arXiv subjects

Nial Friel

Publications and source records attributed to Nial Friel.

At least 55 records · Page 3Linked to original sources

arXiv2015

Choosing the number of clusters in a finite mixture model using an exact Integrated Completed Likelihood criterion

The integrated completed likelihood (ICL) criterion has proven to be a very popular approach in model-based clustering through automatically choosing the number of clusters in a mixture model. This approach effectively maximises the complete data likelihood, thereby including the allocation of observations to clusters in the model selection criterion. However for practical implementation one needs to introduce an approximation in order to estimate the ICL. Our contribution here is to illustrate that through the use of conjugate priors one can derive an exact expression for ICL and so avoiding any approximation. Moreover, we illustrate how one can find both the number of clusters and the best allocation of observations in one algorithmic framework. The performance of our algorithm is presented on several simulated and real examples.

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arXiv2015

Inferring structure in bipartite networks using the latent block model and exact ICL

We consider the task of simultaneous clustering of the two node sets involved in a bipartite network. The approach we adopt is based on use of the exact integrated complete likelihood for the latent block model. Using this allows one to infer the number of clusters as well as cluster memberships using a greedy search. This gives a model-based clustering of the node sets. Experiments on simulated bipartite network data show that the greedy search approach is vastly more scalable than competing Markov chain Monte Carlo based methods. Application to a number of real observed bipartite networks demonstrate the algorithms discussed.

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arXiv2015

Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods

Many popular statistical models for complex phenomena are intractable, in the sense that the likelihood function cannot easily be evaluated. Bayesian estimation in this setting remains challenging, with a lack of computational methodology to fully exploit modern processing capabilities. In this paper we introduce novel control variates for intractable likelihoods that can dramatically reduce the Monte Carlo variance of Bayesian estimators. We prove that our control variates are well-defined and provide a positive variance reduction. Furthermore we show how to optimise these control variates for variance reduction. The methodology is highly parallel and offers a route to exploit multi-core processing architectures that complements recent research in this direction. Indeed, our work shows that it may not be necessary to parallelise the sampling process itself in order to harness the potential of massively multi-core architectures. Simulation results presented on the Ising model, exponential random graph models and non-linear stochastic differential equation models support our theoretical findings.

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arXiv2015

Bayesian Exponential Random Graph Models with Nodal Random Effects

We extend the well-known and widely used Exponential Random Graph Model (ERGM) by including nodal random effects to compensate for heterogeneity in the nodes of a network. The Bayesian framework for ERGMs proposed by Caimo and Friel (2011) yields the basis of our modelling algorithm. A central question in network models is the question of model selection and following the Bayesian paradigm we focus on estimating Bayes factors. To do so we develop an approximate but feasible calculation of the Bayes factor which allows one to pursue model selection. Two data examples and a small simulation study illustrate our mixed model approach and the corresponding model selection.

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arXiv2014

Evidence and Bayes factor estimation for Gibbs random fields

Gibbs random fields play an important role in statistics. However they are complicated to work with due to an intractability of the likelihood function and there has been much work devoted to finding computational algorithms to allow Bayesian inference to be conducted for such so-called doubly intractable distributions. This paper extends this work and addresses the issue of estimating the evidence and Bayes factor for such models. The approach which we develop is shown to yield good performance.

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arXiv2014

Bergm: Bayesian Exponential Random Graphs in R

In this paper we describe the main featuress of the Bergm package for the open-source R software which provides a comprehensive framework for Bayesian analysis for exponential random graph models: tools for parameter estimation, model selection and goodness-of-fit diagnostics. We illustrate the capabilities of this package describing the algorithms through a tutorial analysis of two well-known network datasets.

