Related papers: Detecting Markov Chain Instability: A Monte Carlo …
We propose a new Markov chain Monte Carlo method in which trial configurations are generated by evolving a state, sampled from a prior distribution, using a Markov transition matrix. We present two prototypical algorithms and derive their…
Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of…
A long-standing gap exists between the theoretical analysis of Markov chain Monte Carlo convergence, which is often based on statistical divergences, and the diagnostics used in practice. We introduce the first general convergence…
Contraction analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework in which to study uncertain interconnections or systems with…
Markov chain Monte Carlo (MCMC) algorithms are based on the construction of a Markov chain with transition probabilities leaving invariant a probability distribution of interest. In this work, we look at these transition probabilities as…
Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…
We propose a soft-output detection scheme for Multiple-Input-Multiple-Output (MIMO) systems. The detector employs Markov Chain Monte Carlo method to compute bit reliabilities from the signals received and is thus suited for coded MIMO…
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…
Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in…
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast…
A hierarchical clustering method is stable if small perturbations on the data set produce small perturbations in the result. These perturbations are measured using the Gromov-Hausdorff metric. We study the problem of stability on…
Most methods proposed to uncover communities in complex networks rely on combinatorial graph properties. Usually an edge-counting quality function, such as modularity, is optimized over all partitions of the graph compared against a null…
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
The problem of detecting a sinusoidal signal with randomly varying frequency has a long history. It is one of the core problems in signal processing, arising in many applications including, for example, underwater acoustic frequency line…
The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze…
In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in…
Typical geophysical inversion problems are ill-posed, non-linear and non-unique. Sometimes the problem is trans-dimensional, where the number of unknown parameters is one of the unknowns, which makes the inverse problem even more…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
We present a Monte Carlo simulation framework for analysing the risk involved in deploying real-time control systems in safety-critical applications, as well as an algorithm design technique allowing one (in certain situations) to robustify…
We consider a family of Markov chains whose transition dynamics are affected by model parameters. Understanding the parametric dependence of (complex) performance measures of such Markov chains is often of significant interest. The…