The stretching and folding property of one-dimensional maps causes an information flow from the s... more The stretching and folding property of one-dimensional maps causes an information flow from the small scales to the large scales. With informal arguments, we derive an expression for this flow. This result is confirmed by a direct calculation of the net information flow.
In (Wainwright et al., 2002) a new general class of upper bounds on the log partition function of... more In (Wainwright et al., 2002) a new general class of upper bounds on the log partition function of arbitrary undirected graphical models has been developed. This bound is constructed by taking convex combinations of tractable distributions. The experimental results published so far concentrates on combinations of tree-structured distributions leading to a convexified Bethe free energy, which is minimized by the tree-reweighted belief propagation algorithm. One of the favorable properties of this class of approximations is that increasing the complexity of the approximation is guaranteed to increase the precision. The lack of this guarantee is notorious in standard generalized belief propagation. We increase the complexity of the approximating distributions by taking combinations of junction trees, leading to a convexified Kikuchi free energy, which is minimized by reweighted generalized belief propagation. Experimental results for Ising grids as well as for fully connected Ising mode...
Chaos: An Interdisciplinary Journal of Nonlinear Science
The high-tech industry produces complex devices in which software plays an important role. Since ... more The high-tech industry produces complex devices in which software plays an important role. Since these devices have been developed for many decades, an increasing part of the software can be classified as legacy which is difficult to maintain and to extend. To improve the maintainability of legacy components, domain specific languages (DSLs) provide promising perspectives. We present a DSL for creating configuration files that describe the topology of a fieldbus. This DSL improves the maintainability and extensibility of a legacy component. Compared to the current way-ofworking, the configuration files generated by the DSL are of higher quality due to the concise representation of DSL instances and additional validation checks. To raise the level of abstraction even more, we have created a second DSL which allows a concise description of system configurations and the generation of topologies.
In this article we consider the issue of optimal control in collaborative multi-agent systems wit... more In this article we consider the issue of optimal control in collaborative multi-agent systems with stochastic dynamics. The agents have a joint task in which they have to reach a number of target states. The dynamics of the agents contains additive control and additive noise, and the autonomous part factorizes over the agents. Full observation of the global state is assumed. The goal is to minimize the accumulated joint cost, which consists of integrated instantaneous costs and a joint end cost. The joint end cost expresses the joint task of the agents. The instantaneous costs are quadratic in the control and factorize over the agents. The optimal control is given as a weighted linear combination of single-agent to single-target controls. The single-agent to single-target controls are expressed in terms of diffusion processes. These controls, when not closed form expressions, are formulated in terms of path integrals, which are calculated approximately by Metropolis-Hastings samplin...
In this chapter, mean field theory is introduced fr om an information theoretic view point. The m... more In this chapter, mean field theory is introduced fr om an information theoretic view point. The mean field approximation is defined as t.he factorized distribution that is closest to the target distribution. \Vhen using the KL divergence to define closeness, this factorized distribution must have equal marginals as the target distribution. Such marginals can be approximately computed by using a Taylor series expansion in the couplings around the factorized distribution. To lowest order in the couplings, the usual naive mean field equations are obtained and to second order, olle obtains the TAP equatiolls. An important advantage of this procedure is that it does not require the concept of a fr ee energy. Therefore, it can be applied to arbitrary probability distributions, such as arising in asymmetric stochastic neural networks and graphical models.
We consider a stochastic nonlinear dynamical process with annihilation of particles. This process... more We consider a stochastic nonlinear dynamical process with annihilation of particles. This process can be viewed as the continuous time version of the extended Kalman filter/smoother. It also plays an important role in stochastic optimal control theory. We derive a Gaussian approximation for this process. With the use of the path integral formalism we derive Euler-Lagrange equations for the mode. Furthermore, we derive a linear noise approximation to estimate the size of the fluctuations around the mode, and estimates of the partition function, based on the mode and Gaussian corrections. Numerical experiments confirm the validity of the approximation method. In addition, they show that the Gaussian correction provides a significant improvement of the estimate of the partition function.
We consider loopy belief propagation for approximate inference in probabilistic graphical models.... more We consider loopy belief propagation for approximate inference in probabilistic graphical models. A limitation of the standard algorithm is that clique marginals are computed as if there were no loops in the graph. To overcome this limitation, we introduce fractional belief propagation. Fractional belief propagation is formulated in terms of a family of approximate free energies, which includes the Bethe free energy and the naive mean-field free as special cases. Using the linear response correction of the clique marginals, the scale parameters can be tuned. Simulation results illustrate the potential merits of the approach.
