Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a latent vector $w^* \in \mathbb{R}^d$ that represents the "qualities" of the $d$ items being compared; this class of models includes the two most widely used parametric models--the Bradley-Terry-Luce (BTL) and the Thurstone models. Working within a standard minimax framework, we provide tight upper and lower bounds on the optimal error in estimating the quality score vector $w^*$ under this class of models. The bounds depend on the topology of the comparison graph induced by the subset of pairs being compared via its Laplacian spectrum. Thus, in settings where the subset of pairs may be chosen, our results provide principled guidelines for making this choice. Finally, we compare these error rates to those under cardinal measurement models and show that the error rates in the ordinal and cardinal settings have identical scalings apart from constant pre-factors.

Potential games, originally introduced in the early 1990's by Lloyd Shapley, the 2012 Nobel Laureate in Economics, and his colleague Dov Monderer, are a very important class of models in game theory. They have special properties such as the existence of Nash equilibria in pure strategies. This note introduces graphical versions of potential games. Special cases of graphical potential games have already found applicability in many areas of science and engineering beyond economics, including artificial intelligence, computer vision, and machine learning. They have been effectively applied to the study and solution of important real-world problems such as routing and congestion in networks, distributed resource allocation (e.g., public goods), and relaxation-labeling for image segmentation. Implicit use of graphical potential games goes back at least 40 years. Several classes of games considered standard in the literature, including coordination games, local interaction games, lattice games, congestion games, and party-affiliation games, are instances of graphical potential games. This note provides several characterizations of graphical potential games by leveraging well-known results from the literature on probabilistic graphical models. A major contribution of the work presented here that particularly distinguishes it from previous work is establishing that the convergence of certain type of game-playing rules implies that the agents/players must be embedded in some graphical potential game.

Boosting is a learning scheme that combines weak prediction rules to produce a strong composite estimator, with the underlying intuition that one can obtain accurate prediction rules by combining "rough" ones. Although boosting is proved to be consistent and overfitting-resistant, its numerical convergence rate is relatively slow. The aim of this paper is to develop a new boosting strategy, called the re-scale boosting (RBoosting), to accelerate the numerical convergence rate and, consequently, improve the learning performance of boosting. Our studies show that RBoosting possesses the almost optimal numerical convergence rate in the sense that, up to a logarithmic factor, it can reach the minimax nonlinear approximation rate. We then use RBoosting to tackle both the classification and regression problems, and deduce a tight generalization error estimate. The theoretical and experimental results show that RBoosting outperforms boosting in terms of generalization.

We suggest a novel method of clustering and exploratory analysis of temporal event sequences data (also known as categorical time series) based on three-dimensional data grid models. A data set of temporal event sequences can be represented as a data set of three-dimensional points, each point is defined by three variables: a sequence identifier, a time value and an event value. Instantiating data grid models to the 3D-points turns the problem into 3D-coclustering. The sequences are partitioned into clusters, the time variable is discretized into intervals and the events are partitioned into clusters. The cross-product of the univariate partitions forms a multivariate partition of the representation space, i.e., a grid of cells and it also represents a nonparametric estimator of the joint distribution of the sequences, time and events dimensions. Thus, the sequences are grouped together because they have similar joint distribution of time and events, i.e., similar distribution of events along the time dimension. The best data grid is computed using a parameter-free Bayesian model selection approach. We also suggest several criteria for exploiting the resulting grid through agglomerative hierarchies, for interpreting the clusters of sequences and characterizing their components through insightful visualizations. Extensive experiments on both synthetic and real-world data sets demonstrate that data grid models are efficient, effective and discover meaningful underlying patterns of categorical time series data.

Principal component analysis (PCA) is an unsupervised method for learning low-dimensional features with orthogonal projections. Multilinear PCA methods extend PCA to deal with multidimensional data (tensors) directly via tensor-to-tensor projection or tensor-to-vector projection (TVP). However, under the TVP setting, it is difficult to develop an effective multilinear PCA method with the orthogonality constraint. This paper tackles this problem by proposing a novel Semi-Orthogonal Multilinear PCA (SO-MPCA) approach. SO-MPCA learns low-dimensional features directly from tensors via TVP by imposing the orthogonality constraint in only one mode. This formulation results in more captured variance and more learned features than full orthogonality. For better generalization, we further introduce a relaxed start (RS) strategy to get SO-MPCA-RS by fixing the starting projection vectors, which increases the bias and reduces the variance of the learning model. Experiments on both face (2D) and gait (3D) data demonstrate that SO-MPCA-RS outperforms other competing algorithms on the whole, and the relaxed start strategy is also effective for other TVP-based PCA methods.

