Bert Kappen

Bert (HJ) Kappen

Bert (HJ) Kappen is professor of physics at the Department of Biophysics, Radboud University, Nijmegen
Together with Ton Coolen he forms the research group on Physics of machine learning and complex systems
He is director of the Dutch foundation for Neural networks
He is visiting professor at Gatsby computational neuroscience unit at UCL London
Together with Riccardo Zecchina he leads the European Ellis program on machine learning called "Quantum and physics based machine learning".
Address: Department of Biophysics, Huygens Gebouw, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands

The physics of machine learning

Keywords: Bayesian inference, learning and reasoning, stochastic control theory, neural networks, statistical physics

One of the marked differences between computers and animals is the ability of the latter to learn and flexibly adapt to changing situations. Whereas computers need to be programmed with provisions for all possible future circumstances, the brain adapts its 'program' when needed, striking a remarkable balance between flexibility to adapt on the one hand and persistence by re-using pre-learned facts and skills on the other. This is commonly referred to as intelligent behavior. Particular examples of intelligence are pattern recognition, learning and memory, reasoning, planning and motor control.

Due to the essential roles that noise and uncertainty play in perception and learning, a useful way to model intelligence is to use probability models. In the mid 90s, the fields of analog and digital computing as separate approaches to model intelligence, have begun to merge using the idea of Bayesian inference: One can generalize the logic of digital computation to a probabilistic calculus, embodied in a so-called graphical model. Similarly, one can generalize dynamical systems to stochastic dynamical systems that allow for a probabilistic description in terms of a Markov process. The Bayesian paradigm has greatly helped to integrate different schools of thought in particular in the field of artificial intelligence and machine learning but also provides a computational paradigm for neuroscience.

My research is dedicated to the design of efficient and novel computational methods for Bayesian inference and stochastic control theory using ideas and methods from statistical physics. These novel methods are used by me and by others in artificial intelligence research and computational models of brain function.

Bayesian Inference

Bayesian models are probability models and the typical computation, whether in the context of a complex data analysis problem or in a stochastic neural network, is to compute an expectation value, which is referred to as Bayesian inference. Bayesian inference is intractable, which means that computation time and memory use scale exponentially with the problem size. However, many methods exist to compute these quantities approximately. Most of these methods origin from statistical physics, such as the mean field method, belief propagation or Monte Carlo sampling. Application of these methods to machine learning problems is challenging and an active field of research to which I have made several contributions. Current projects focus on the application of these ideas in concrete problems:

Control theory

Control theory is a theory from engineering that gives a formal description of how a system, such as a robot or animal, can move from a current state to a future state at minimal cost, where cost can mean time spent, or energy spent or any other quantity. Control theory is used traditionally to control industrial plants, airplanes or missiles, but is also the natural framework to model intelligent behavior in animals or robots. The mathematical formulation of deterministic control theory is very similar to classical mechanics. In fact, classical mechanics can be viewed as a special case of control theory. Stochastic control theory uses the language of stochastic differential equations. For a certain class of stochastic control problems, the solution is described by a linear partial differential equation that can be solved formally as a path integral. This so-called path integral control method provides a deep link between control, inference and statistical physics. This statistical physics view of control theory shows that qualitative different control solutions exist for different noise levels separated by phase transitions. The control solutions can be computed using efficient approximate inference methods such as Monte Carlo sampling or deterministic approximation methods. The path integral control theory is successfully being used by leading research groups in robotics world wide. For more information see the path integral control theory page.

Computational neuroscience

A line of research that was started in 2000 and is still continued, is on the effect that short-term synaptic plasticity has on memory storage. The common understanding of long term memory is that it is stored in the synaptic connections between neurons in such a way that memory retrieval occurs as the relaxation of the neural activity to a constant spiking pattern, that represents the memory. This idea was put forward by Hopfield (1982) and others as the attractor neural network. Synaptic dynamics challenges this mechanism, since persistent pre-synaptic activity typically weakens the synaptic strength. The inclusion of short-term synaptic plasticity in an attractor neural network make memories metastable states that rapidly switch from one state to the next, depending on the sensory context. This work provides some insights on the puzzle how the brain, viewed as a dynamical system, is able to build stable representations of the world and at the same time is capable to effortlessly switch between them (with Joaquin Torres, University of Granada). We recently addressed the question how the path integral control computation can be implemented in stochastic neural networks. We demonstrated that the samples generated by such networks provide the data to learn a feed-back controller. Using this approach we have demonstrated to control a stochastic inverted pendulum (Thalmeier et al. 2016).

