We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data. Sparsity in the kernel weights is obtained by adopting a hierarchical Bayesian approach: Gaussian process priors are imposed over the latent functions and generalised inverse Gaussians on their associated weights. This construction is equivalent to imposing a product of heavy-tailed process priors over function space. A variational inference algorithm is derived for regression and binary classification. 1 Introduction Kernel-based methods are well-established tools for supervised learning, allowing to perform various tasks, such as regression or binary classification, with linear and nonlinear predictors.

We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers $\mathbb{N}$ via a Poisson point process with mean measure $\Lambda$ on the power set of $\mathbb{N}$. Each $E\in\cate$ has a least monotone cover in $\catf$, the collection of monotone subsets of $\cate$, and every monotone subset maps to an undirected graph $G\in\catg$, the space of undirected graphs with vertex set $\mathbb{N}$. We show a natural mapping $\cate\rightarrow\catf\rightarrow\catg$ which induces an infinitely exchangeable measure on the projective system $\catg^{\rest}$ of graphs $\catg$ under permutation and restriction mappings given an infinitely exchangeable family of measures on the projective system $\cate^{\rest}$ of subsets with permutation and restriction maps. We show potential connections of this process to applications in cluster analysis, machine learning, classification and Bayesian inference.

Information diffusion and virus propagation are fundamental processes taking place in networks. While it is often possible to directly observe when nodes become infected with a virus or adopt the information, observing individual transmissions (i.e., who infects whom, or who influences whom) is typically very difficult. Furthermore, in many applications, the underlying network over which the diffusions and propagations spread is actually unobserved. We tackle these challenges by developing a method for tracing paths of diffusion and influence through networks and inferring the networks over which contagions propagate. Given the times when nodes adopt pieces of information or become infected, we identify the optimal network that best explains the observed infection times. Since the optimization problem is NP-hard to solve exactly, we develop an efficient approximation algorithm that scales to large datasets and finds provably near-optimal networks. We demonstrate the effectiveness of our approach by tracing information diffusion in a set of 170 million blogs and news articles over a one year period to infer how information flows through the online media space. We find that the diffusion network of news for the top 1,000 media sites and blogs tends to have a core-periphery structure with a small set of core media sites that diffuse information to the rest of the Web. These sites tend to have stable circles of influence with more general news media sites acting as connectors between them.

Efficient global optimization is the problem of minimizing an unknown function f, using as few evaluations f(x) as possible. It can be considered as a continuum-armed bandit problem, with noiseless data and simple regret. Expected improvement is perhaps the most popular method for solving this problem; the algorithm performs well in experiments, but little is known about its theoretical properties. Implementing expected improvement requires a choice of Gaussian process prior, which determines an associated space of functions, its reproducing-kernel Hilbert space (RKHS). When the prior is fixed, expected improvement is known to converge on the minimum of any function in the RKHS. We begin by providing convergence rates for this procedure. The rates are optimal for functions of low smoothness, and we modify the algorithm to attain optimal rates for smoother functions. For practitioners, however, these results are somewhat misleading. Priors are typically not held fixed, but depend on parameters estimated from the data. For standard estimators, we show this procedure may never discover the minimum of f. We then propose alternative estimators, chosen to minimize the constants in the rate of convergence, and show these estimators retain the convergence rates of a fixed prior.

We study a variation of this concept, in which the documents' mixture weight beliefs are replaced with squashed Gaussian distributions. This allows documents to be associated with elements of a Hilbert space, admitting kernel topic models (KTM), modelling temporal, spatial, hierarchical, social and other structure between documents. The main challenge is efficient approximate inference on the latent Gaussian. We present an approximate algorithm cast around a Laplace approximation in a transformed basis. The KTM can also be interpreted as a type of Gaussian process latent variable model, or as a topic model conditional on document features, uncovering links between earlier work in these areas.

We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates input dependent signal and noise correlations between multiple response variables, input dependent length-scales and amplitudes, and heavy-tailed predictive distributions. We derive both efficient Markov chain Monte Carlo and variational Bayes inference procedures for this model. We apply GPRN as a multiple output regression and multivariate volatility model, demonstrating substantially improved performance over eight popular multiple output (multi-task) Gaussian process models and three multivariate volatility models on benchmark datasets, including a 1000 dimensional gene expression dataset.

The success of an agent mediated e-market system lies in the underlying reputation management system to improve the quality of services in an information asymmetric e-market. Reputation provides an operatable metric for establishing trustworthiness between mutually unknown online entities. Reputation systems encourage honest behaviour and discourage malicious behaviour of participating agents in the e-market. A dynamic reputation model would provide virtually instantaneous knowledge about the changing e-market environment and would utilise Internets' capacity for continuous interactivity for reputation computation. This paper proposes a dynamic reputation framework using reinforcement learning and fuzzy set theory that ensures judicious use of information sharing for inter-agent cooperation. This framework is sensitive to the changing parameters of e-market like the value of transaction and the varying experience of agents with the purpose of improving inbuilt defense mechanism of the reputation system against various attacks so that e-market reaches an equilibrium state and dishonest agents are weeded out of the market.

Satisfied customers establishes loyalty, provides opportunities of selling additional products and services. Satisfied customers also reduce the probability of losing business to competitors. However, customer dissatisfaction results in direct revenue losses due to customer churn as well as damage to business reputation. Therefore, the improvement of customer experience is a vital priority for contact centres across all industries. Interactive Voice Response (IVR) systems are used by businesses to provide customers with a convenient, consistent and reliable contact channel to access information fast.

We introduce a factor analysis model that summarizes the dependencies between observed variable groups, instead of dependencies between individual variables as standard factor analysis does. A group may correspond to one view of the same set of objects, one of many data sets tied by co-occurrence, or a set of alternative variables collected from statistics tables to measure one property of interest. We show that by assuming group-wise sparse factors, active in a subset of the sets, the variation can be decomposed into factors explaining relationships between the sets and factors explaining away set-specific variation. We formulate the assumptions in a Bayesian model which provides the factors, and apply the model to two data analysis tasks, in neuroimaging and chemical systems biology.

Detection of emerging topics are now receiving renewed interest motivated by the rapid growth of social networks. Conventional term-frequency-based approaches may not be appropriate in this context, because the information exchanged are not only texts but also images, URLs, and videos. We focus on the social aspects of theses networks. That is, the links between users that are generated dynamically intentionally or unintentionally through replies, mentions, and retweets. We propose a probability model of the mentioning behaviour of a social network user, and propose to detect the emergence of a new topic from the anomaly measured through the model. We combine the proposed mention anomaly score with a recently proposed change-point detection technique based on the Sequentially Discounting Normalized Maximum Likelihood (SDNML), or with Kleinberg's burst model. Aggregating anomaly scores from hundreds of users, we show that we can detect emerging topics only based on the reply/mention relationships in social network posts. We demonstrate our technique in a number of real data sets we gathered from Twitter. The experiments show that the proposed mention-anomaly-based approaches can detect new topics at least as early as the conventional term-frequency-based approach, and sometimes much earlier when the keyword is ill-defined.