to summarize images. Our model generates the summary images which can best reconstruct the original collection. Based on the assumption that an image with representative content should also have typical tags, we introduce a similarity-inducing regularizer to our model. Furthermore, we impose the lasso penalty on the objective function to yield a concise summary set. Extensive experiments demonstrate our model outperforms the state-of-the-art approaches.

In this paper, we study the low-rank tensor completion problem, where a high-order tensor with missing entries is given and the goal is to complete the tensor. We propose to minimize a new convex objective function, based on log sum of exponentials of nuclear norms, that promotes the low-rankness of unfolding matrices of the completed tensor. We show for the first time that the proximal operator to this objective function is readily computable through a hybrid singular value thresholding scheme. This leads to a new solution to high-order (low-rank) tensor completion via convex relaxation. We show that this convex relaxation and the resulting solution are much more effective than existing tensor completion methods (including those also based on minimizing ranks of unfolding matrices). The hybrid singular value thresholding scheme can be applied to any problem where the goal is to minimize the maximum rank of a set of low-rank matrices.

We study techniques to incentivize self-interested agents to form socially desirable solutions in scenarios where they benefit from mutual coordination. Towards this end, we consider coordination games where agents have different intrinsic preferences but they stand to gain if others choose the same strategy as them. For non-trivial versions of our game, stable solutions like Nash Equilibrium may not exist, or may be socially inefficient even when they do exist. This motivates us to focus on designing efficient algorithms to compute (almost) stable solutions like Approximate Equilibrium that can be realized if agents are provided some additional incentives. Our results apply in many settings like adoption of new products, project selection, and group formation, where a central authority can direct agents towards a strategy but agents may defect if they have better alternatives. We show that for any given instance, we can either compute a high quality approximate equilibrium or a near-optimal solution that can be stabilized by providing small payments to some players. Our results imply that a little influence is necessary in order to ensure that selfish players coordinate and form socially efficient solutions.

Markov Chains are a fundamental tool for the analysis of real world phenomena and randomized algorithms. Given a graph with some specified sink nodes and an initial probability distribution,we consider the problem of designing an absorbing Markov Chain that minimizes the time required to reach a sink node, by selecting transition probabilities subject to some natural regularity constraints. By exploiting the Markovian structure, we obtain closed form expressions for the objective function as well as its gradient, which can be thus evaluated efficiently without any simulation of the underlying process and fed to a gradient-based optimization package. For the special case of designing reversible Markov Chains, we show that global optimum can be efficiently computed by exploiting convexity. We demonstrate how our method can be used for the evaluation and design of local search methods tailored for certain domains.