We consider optimizing the coalition structure in Coalitional Skill Games (CSGs), a succinct representation of coalitional games. In CSGs, the value of a coalition depends on the tasks its members can achieve. The tasks require various skills to complete them, and agents may have different skill sets. The optimal coalition structure is a partition of the agents to coalitions, that maximizes the sum of utilities obtained by the coalitions. We show that CSGs can represent any characteristic function, and consider optimal coalition structure generation in this representation. We provide hardness results, showing that in general CSGs, as well as in very restricted versions of them, computing the optimal coalition structure is hard. On the positive side, we show that the problem can be reformulated as constraint satisfaction on a hyper graph, and present an algorithm that finds the optimal coalition structure in polynomial time for instances with bounded tree-width and number of tasks.

We study the computational complexity of the counting version of the Possible-Winner problem for elections. In the Possible-Winner problem we are given a profile of voters, each with a partial preference order, and ask if there are linear extensions of the votes such that a designated candidate wins. We also analyze a special case of Possible-Winner, the Manipulation problem. We provide polynomial-time algorithms for counting manipulations in a class of scoring protocols and in several other voting rules. We show #P-hardness of the counting variant of Possible-Winner for plurality and veto and give a simple yet general and practically useful randomized algorithm for a variant of Possible-Winner for all voting rules for which a winner can be computed in polynomial time.

Previous work on machine scheduling has considered the case of agents who control the scheduled jobs and attempt to minimize their own completion time. We argue that in cloud and grid computing settings, different machines cannot be considered to be fully cooperative as they may belong to competing economic entities, and that agents can easily move their jobs between competing providers. We therefore consider a setting in which the machines are also controlled by selfish agents, and attempt to maximize their own gains by strategically selecting their scheduling policy. We analyze the equilibria that arise due to competition in this 2-sided setting. In particular, not only do we require that the jobs will be in equilibrium with one another, but also that the schedulers' policies will be in equilibrium. We also consider different mixtures of classic deterministic scheduling policies and random scheduling policies.

Graph-based semi-supervised learning methods are based on some smoothness assumption about the data. As a discrete approximation of the data manifold, the graph plays a crucial role in the success of such graph-based methods. In most existing methods, graph construction makes use of a predefined weighting function without utilizing label information even when it is available. In this work, by incorporating label information, we seek to enhance the performance of graph-based semi-supervised learning by learning the graph and label inference simultaneously. In particular, we consider a particular setting of semi-supervised learning called transductive learning. Using the LogDet divergence to define the objective function, we propose an iterative algorithm to solve the optimization problem which has closed-form solution in each step. We perform experiments on both synthetic and real data to demonstrate improvement in the graph and in terms of classification accuracy.

Traditional clustering methods deal with a single clustering task on a single data set. However, in some newly emerging applications, multiple similar clustering tasks are involved simultaneously. In this case, we not only desire a partition for each task, but also want to discover the relationship among clusters of different tasks. It's also expected that the learnt relationship among tasks can improve performance of each single task. In this paper, we propose a general framework for this problem and further suggest a specific approach. In our approach, we alternatively update clusters and learn relationship between clusters of different tasks, and the two phases boost each other. Our approach is based on the general Bregman divergence, hence it's suitable for a large family of assumptions on data distributions and divergences. Empirical results on several benchmark data sets validate the approach.

The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called least-squares independence regression (LSIR). LSIR learns the additive noise model through minimization of an estimator of the squared-loss mutual information between inputs and residuals. A notable advantage of LSIR over existing approaches is that tuning parameters such as the kernel width and the regularization parameter can be naturally optimized by cross-validation, allowing us to avoid overfitting in a data-dependent fashion. Through experiments with real-world datasets, we show that LSIR compares favorably with the state-of-the-art causal inference method.

Non-metric distances are often more reasonable compared with metric ones in terms of consistency with human perceptions. However, existing locality-sensitive hashing (LSH) algorithms can only support data which are gauged with metrics. In this paper we propose a novel locality-sensitive hashing algorithm targeting such non-metric data. Data in original feature space are embedded into an implicit reproducing kernel Krein space and then hashed to obtain binary bits. Here we utilize the norm-keeping property of p-stable functions to ensure that two data's collision probability reflects their non-metric distance in original feature space. We investigate various concrete examples to validate the proposed algorithm. Extensive empirical evaluations well illustrate its effectiveness in terms of accuracy and retrieval speedup.

Methods for discovering causal knowledge from observational data have been a persistent topic of AI research for several decades. Essentially all of this work focuses on knowledge representations for propositional domains. In this paper, we present several key algorithmic and theoretical innovations that extend causal discovery to relational domains. We provide strong evidence that effective learning of causal models is enhanced by relational representations. We present an algorithm, relational PC, that learns causal dependencies in a state-of-the-art relational representation, and we identify the key representational and algorithmic innovations that make the algorithm possible. Finally, we prove the algorithm's theoretical correctness and demonstrate its effectiveness on synthetic and real data sets.

Dimensionality reduction plays an important role in many machine learning and pattern recognition tasks. In this paper, we present a novel dimensionality reduction algorithm called multilinear maximum distance embedding (M2DE), which includes three key components. To preserve the local geometry and discriminant information in the embedded space, M2DE utilizes a new objective function, which aims to maximize the distances between some particular pairs of data points, such as the distances between nearby points and the distances between data points from different classes. To make the mapping of new data points straightforward, and more importantly, to keep the natural tensor structure of high-order data, M2DE integrates multilinear techniques to learn the transformation matrices sequentially. To provide reasonable and stable embedding results, M2DE employs the L1-norm, which is more robust to outliers, to measure the dissimilarity between data points. Experiments on various datasets demonstrate that M2DE achieves good embedding results of high-order data for classification tasks.

Vectored data frequently occur in a variety of fields, which are easy to handle since they can be mathematically abstracted as points residing in a Euclidean space. An appropriate distance metric in the data space is quite demanding for a great number of applications. In this paper, we pose robust and tractable metric learning under pairwise constraints that are expressed as similarity judgements between data pairs. The major features of our approach include: 1) it maximizes the gap between the average squared distance among dissimilar pairs and the average squared distance among similar pairs; 2) it is capable of propagating similar constraints to all data pairs; and 3) it is easy to implement in contrast to the existing approaches using expensive optimization such as semidefinite programming. Our constrained metric learning approach has widespread applicability without being limited to particular backgrounds. Quantitative experiments are performed for classification and retrieval tasks, uncovering the effectiveness of the proposed approach.