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Register a new userA Bayesian Tensor Factorization Model via Variational Inference for Link Prediction
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Beyza Ermis Ms
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large scale models. This paper presents full Bayesian inference via VB on both single and coupled tensor factorization models. Our method can be run even for very large models and is easily implemented. It exhibits better prediction performance than existing approaches based on maximum likelihood on several real-world datasets for missing link prediction problem.
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Probabilistic Latent Tensor Factorization (PLTF) is a recently proposed probabilistic framework for modelling multi-way data. Not only the common tensor factorization models but also any arbitrary tensor factorization structure can be realized by the PLTF framework. This paper presents full Bayesian inference via variational Bayes that facilitates more powerful modelling and allows more sophisticated inference on the PLTF framework. We illustrate our approach on model order selection and link prediction.
This study deals with the missing link prediction problem: the problem of predicting the existence of missing connections between entities of interest. We address link prediction using coupled analysis of relational datasets represented as heterogeneous data, i.e., datasets in the form of matrices and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links.
Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been derived for nonlinear model inference on data with additive gaussian noise as an alternative to nonlinear least squares. Here a stochastic solution is derived that avoids some of the approximations required of the analytical formulation, offering a solution that can be more flexibly deployed for nonlinear model inference problems. The stochastic VB solution was used for inference on a biexponential toy case and the algorithmic parameter space explored, before being deployed on real data from a magnetic resonance imaging study of perfusion. The new method was found to achieve comparable parameter recovery to the analytic solution and be competitive in terms of computational speed despite being reliant on sampling.
Clustering has become a core technology in machine learning, largely due to its application in the field of unsupervised learning, clustering, classification, and density estimation. A frequentist approach exists to hand clustering based on mixture model which is known as the EM algorithm where the parameters of the mixture model are usually estimated into a maximum likelihood estimation framework. Bayesian approach for finite and infinite Gaussian mixture model generates point estimates for all variables as well as associated uncertainty in the form of the whole estimates posterior distribution. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in Bayesian inference for finite and infinite Gaussian mixture model in order to seamlessly introduce their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning this field and given the paucity of scope to present this discussion, e.g., the separated analysis of the generation of Dirichlet samples by stick-breaking and Polyas Urn approaches. We refer the reader to literature in the field of the Dirichlet process mixture model for a much detailed introduction to the related fields. Some excellent examples include (Frigyik et al., 2010; Murphy, 2012; Gelman et al., 2014; Hoff, 2009). This survey is primarily a summary of purpose, significance of important background and techniques for Gaussian mixture model, e.g., Dirichlet prior, Chinese restaurant process, and most importantly the origin and complexity of the methods which shed light on their modern applications. The mathematical prerequisite is a first course in probability. Other than this modest background, the development is self-contained, with rigorous proofs provided throughout.
Learning the causal structure that underlies data is a crucial step towards robust real-world decision making. The majority of existing work in causal inference focuses on determining a single directed acyclic graph (DAG) or a Markov equivalence class thereof. However, a crucial aspect to acting intelligently upon the knowledge about causal structure which has been inferred from finite data demands reasoning about its uncertainty. For instance, planning interventions to find out more about the causal mechanisms that govern our data requires quantifying epistemic uncertainty over DAGs. While Bayesian causal inference allows to do so, the posterior over DAGs becomes intractable even for a small number of variables. Aiming to overcome this issue, we propose a form of variational inference over the graphs of Structural Causal Models (SCMs). To this end, we introduce a parametric variational family modelled by an autoregressive distribution over the space of discrete DAGs. Its number of parameters does not grow exponentially with the number of variables and can be tractably learned by maximising an Evidence Lower Bound (ELBO). In our experiments, we demonstrate that the proposed variational posterior is able to provide a good approximation of the true posterior.
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