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arXiv2013

Bayesian model selection for the latent position cluster model for Social Networks

The latent position cluster model is a popular model for the statistical analysis of network data. This approach assumes that there is an underlying latent space in which the actors follow a finite mixture distribution. Moreover, actors which are close in this latent space tend to be tied by an edge. This is an appealing approach since it allows the model to cluster actors which consequently provides the practitioner with useful qualitative information. However, exploring the uncertainty in the number of underlying latent components in the mixture distribution is a very complex task. The current state-of-the-art is to use an approximate form of BIC for this purpose, where an approximation of the log-likelihood is used instead of the true log-likelihood which is unavailable. The main contribution of this paper is to show that through the use of conjugate prior distributions it is possible to analytically integrate out almost all of the model parameters, leaving a posterior distribution which depends on the allocation vector of the mixture model. A consequence of this is that it is possible to carry out posterior inference over the number of components in the latent mixture distribution without using trans-dimensional MCMC algorithms such as reversible jump MCMC. Moreover, our algorithm allows for more reasonable computation times for larger networks than the standard methods using the latentnet package (Krivitsky and Handcock 2008; Krivitsky and Handcock 2013).

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arXiv2013

Improving power posterior estimation of statistical evidence

The statistical evidence (or marginal likelihood) is a key quantity in Bayesian statistics, allowing one to assess the probability of the data given the model under investigation. This paper focuses on refining the power posterior approach to improve estimation of the evidence. The power posterior method involves transitioning from the prior to the posterior by powering the likelihood by an inverse temperature. In common with other tempering algorithms, the power posterior involves some degree of tuning. The main contributions of this article are twofold -- we present a result from the numerical analysis literature which can reduce the bias in the estimate of the evidence by addressing the error arising from numerically integrating across the inverse temperatures. We also tackle the selection of the inverse temperature ladder, applying this approach additionally to the Stepping Stone sampler estimation of evidence.

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arXiv2013

Efficient Estimation of the number of neighbours in Probabilistic K Nearest Neighbour Classification

Probabilistic k-nearest neighbour (PKNN) classification has been introduced to improve the performance of original k-nearest neighbour (KNN) classification algorithm by explicitly modelling uncertainty in the classification of each feature vector. However, an issue common to both KNN and PKNN is to select the optimal number of neighbours, $k$. The contribution of this paper is to incorporate the uncertainty in $k$ into the decision making, and in so doing use Bayesian model averaging to provide improved classification. Indeed the problem of assessing the uncertainty in $k$ can be viewed as one of statistical model selection which is one of the most important technical issues in the statistics and machine learning domain. In this paper, a new functional approximation algorithm is proposed to reconstruct the density of the model (order) without relying on time consuming Monte Carlo simulations. In addition, this algorithm avoids cross validation by adopting Bayesian framework. The performance of this algorithm yielded very good performance on several real experimental datasets.

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arXiv2013

Bayesian model selection for exponential random graph models

Exponential random graph models are a class of widely used exponential family models for social networks. The topological structure of an observed network is modelled by the relative prevalence of a set of local sub-graph configurations termed network statistics. One of the key tasks in the application of these models is which network statistics to include in the model. This can be thought of as statistical model selection problem. This is a very challenging problem---the posterior distribution for each model is often termed "doubly intractable" since computation of the likelihood is rarely available, but also, the evidence of the posterior is, as usual, intractable. The contribution of this paper is the development of a fully Bayesian model selection method based on a reversible jump Markov chain Monte Carlo algorithm extension of Caimo and Friel (2011) which estimates the posterior probability for each competing model.

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arXiv2012

Clustering in networks with the collapsed Stochastic Block Model

An efficient MCMC algorithm is presented to cluster the nodes of a network such that nodes with similar role in the network are clustered together. This is known as block-modelling or block-clustering. The model is the stochastic blockmodel (SBM) with block parameters integrated out. The resulting marginal distribution defines a posterior over the number of clusters and cluster memberships. Sampling from this posterior is simpler than from the original SBM as transdimensional MCMC can be avoided. The algorithm is based on the allocation sampler. It requires a prior to be placed on the number of clusters, thereby allowing the number of clusters to be directly estimated by the algorithm, rather than being given as an input parameter. Synthetic and real data are used to test the speed and accuracy of the model and algorithm, including the ability to estimate the number of clusters. The algorithm can scale to networks with up to ten thousand nodes and tens of millions of edges.

