Mining graph data is an active research area. Several data mining methods and algorithms have been proposed to identify structures from graphs; still, the evaluation of those results is lacking. Within the framework of statistical hypothesis testing, we focus in this paper on randomization techniques for unweighted undirected graphs. Randomization is an important approach to assess the statisti...

Fitness functions based on the Ising model are suited excellently for studying the adaption capabilities of randomised search heuristics. The one-dimensional Ising model was considered a hard problem for mutation-based algorithms, and the two-dimensional Ising model was even thought to amplify the difficulties. While in one dimension the Ising model does not have any local optima, in two dimens...

The authors investigate the use of metropolis adjusted Langevin algorithms (MALA) in the context of particle MCMC algorithms. The ability to use this type of updates can lead to more efficient MCMC algorithms. The challenge in this context is that MALA and more sophisticated versions require the evaluation of the gradient of the loglikelihood and/or its Hessian, which are not available analytic...

Recent interest in graph pattern mining has shifted from finding all frequent subgraphs to obtaining a small subset of frequent subgraphs that are representative, discriminative or significant. The main motivation behind that is to cope with the scalability problem that the graph mining algorithms suffer when mining databases of large graphs. Another motivation is to obtain a succinct output se...

The random walk Metropolis algorithm is a simple Markov chain Monte Carlo scheme which is frequently used in Bayesian statistical problems. We propose a guided walk Metropolis algorithm which suppresses some of the random walk behavior in the Markov chain. This alternative algorithm is no harder to implement than the random walk Metropolis algorithm, but empirical studies show that it performs ...

We describe a novel algorithm for random sampling of freely reduced words equal to the identity in a finitely presented group. The algorithm is based on Metropolis Monte Carlo sampling. The algorithm samples from a stretched Boltzmann distribution π(w) = (|w|+ 1)αβ|w| · Z−1 where |w| is the length of a word w, α and β are parameters of the algorithm, and Z is a normalising constant. It follows ...

Now, if π has simple form, then we might be able to compute such quantities analytically using elementary calculus. Or, if the dimension d is fairly small, then we might be able to use standard numerical integration techniques. But such simple approaches fail in many situations. For example, the variance components model is a typical statistical model which has been used to study such diverse t...

Relational learning can be used to augment one data source with other correlated sources of information, to improve predictive accuracy. We frame a large class of relational learning problems as matrix factorization problems, and propose a hierarchical Bayesian model. Training our Bayesian model using random-walk Metropolis-Hastings is impractically slow, and so we develop a block Metropolis-Ha...

We introduce an object-oriented paradigm for probabilistic programming, embodied in the Figaro language. Models in Figaro are objects, and may have properties such as conditions, constraints and relationships to other objects. Figaro model classes are created by inheriting functionality from existing classes. Figaro provides a modular, compositional Metropolis-Hastings algorithm, and gives the ...