Recently, a theory for stochastic optimal control in non-linear dynamical systems in continuous s... more Recently, a theory for stochastic optimal control in non-linear dynamical systems in continuous space-time has been developed (Kappen, 2005). We apply this theory to collaborative multi-agent systems. The agents evolve according to a given non-linear dynamics with additive Wiener noise. Each agent can control its own dynamics. The goal is to minimize the accumulated joint cost, which consists of a state dependent term and a term that is quadratic in the control. We focus on systems of non-interacting agents that have to distribute themselves optimally over a number of targets, given a set of end-costs for the different possible agent-target combinations. We show that optimal control is the combinatorial sum of independent singleagent single-target optimal controls weighted by a factor proportional to the end-costs of the different combinations. Thus, multiagent control is related to a standard graphical model inference problem. The additional computational cost compared to single-agent control is exponential in the tree-width of the graph specifying the combinatorial sum times the number of targets. We illustrate the result by simulations of systems with up to 42 agents.
Exact inference in large and complex graphical models (e.g. Bayesian networks) is computationally... more Exact inference in large and complex graphical models (e.g. Bayesian networks) is computationally intractable. Approximate schemes are therefore of great importance for real world computation. In this paper we consider a general scheme in which the original intractable graphical model is approximated by a model with a tractable structure. The approximating model is optimised by an iterative procedure, which minimises the Kullback-Leibler divergence between the two models. The procedure is guaranteed to converge to a local minimum of the Kullback-Leibler divergence. The scheme provides a bridge between naive mean-eld theory and exact computation. Simulation results are provided to illustrate the method.
ABSTRACT The Netherlands Forensic Institute (NFI), together with SNN at Radboud University Nijmeg... more ABSTRACT The Netherlands Forensic Institute (NFI), together with SNN at Radboud University Nijmegen, have developed new software for pedigree matching which can handle autosomal, Y chromosomal and mitochondrial DNA profiles. Initially this software, called Bonaparte, has been developed for DNA DVI. Bonaparte has been successfully applied in a real DVI case: the Afriqiyah Airways crash in Tripoli, Libya on 12 May 2010 in which 103 persons perished. The software performed excellently in terms of computational performance, stability and user-friendliness. This showed that Bonaparte is a reliable and time-saving tool which significantly simplifies and enhances a large-scale victim identification process.Bonaparte has been applied in NFIs missing persons program. For this, the software is connected to the NFI's missing persons database (CODIS). Since Bonaparte uses XML as import format, data from any source can be imported. In the new configuration, CODIS data is automatically imported into Bonaparte. Then the software automatically performs a set of direct searches, as well as searches against both partial and full family trees. For the autosomal DNA results, exact likelihood ratios are computed. Finally, match reports can be generated on demand by Bonaparte's customized reporting modules. In this way, an advanced search strategy combined with a modern, efficient work flow is realized in NFI's missing persons program.
We describe a software system, called just enough delivery (JED), for optimising single-copy news... more We describe a software system, called just enough delivery (JED), for optimising single-copy newspaper sales, based on a combination of neural and Bayesian technology. The prediction model is a huge feedforward neural network, in which each output corresponds to the sales prediction for a single outlet. Input-to-hidden weights are shared between outlets. The hidden-to-output weights are specific to each outlet, but linked through the introduction of priors. All weights and hyperparameters can be inferred using (empirical) Bayesian inference. The system has been tested on data for several different newspapers and magazines. Consistent performance improvements of 1 to 3% more sales with the same total amount of deliveries have been obtained. Keywords Bayesian inference AE Feed forward AE Multi-task learning AE Neural networks AE Time-series prediction
In this article we consider the problem of stochastic optimal control in continuous-time and stat... more In this article we consider the problem of stochastic optimal control in continuous-time and state-action space of systems with state constraints. These systems typically appear in the area of robotics, where hard obstacles constrain the state space of the robot. A common approach is to solve the problem locally using a linear-quadratic Gaussian (LQG) method. We take a different approach and apply path integral control as introduced by Kappen (Kappen, H.J. (2005a), ‘Path Integrals and Symmetry Breaking for Optimal Control Theory’, Journal of Statistical Mechanics: Theory and Experiment, 2005, P11011; Kappen, H.J. (2005b), ‘Linear Theory for Control of Nonlinear Stochastic Systems’, Physical Review Letters, 95, 200201). We use hybrid Monte Carlo sampling to infer the control. We introduce an adaptive time discretisation scheme for the simulation of the controlled dynamics. We demonstrate our approach on two examples, a simple particle in a halfspace and a more complex two-joint manipulator, and we show that in a high noise regime our approach outperforms the iterative LQG method.