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arXiv2012

Model-based clustering in networks with Stochastic Community Finding

In the model-based clustering of networks, blockmodelling may be used to identify roles in the network. We identify a special case of the Stochastic Block Model (SBM) where we constrain the cluster-cluster interactions such that the density inside the clusters of nodes is expected to be greater than the density between clusters. This corresponds to the intuition behind community-finding methods, where nodes tend to clustered together if they link to each other. We call this model Stochastic Community Finding (SCF) and present an efficient MCMC algorithm which can cluster the nodes, given the network. The algorithm is evaluated on synthetic data and is applied to a social network of interactions at a karate club and at a monastery, demonstrating how the SCF finds the 'ground truth' clustering where sometimes the SBM does not. The SCF is only one possible form of constraint or specialization that may be applied to the SBM. In a more supervised context, it may be appropriate to use other specializations to guide the SBM.

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arXiv2012

Bayesian inference for Gibbs random fields using composite likelihoods

Gibbs random fields play an important role in statistics, for example the autologistic model is commonly used to model the spatial distribution of binary variables defined on a lattice. However they are complicated to work with due to an intractability of the likelihood function. It is therefore natural to consider tractable approximations to the likelihood function. Composite likelihoods offer a principled approach to constructing such approximation. The contribution of this paper is to examine the performance of a collection of composite likelihood approximations in the context of Bayesian inference.

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arXiv2011

Estimating the evidence -- a review

The model evidence is a vital quantity in the comparison of statistical models under the Bayesian paradigm. This paper presents a review of commonly used methods. We outline some guidelines and offer some practical advice. The reviewed methods are compared for two examples; non-nested Gaussian linear regression and covariate subset selection in logistic regression.

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arXiv2011

Approximate simulation-free Bayesian inference for multiple changepoint models with dependence within segments

This paper proposes approaches for the analysis of multiple changepoint models when dependency in the data is modelled through a hierarchical Gaussian Markov random field. Integrated nested Laplace approximations are used to approximate data quantities, and an approximate filtering recursions approach is proposed for savings in compuational cost when detecting changepoints. All of these methods are simulation free. Analysis of real data demonstrates the usefulness of the approach in general. The new models which allow for data dependence are compared with conventional models where data within segments is assumed independent.

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arXiv2010

Simulation-based Bayesian analysis for multiple changepoints

This paper presents a Markov chain Monte Carlo method to generate approximate posterior samples in retrospective multiple changepoint problems where the number of changes is not known in advance. The method uses conjugate models whereby the marginal likelihood for the data between consecutive changepoints is tractable. Inclusion of hyperpriors gives a near automatic algorithm providing a robust alternative to popular filtering recursions approaches in cases which may be sensitive to prior information. Three real examples are used to demonstrate the proposed approach.

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arXiv2010

Block clustering with collapsed latent block models

We introduce a Bayesian extension of the latent block model for model-based block clustering of data matrices. Our approach considers a block model where block parameters may be integrated out. The result is a posterior defined over the number of clusters in rows and columns and cluster memberships. The number of row and column clusters need not be known in advance as these are sampled along with cluster memberhips using Markov chain Monte Carlo. This differs from existing work on latent block models, where the number of clusters is assumed known or is chosen using some information criteria. We analyze both simulated and real data to validate the technique.

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arXiv2010

Tuning Tempered Transitions

The method of tempered transitions was proposed by Neal (1996) for tackling the difficulties arising when using Markov chain Monte Carlo to sample from multimodal distributions. In common with methods such as simulated tempering and Metropolis-coupled MCMC, the key idea is to utilise a series of successively easier to sample distributions to improve movement around the state space. Tempered transitions does this by incorporating moves through these less modal distributions into the MCMC proposals. Unfortunately the improved movement between modes comes at a high computational cost with a low acceptance rate of expensive proposals. We consider how the algorithm may be tuned to increase the acceptance rates for a given number of temperatures. We find that the commonly assumed geometric spacing of temperatures is reasonable in many but not all applications.

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