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In this paper we build on previous work which uses inferences techniques, in particular Markov Chain Monte Carlo (MCMC) methods, to solve parameterized control problems. We propose a number of modifications in order to make this approach…
Multimodal structures in the sampling density (e.g. two competing phases) can be a serious problem for traditional Markov Chain Monte Carlo (MCMC), because correct sampling of the different structures can only be guaranteed for infinite…
The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…
The Incremental K-means (IKM), an improved version of K-means (KM), was introduced to improve the clustering quality of KM significantly. However, the speed of IKM is slower than KM. My thesis proposes two algorithms to speed up IKM while…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
We provide a framework for speeding up algorithms for time-bounded reachability analysis of continuous-time Markov decision processes. The principle is to find a small, but almost equivalent subsystem of the original system and only analyse…
We describe convergence acceleration schemes for multistep optimization algorithms. The extrapolated solution is written as a nonlinear average of the iterates produced by the original optimization method. Our analysis does not need the…
It is well-known that irreversible MCMC algorithms converge faster to their stationary distributions than reversible ones. Using the special geometric structure of Lie groups $\mathcal G$ and dissipation fields compatible with the…
Most Markov chain Monte Carlo methods operate in discrete time and are reversible with respect to the target probability. Nevertheless, it is now understood that the use of non-reversible Markov chains can be beneficial in many contexts. In…
Equilibrium systems evolve according to Detailed Balance (DB). This principe guided development of the Monte-Carlo sampling techniques, of which Metropolis-Hastings (MH) algorithm is the famous representative. It is also known that DB is…
When approaching the continuum limit in lattice QCD or other theories in a setup with topological sectors, conventional update algorithms experience a particularly severe form of critical slowing down that is caused by high action barriers…
Recent studies have illustrated that stochastic gradient Markov Chain Monte Carlo techniques have a strong potential in non-convex optimization, where local and global convergence guarantees can be shown under certain conditions. By…
We present here two novel algorithms for simulated tempering simulations, which break detailed balance condition (DBC) but satisfy the skewed detailed balance to ensure invariance of the target distribution. The irreversible methods we…
Markov Chain Monte Carlo (MCMC) sampling is computationally expensive, especially for complex models. Alternative methods make simplifying assumptions about the posterior to reduce computational burden, but their impact on predictive…
The Pseudo-Marginal (PM) algorithm is a popular Markov chain Monte Carlo (MCMC) method used to sample from a target distribution when its density is inaccessible, but can be estimated with a non-negative unbiased estimator. Its performance…
Partially observable Markov decision processes (POMDPs) have recently become popular among many AI researchers because they serve as a natural model for planning under uncertainty. Value iteration is a well-known algorithm for finding…
We investigate the lattice spacing dependence of the equilibration time for a recently proposed multiscale thermalization algorithm for Markov chain Monte Carlo simulations. The algorithm uses a renormalization-group matched coarse lattice…
We present a Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithm for detecting hidden variables in a continuous time Bayesian network (CTBN), which uses reversible jumps in the sense defined by (Green 1995). In common with several…
Markov decision processes (MDP) are useful to model concurrent process optimisation problems, but verifying them with numerical methods is often intractable. Existing approximative approaches do not scale well and are limited to memoryless…
Filtering---estimating the state of a partially observable Markov process from a sequence of observations---is one of the most widely studied problems in control theory, AI, and computational statistics. Exact computation of the posterior…