The stretching and folding property of one-dimensional maps causes an information flow from the s... more The stretching and folding property of one-dimensional maps causes an information flow from the small scales to the large scales. With informal arguments, we derive an expression for this flow. This result is confirmed by a direct calculation of the net information flow.
In (Wainwright et al., 2002) a new general class of upper bounds on the log partition function of... more In (Wainwright et al., 2002) a new general class of upper bounds on the log partition function of arbitrary undirected graphical models has been developed. This bound is constructed by taking convex combinations of tractable distributions. The experimental results published so far concentrates on combinations of tree-structured distributions leading to a convexified Bethe free energy, which is minimized by the tree-reweighted belief propagation algorithm. One of the favorable properties of this class of approximations is that increasing the complexity of the approximation is guaranteed to increase the precision. The lack of this guarantee is notorious in standard generalized belief propagation. We increase the complexity of the approximating distributions by taking combinations of junction trees, leading to a convexified Kikuchi free energy, which is minimized by reweighted generalized belief propagation. Experimental results for Ising grids as well as for fully connected Ising mode...
Chaos: An Interdisciplinary Journal of Nonlinear Science
The high-tech industry produces complex devices in which software plays an important role. Since ... more The high-tech industry produces complex devices in which software plays an important role. Since these devices have been developed for many decades, an increasing part of the software can be classified as legacy which is difficult to maintain and to extend. To improve the maintainability of legacy components, domain specific languages (DSLs) provide promising perspectives. We present a DSL for creating configuration files that describe the topology of a fieldbus. This DSL improves the maintainability and extensibility of a legacy component. Compared to the current way-ofworking, the configuration files generated by the DSL are of higher quality due to the concise representation of DSL instances and additional validation checks. To raise the level of abstraction even more, we have created a second DSL which allows a concise description of system configurations and the generation of topologies.
In this article we consider the issue of optimal control in collaborative multi-agent systems wit... more In this article we consider the issue of optimal control in collaborative multi-agent systems with stochastic dynamics. The agents have a joint task in which they have to reach a number of target states. The dynamics of the agents contains additive control and additive noise, and the autonomous part factorizes over the agents. Full observation of the global state is assumed. The goal is to minimize the accumulated joint cost, which consists of integrated instantaneous costs and a joint end cost. The joint end cost expresses the joint task of the agents. The instantaneous costs are quadratic in the control and factorize over the agents. The optimal control is given as a weighted linear combination of single-agent to single-target controls. The single-agent to single-target controls are expressed in terms of diffusion processes. These controls, when not closed form expressions, are formulated in terms of path integrals, which are calculated approximately by Metropolis-Hastings samplin...
In this chapter, mean field theory is introduced fr om an information theoretic view point. The m... more In this chapter, mean field theory is introduced fr om an information theoretic view point. The mean field approximation is defined as t.he factorized distribution that is closest to the target distribution. \Vhen using the KL divergence to define closeness, this factorized distribution must have equal marginals as the target distribution. Such marginals can be approximately computed by using a Taylor series expansion in the couplings around the factorized distribution. To lowest order in the couplings, the usual naive mean field equations are obtained and to second order, olle obtains the TAP equatiolls. An important advantage of this procedure is that it does not require the concept of a fr ee energy. Therefore, it can be applied to arbitrary probability distributions, such as arising in asymmetric stochastic neural networks and graphical models.
We consider a stochastic nonlinear dynamical process with annihilation of particles. This process... more We consider a stochastic nonlinear dynamical process with annihilation of particles. This process can be viewed as the continuous time version of the extended Kalman filter/smoother. It also plays an important role in stochastic optimal control theory. We derive a Gaussian approximation for this process. With the use of the path integral formalism we derive Euler-Lagrange equations for the mode. Furthermore, we derive a linear noise approximation to estimate the size of the fluctuations around the mode, and estimates of the partition function, based on the mode and Gaussian corrections. Numerical experiments confirm the validity of the approximation method. In addition, they show that the Gaussian correction provides a significant improvement of the estimate of the partition function.
We consider loopy belief propagation for approximate inference in probabilistic graphical models.... more We consider loopy belief propagation for approximate inference in probabilistic graphical models. A limitation of the standard algorithm is that clique marginals are computed as if there were no loops in the graph. To overcome this limitation, we introduce fractional belief propagation. Fractional belief propagation is formulated in terms of a family of approximate free energies, which includes the Bethe free energy and the naive mean-field free as special cases. Using the linear response correction of the clique marginals, the scale parameters can be tuned. Simulation results illustrate the potential merits of the approach.