Quantum Machine Learning

Current successes in machine learning has ignited interesting new connections between machine learning and quantum physics, loosely referred to as quantum machine learning. Quantum annealing has been successfully applied to optimisation problems that arise in machine learning. Machine learning methods also find useful applications in quantum physics, such as characterizing the ground state of a quantum Hamiltonian or to learn different phases of matter. Since 2018, I am interested in how the quantum formalism can be used to advance machine learning. The objective is two-fold. One is to exploit quantum properties, such as entanglement, in classical data analysis. The second is to accellerate learning by implementing such models on quantum hardware.

Here is a recent paper: QBM Paper

Here is a recent talk:


Bayesian methods have a big potential for immediate application in areas outside science. There is a long-standing and quite unique tradition in the SNN group to build such application together with her spin-off companies Smart Research and Promedas. Here are a few examples:

Genetic inference

We have applied an advanced approximate inference method (the Cluster Variation Method) to construct haplotypes in complex pedigrees. The method was shown to outperform the state-of-the-art Monte Carlo sampling approach on a subset of problems. The software is publicly available. Contact Kees Albers for details caa at sanger dot ac dot uk.
Aladin is a software tool for performing efficient linkage analysis of a small number of distantly-related individuals. It estimates multipoint IBD probabilities and parametric LOD scores. Contact Kees Albers for details caa at sanger dot ac dot uk.

Oil exploration

For Shell, we built a petrophysical expert system. It estimates the type of soil and the probability that it contains oil, gas or other valuable minerals, based on drilling measurements. The system is based on a Bayesian network where the probability computation is done using a Monte Carlo sampling method. See Smart Research for further details and other products.

Victim identification

For the Netherlands Forensic Institute, we are building a victim identification system by matching of their DNA profiles against the Pedigrees of Relatives from Missing Person's DNA profiles in large databases, using a Bayesian network. See Bonaparte for further details.


We have built the world largest and most up-to-date medical expert system for diagnostic advice in internal medicine. The system is being commercialized by Promedas bv. The system is since end 2008 operational at the Utrecht academic hospital. See Promedas for further details.

Wine and food

We have built a system that selects the most appropriate wines to combine with your food Wine wine wine.


Inleiding Machine Learning BA NWI physics and math
Statistical Machine Learning MA NWI computer science and FSS AI
Advanced computational Neuroscience MA NWI physics and math and MA Donders research
Machine Learning MA NWI physics and math and MA Donders research
Advanced machine Learning MA NWI physics and math and MA Donders research

Short course on control theory, ACNS
Short course on machine learning, Pompeu Fabra spring 2003
Short course on control theory, Madrid fall 2010
Short course on control theory, UCL 2011
Short course on control theory, Madrid 2012
Tutorial ICTP Summer school Machine Learning, Trieste 2012
Short course on control theory, Madrid 2013
Tutorial ICTP Spring College on Physics of Complex systems, Trieste May-June 2013
Short course on control theory, Madrid 2014
Information, Physics, and Computation MA 2014

Introduction to Biophysics BA (discontinued)
Neural networks and Information theory BA (discontinued, content moved to Inleiding Machine Learning BA from 2012-2013)
Neurophysics BA (discontinued, content moved to Computational Neuroscience MA from 2013-2014)
Neurophysics MA (discontinued)
Computational Physics MA (discontinued)