How should we gather information in a network, where each node's visibility is limited to its local neighborhood? This problem arises in numerous real-world applications, such as surveying and task routing in social networks, team formation in collaborative networks and experimental design with dependency constraints. Often the informativeness of a set of nodes can be quantified via a submodular utility function. Existing approaches for submodular optimization, however, require that the set of all nodes that can be selected is known ahead of time, which is often unrealistic. In contrast, we propose a novel model where we start our exploration from an initial node, and new nodes become visible and available for selection only once one of their neighbors has been chosen. We then present a general algorithm NetExp for this problem, and provide theoretical bounds on its performance dependent on structural properties of the underlying network. We evaluate our methodology on various simulated problem instances as well as on data collected from social question answering system deployed within a large enterprise.

Common complex diseases are likely influenced by the interplay of hundreds, or even thousands, of genetic variants. Converging evidence shows that genetic variants with low marginal effects (LME) play an important role in disease development. Despite their potential significance, discovering LME genetic variants and assessing their joint association on high dimensional data (e.g., genome wide association studies) remain a great challenge. To facilitate joint association analysis among a large ensemble of LME genetic variants, we proposed a computationally efficient and powerful approach, which we call Trees Assembling Mann whitney (TAMW). Through simulation studies and an empirical data application, we found that TAMW outperformed multifactor dimensionality reduction (MDR) and the likelihood ratio based Mann whitney approach (LRMW) when the underlying complex disease involves multiple LME loci and their interactions. For instance, in a simulation with 20 interacting LME loci, TAMW attained a higher power (power=0.931) than both MDR (power=0.599) and LRMW (power=0.704). In an empirical study of 29 known Crohn's disease (CD) loci, TAMW also identified a stronger joint association with CD than those detected by MDR and LRMW. Finally, we applied TAMW to Wellcome Trust CD GWAS to conduct a genome wide analysis. The analysis of 459K single nucleotide polymorphisms was completed in 40 hours using parallel computing, and revealed a joint association predisposing to CD (p-value=2.763e-19). Further analysis of the newly discovered association suggested that 13 genes, such as ATG16L1 and LACC1, may play an important role in CD pathophysiological and etiological processes.

As language and visual understanding by machines progresses rapidly, we are observing an increasing interest in holistic architectures that tightly interlink both modalities in a joint learning and inference process. This trend has allowed the community to progress towards more challenging and open tasks and refueled the hope at achieving the old AI dream of building machines that could pass a turing test in open domains. In order to steadily make progress towards this goal, we realize that quantifying performance becomes increasingly difficult. Therefore we ask how we can precisely define such challenges and how we can evaluate different algorithms on this open tasks? In this paper, we summarize and discuss such challenges as well as try to give answers where appropriate options are available in the literature. We exemplify some of the solutions on a recently presented dataset of question-answering task based on real-world indoor images that establishes a visual turing challenge. Finally, we argue despite the success of unique ground-truth annotation, we likely have to step away from carefully curated dataset and rather rely on 'social consensus' as the main driving force to create suitable benchmarks. Providing coverage in this inherently ambiguous output space is an emerging challenge that we face in order to make quantifiable progress in this area.

Several rules for social choice are examined from a unifying point of view that looks at them as procedures for revising a system of degrees of belief in accordance with certain specified logical constraints. Belief is here a social attribute, its degrees being measured by the fraction of people who share a given opinion. Different known rules and some new ones are obtained depending on which particular constraints are assumed. These constraints allow to model different notions of choiceness. In particular, we give a new method to deal with approval-disapproval-preferential voting.

Understanding how housing values evolve over time is important to policy makers, consumers and real estate professionals. Existing methods for constructing housing indices are computed at a coarse spatial granularity, such as metropolitan regions, which can mask or distort price dynamics apparent in local markets, such as neighborhoods and census tracts. A challenge in moving to estimates at, for example, the census tract level is the sparsity of spatiotemporally localized house sales observations. Our work aims at addressing this challenge by leveraging observations from multiple census tracts discovered to have correlated valuation dynamics. Our proposed Bayesian nonparametric approach builds on the framework of latent factor models to enable a flexible, data-driven method for inferring the clustering of correlated census tracts. We explore methods for scalability and parallelizability of computations, yielding a housing valuation index at the level of census tract rather than zip code, and on a monthly basis rather than quarterly. Our analysis is provided on a large Seattle metropolitan housing dataset.