Recently, a theory for stochastic optimal control in non-linear dynamical systems in continuous s... more Recently, a theory for stochastic optimal control in non-linear dynamical systems in continuous space-time has been developed (Kappen, 2005). We apply this theory to collaborative multi-agent systems. The agents evolve according to a given non-linear dynamics with additive Wiener noise. Each agent can control its own dynamics. The goal is to minimize the accumulated joint cost, which consists of a state dependent term and a term that is quadratic in the control. We focus on systems of non-interacting agents that have to distribute themselves optimally over a number of targets, given a set of end-costs for the different possible agent-target combinations. We show that optimal control is the combinatorial sum of independent singleagent single-target optimal controls weighted by a factor proportional to the end-costs of the different combinations. Thus, multiagent control is related to a standard graphical model inference problem. The additional computational cost compared to single-agent control is exponential in the tree-width of the graph specifying the combinatorial sum times the number of targets. We illustrate the result by simulations of systems with up to 42 agents.
Exact inference in large and complex graphical models (e.g. Bayesian networks) is computationally... more Exact inference in large and complex graphical models (e.g. Bayesian networks) is computationally intractable. Approximate schemes are therefore of great importance for real world computation. In this paper we consider a general scheme in which the original intractable graphical model is approximated by a model with a tractable structure. The approximating model is optimised by an iterative procedure, which minimises the Kullback-Leibler divergence between the two models. The procedure is guaranteed to converge to a local minimum of the Kullback-Leibler divergence. The scheme provides a bridge between naive mean-eld theory and exact computation. Simulation results are provided to illustrate the method.
ABSTRACT The Netherlands Forensic Institute (NFI), together with SNN at Radboud University Nijmeg... more ABSTRACT The Netherlands Forensic Institute (NFI), together with SNN at Radboud University Nijmegen, have developed new software for pedigree matching which can handle autosomal, Y chromosomal and mitochondrial DNA profiles. Initially this software, called Bonaparte, has been developed for DNA DVI. Bonaparte has been successfully applied in a real DVI case: the Afriqiyah Airways crash in Tripoli, Libya on 12 May 2010 in which 103 persons perished. The software performed excellently in terms of computational performance, stability and user-friendliness. This showed that Bonaparte is a reliable and time-saving tool which significantly simplifies and enhances a large-scale victim identification process.Bonaparte has been applied in NFIs missing persons program. For this, the software is connected to the NFI's missing persons database (CODIS). Since Bonaparte uses XML as import format, data from any source can be imported. In the new configuration, CODIS data is automatically imported into Bonaparte. Then the software automatically performs a set of direct searches, as well as searches against both partial and full family trees. For the autosomal DNA results, exact likelihood ratios are computed. Finally, match reports can be generated on demand by Bonaparte's customized reporting modules. In this way, an advanced search strategy combined with a modern, efficient work flow is realized in NFI's missing persons program.
We describe a software system, called just enough delivery (JED), for optimising single-copy news... more We describe a software system, called just enough delivery (JED), for optimising single-copy newspaper sales, based on a combination of neural and Bayesian technology. The prediction model is a huge feedforward neural network, in which each output corresponds to the sales prediction for a single outlet. Input-to-hidden weights are shared between outlets. The hidden-to-output weights are specific to each outlet, but linked through the introduction of priors. All weights and hyperparameters can be inferred using (empirical) Bayesian inference. The system has been tested on data for several different newspapers and magazines. Consistent performance improvements of 1 to 3% more sales with the same total amount of deliveries have been obtained. Keywords Bayesian inference AE Feed forward AE Multi-task learning AE Neural networks AE Time-series prediction
In this article we consider the problem of stochastic optimal control in continuous-time and stat... more In this article we consider the problem of stochastic optimal control in continuous-time and state-action space of systems with state constraints. These systems typically appear in the area of robotics, where hard obstacles constrain the state space of the robot. A common approach is to solve the problem locally using a linear-quadratic Gaussian (LQG) method. We take a different approach and apply path integral control as introduced by Kappen (Kappen, H.J. (2005a), ‘Path Integrals and Symmetry Breaking for Optimal Control Theory’, Journal of Statistical Mechanics: Theory and Experiment, 2005, P11011; Kappen, H.J. (2005b), ‘Linear Theory for Control of Nonlinear Stochastic Systems’, Physical Review Letters, 95, 200201). We use hybrid Monte Carlo sampling to infer the control. We introduce an adaptive time discretisation scheme for the simulation of the controlled dynamics. We demonstrate our approach on two examples, a simple particle in a halfspace and a more complex two-joint manipulator, and we show that in a high noise regime our approach outperforms the iterative LQG method.
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Papers by Wim Wiegerinck