Master Projects

Quantum machine learning

There is an exciting possibility to use a quantum mechanical wave function to represent a probability distribution. While classically the probability distribution p(x) is computed for each x separately, the quantum physics computes all 'compoonents' of the wave function simulatenously and in parallel. This implies that the computation of statistics (means, correlations) of high dimensional distribution, which requires exponentially long computation times using classical machines, could be computed in constant time on a quantum device. My recent work focusses on learning such quantum systems. The learning step requires the estimation of the above statistics and is done classically using Monte Carlo sampling. The long term aim is to replace this step by a quantum computer. The use of the quantum formalism for learning also yields novel quantum statistics for purely classical data analysis. These statistics signal entanglement in classical data. The research focuses on 1) developing fast approximate inference methods for quantum learning 2) data analysis using quantum statistics.

Sparse regression with the Garrote

Standard learning problems are to explain a dependent variable ('the output') in terms of independent variables ('the inputs'). In many learning problems, the number of input variables is large compared to the number of available data samples. Examples are found in genetics, neuro imaging and in general in many pattern recognition problems. In order to obtain a reasonable solution in these cases, the problem needs to be regularized, typically by adding a constraint that enforces a solution with small norm. In addition often a sparse solution is desired, which explains the output in terms of a (small) subset of the input variables. The Lasso method is a sparse regression method that uses an L1 norm as regularizer. The Lasso is very fast and can be applied to very large problems. However, the method suffers from 'shrinkage' which means that in certain cases the wrong inputs are identified. Ideally, one would use a regularizes which penalizes the number of inputs rather than their strength. This is achieved using the so-called L0 regularizer. However, to find the solution in this case is significantly more difficult. Examples of approaches are Monte Carlo methods or the variational garrote. All sparse methods suffer from strongly correlated inputs. Examples are the spatial correlations between nearby genetic measurements, or pixels in images. In this project, the student will extend the variational garrote to take these correlations into account and to demonstrate the improved performance on neuro-imaging or genetic data.

Data analyis for sustainable energy consumption

In collaboration with NRLytics, a young start-up in the energy sector, this project aims to use machine learning methods to analyse and optimize energy consumption. See Project description (in Dutch)

Contact information

SNN Machine Learning
Radboud University
Huygensgebouw 00.829
Heyendaalseweg 135
NL 6525 AJ Nijmegen
The Netherlands
+31 24 3614241 (phone)

Recent meetings organized

NIPS Workshop Probabilistic optimal control, Whistler 2009
SNN Symposium Intelligent Machines, Nijmegen 2010
School on large scale problems in machine learning and workshop on common concepts in machine learning and statistical physics, ICTP Trieste 2012
Workshop on the statistical physics of inference and control theory, Granada 2012 website and videolectures
NIPS 2013 Workshop Planning with Information Constraints for control, reinforcement learning, computational neuroscience, robotics and games
Intelligent Machines 2015


Foundation for Neural Networks (SNN)
Visiting professor at Gatsby Computational Neuroscience Unit, University College London

Current group members

Wim Wiegerinck is senior researcher and is working on approximate inference, genetic inference and various applications and is associate director of Smart Research bv
Giel van Bergen is a PhD student on the GenoMiX (with Kees Albers) project. He works on the application of Bayesian learning methods for genetics and optimization of animal breeding.
Willem Burgers is senior program developer for Smart Research bv.
Eduardo Dominguez is a postdoc working on approximate inference for quantum machine learning (start 2/2019).
Roeland Wiersema is a master student working on the quantum perceptron
Alex Kolmus is a master student working on a nano scale realisation of a Hopfield networks (with Alex Khajetoorians and Misha Katsnelson)
Manu Compen is a master student working on efficient learning methods for the quantum Boltzmann Machine
Jordi Riemens is a master student working on risk sensitive reinforcement learning
Yannick Lingelman is a phd student working on sensori motor control for autonomous driving (start 4/2019)

