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.

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.

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, $k$-means, $k$-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a number of interesting interpretations of the low rank factors, which allow clustering of examples or of features. We propose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical results.

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.

Current status data is a data format where the time to event is restricted to knowledge of whether or not the failure time exceeds a random monitoring time. We develop a support vector machine learning method for current status data that estimates the failure time expectation as a function of the covariates. In order to obtain the support vector machine decision function, we minimize a regularized version of the empirical risk with respect to a data-dependent loss. We show that the decision function has a closed form. Using finite sample bounds and novel oracle inequalities, we prove that the obtained decision function converges to the true conditional expectation for a large family of probability measures and study the associated learning rates. Finally we present a simulation study that compares the performance of the proposed approach to current state of the art.

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.

We introduce an adaptive output-sensitive Metropolis-Hastings algorithm for probabilistic models expressed as programs, Adaptive Lightweight Metropolis-Hastings (AdLMH). The algorithm extends Lightweight Metropolis-Hastings (LMH) by adjusting the probabilities of proposing random variables for modification to improve convergence of the program output. We show that AdLMH converges to the correct equilibrium distribution and compare convergence of AdLMH to that of LMH on several test problems to highlight different aspects of the adaptation scheme. We observe consistent improvement in convergence on the test problems.

Using geometric data analysis, our objective is the analysis of narrative, with narrative of emotion being the focus in this work. The following two principles for analysis of emotion inform our work. Firstly, emotion is revealed not as a quality in its own right but rather through interaction. We study the 2-way relationship of Ilsa and Rick in the movie Casablanca, and the 3-way relationship of Emma, Charles and Rodolphe in the novel {\em Madame Bovary}. Secondly, emotion, that is expression of states of mind of subjects, is formed and evolves within the narrative that expresses external events and (personal, social, physical) context. In addition to the analysis methodology with key aspects that are innovative, the input data used is crucial. We use, firstly, dialogue, and secondly, broad and general description that incorporates dialogue. In a follow-on study, we apply our unsupervised narrative mapping to data streams with very low emotional expression. We map the narrative of Twitter streams. Thus we demonstrate map analysis of general narratives.