Breaking Sticks and Ambiguities with Adaptive Skip-gram

Recently proposed Skip-gram model is a powerful method for learning high-dimensional word representations that capture rich semantic relationships between words. However, Skip-gram as well as most prior work on learning word representations does not take into account word ambiguity and maintain only single representation per word. Although a number of Skip-gram modifications were proposed to overcome this limitation and learn multi-prototype word representations, they either require a known number of word meanings or learn them using greedy heuristic approaches. In this paper we propose the Adaptive Skip-gram model which is a nonparametric Bayesian extension of Skip-gram capable to automatically learn the required number of representations for all words at desired semantic resolution. We derive efficient online variational learning algorithm for the model and empirically demonstrate its efficiency on word-sense induction task

An efficient and versatile approach to trust and reputation using hierarchical Bayesian modelling

In many dynamic open systems, autonomous agents must interact with one another to achieve their goals. Such agents may be self-interested and, when trusted to perform an action, may betray that trust by not performing the action as required. Due to the scale and dynamism of these systems, agents will often need to interact with other agents with which they have little or no past experience. Each agent must therefore be capable of assessing and identifying reliable interaction partners, even if it has no personal experience with them. To this end, we present HABIT, a Hierarchical And Bayesian Inferred Trust model for assessing how much an agent should trust its peers based on direct and third party information. This model is robust in environments in which third party information is malicious, noisy, or otherwise inaccurate. Although existing approaches claim to achieve this, most rely on heuristics with little theoretical foundation. In contrast, HABIT is based exclusively on principled statistical techniques: it can cope with multiple discrete or continuous aspects of trustee behaviour; it does not restrict agents to using a single shared representation of behaviour; it can improve assessment by using any observed correlation between the behaviour of similar trustees or information sources; and it provides a pragmatic solution to the whitewasher problem (in which unreliable agents assume a new identity to avoid bad reputation). In this paper, we describe the theoretical aspects of HABIT, and present experimental results that demonstrate its ability to predict agent behaviour in both a simulated environment, and one based on data from a real-world webserver domain. In particular, these experiments show that HABIT can predict trustee performance based on multiple representations of behaviour, and is up to twice as accurate as BLADE, an existing state-of-the-art trust model that is both statistically principled and has been previously shown to outperform a number of other probabilistic trust models

Optimal Clustering under Uncertainty

Classical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by developing a probabilistic framework based on the theory of random labeled point processes and characterizing a Bayes clusterer that minimizes the number of misclustered points. The Bayes clusterer is analogous to the Bayes classifier. Whereas determining a Bayes classifier requires full knowledge of the feature-label distribution, deriving a Bayes clusterer requires full knowledge of the point process. When uncertain of the point process, one would like to find a robust clusterer that is optimal over the uncertainty, just as one may find optimal robust classifiers with uncertain feature-label distributions. Herein, we derive an optimal robust clusterer by first finding an effective random point process that incorporates all randomness within its own probabilistic structure and from which a Bayes clusterer can be derived that provides an optimal robust clusterer relative to the uncertainty. This is analogous to the use of effective class-conditional distributions in robust classification. After evaluating the performance of robust clusterers in synthetic mixtures of Gaussians models, we apply the framework to granular imaging, where we make use of the asymptotic granulometric moment theory for granular images to relate robust clustering theory to the application.Comment: 19 pages, 5 eps figures, 1 tabl

Ultra-Light Scalar Fields and the Growth of Structure in the Universe

Ultra-light scalar fields, with masses of between m=10^{-33} eV and m=10^{-22} eV, can affect the growth of structure in the Universe. We identify the different regimes in the evolution of ultra-light scalar fields, how they affect the expansion rate of the universe and how they affect the growth rate of cosmological perturbations. We find a number of interesting effects, discuss how they might arise in realistic scenarios of the early universe and comment on how they might be observed.Comment: 12 pages, 11 figure

Comparing Community Structure to Characteristics in Online Collegiate Social Networks

We study the structure of social networks of students by examining the graphs of Facebook "friendships" at five American universities at a single point in time. We investigate each single-institution network's community structure and employ graphical and quantitative tools, including standardized pair-counting methods, to measure the correlations between the network communities and a set of self-identified user characteristics (residence, class year, major, and high school). We review the basic properties and statistics of the pair-counting indices employed and recall, in simplified notation, a useful analytical formula for the z-score of the Rand coefficient. Our study illustrates how to examine different instances of social networks constructed in similar environments, emphasizes the array of social forces that combine to form "communities," and leads to comparative observations about online social lives that can be used to infer comparisons about offline social structures. In our illustration of this methodology, we calculate the relative contributions of different characteristics to the community structure of individual universities and subsequently compare these relative contributions at different universities, measuring for example the importance of common high school affiliation to large state universities and the varying degrees of influence common major can have on the social structure at different universities. The heterogeneity of communities that we observe indicates that these networks typically have multiple organizing factors rather than a single dominant one.Comment: Version 3 (17 pages, 5 multi-part figures), accepted in SIAM Revie