Former group members

Tom Heskes (Radboud University Nijmegen) was PhD student and postdoc on online learning.
Martijn Leisink (D66) was PhD student and postdoc on approximate inference
Taylan Cemgil (Bogazici University, Turkey) was PhD student on time-series modeling of music
Joris Mooij was PhD student on approximate inference.
Kees Albers was PhD student and postdoc on approximate inference methods for genetic linkage analysis. Kees was 4 years at Sanger Institute, Cambridge UK and is since 2012 at Human Genetics in Nijmegen.
Bram Kasteel was Bachelor student on the topic of multi-agent control
Stijn Tonk was Master student on the topic of multi-agent control
Ender Akay was programmer for Smart Research bv and Promedas bv
Gulliver de Boer was Bachelor student on the topic of multi-agent control applied to poker
Max Bakker was a Bachelor student on the topic of multi-agent systems
Ben Ruijl was a Bachelor student on the topic of multi-agent systems
Henk Griffioen was Master student on the topic of genetic association studies
Bart van den broek was PhD student on the topic of stochastic optimal control theory
Mohammad Azar was PhD student on the topic of reinforcement learning, now at Carnegie Mellon University
Patrick Lessmann was PhD student on the topic of stochastic optimal control in the CompLACS (EU FP7) project.
Elena Zavgorodnyaya was Master student on the topic of Brain Computer Interfaces.
Martin Mittag was a master student on the topic of stochastic optimal control theory with neural networks
Dick van den Broek was a master physics student on the topic of multi-agent systems
Bram Kasteel was a master physics student on the topic of stochastic optimal control theory
Christiaan Schoenaker was a master physics student on the topic of Super Modeling by combining imperfect models (SUMO)
Jonas Ahrendt was a Artificial Intelligence student on the topic of genetic pedigrees and Bonaparte
Joris Bukala was a bachelor physics student on the topic of Monte Carlo methods
Gulliver de Boer was a master physics student on the topic of genetic linkage analysis with Gaussian Process Regression and implementation on GPUs
Vicenç Gómez was postdoc on approximate inference and stochastic optimal control in the CompLACS (EU FP7) project, now at Universidad Pompeu Fabra in Barcelona
Kevin Sharp was a postdoc on a project to develop Bayesian Gaussian process methodes for genetic association studies, now at Oxford University
Joris Bierkens was postdoc on the topic of stochastic optimal control in the CompLACS (EU FP7) project, now at Warwick University
Takamitsu Matsubara is assistant professor of robotics at the Nara Institue of Science and Technology on sabatical leave in our group in 2013
Alberto Llera was PhD student on the topic of Brain Computer Interfaces, now postdoc with Christian Beckman at the Donders Center for Imaging
Satoshi Satoh is assistant professor at the faculty of engineering of Hiroshima University in Japan. He visited in 2011-2012 to generalize the path integral control method and to apply this method to concrete problems in control and robotics.
Sep Thijssen was a PhD student funded by Thales Nederland and on the Complacs project, working on application of stochastic optimal control methods for multi-agent systems. See here his very readable PhD Thesis.
Han Nauta was Master student working on path integral control problems
Hans Ruiz was a PhD student on the NETT project. He works on the application of stochastic optimal control methods in neuroscience for multi-agent systems
Dominik Thalmeier was a PhD student on the NETT project. He works on the application of stochastic optimal control methods in neuroscience for multi-agent systems
Silvia Menchon is assistant professor at the University of Cordoba (Argentina), visiting in 2015-2016 funded by the Radboud Excellence Initiative.

Externally funded projects

BrainGain (Smart mix) (ended)
Genetic association study using machine learning methods (Donders internal round) (ended)
Brain imaging, genetics and psychiatry using machine learning methods (NWO Cognition) (ended)
Multi-agent systems (with Thales D-Cis lab) (ended)
Bovinose (Smart Research, EU FP7) (ended)
CompLACS (EU FP7) (ended)
SUMO (EU FP7) (ended)
NETT (ended)
Genomix. Using neural networks to improve animal breeding (with U Wageningen, funded by STW)
Decentralized UAV control (with TU Delft Micro Air Vehicle laboratory, funded by NWO)
Learning and control of next generation deep neural technologies (with Riccardo Zecchina at Bocconi University, funded by ONR)
Quantum Learning (funded by NWA)


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