NETADIS Workshop on Modelling and Inference for Dynamics on Complex Interaction Networks: Joining Up Machine Learning and Statistical Physics, Montréal 2015

Inference and learning on large graphical models, i.e. large systems of simple probabilistic units linked by a complex network of interactions, is a classical topic in machine learning. Such systems are also an active research topic in the field of statistical physics.

The main interaction between statistical physics and machine learning has so far been in the area of analysing data sets without explicit temporal structure. Here methods of equilibrium statistical physics, developed for studying Boltzmann distributions on networks of nodes with e.g. pairwise interactions, are closely related to graphical model inference techniques; accordingly there has been much cross-fertilization leading to both conceptual insights and more efficient algorithms. Models can be learned from recorded experimental or other empirical data, but even when samples come from e.g. a time series this aspect of the data is typically ignored.

More recently, interest has shifted towards dynamical models. This shift has occurred for two main reasons:

• Most of the interesting systems for which statistical analysis techniques are required, e.g. networks of biological neurons, gene regulatory networks, protein-protein interaction networks, stock markets, exhibit very rich temporal or spatiotemporal dynamics; if this is ignored by focusing on stationary distributions alone this can lead to the loss of a significant amount of interesting information and possibly even qualitatively wrong conclusions.
• Current technological breakthroughs in collecting data from the complex systems referred to above are yielding ever increasing temporal resolution. This in turn allows in depth analyses of the fundamental temporal aspects of the function of the system, if combined with strong theoretical methods. It is widely accepted that these dynamical aspects are crucial for understanding the function of biological and financial systems, warranting the development of techniques for studying them.

In the past, the fields of machine learning and statistical physics have cross-fertilised each other significantly. E.g. the establishment of the relation between loopy belief propagation, message passing algorithms and the Bethe free energy formulation has stimulated a large amount of research in approximation techniques for inference and the corresponding equilibrium analysis of disordered systems in statistical physics.

It is the goal of the proposed workshop to bring together researchers from the fields of machine learning and statistical physics in order to discuss the new challenges originating from dynamical data. Such data are modeled using a variety of approaches such as dynamic belief networks, continuous time analogues of these – as often used for disordered spin systems in statistical physics –, coupled stochastic differential equations for continuous random variables etc. The workshop provides a forum for exploring possible synergies between the inference and learning approaches developed for the various models. The experience from joint advances in the equilibrium domain suggests that there is much unexplored scope for progress on dynamical data.

Possible topics to be addressed will be:

Inference on state dynamics:

• efficient approximation of dynamics on a given network, filtering, smoothing
• inference with hidden nodes
• existing methods including dynamical belief propagation & expectation propagation, variational approximations, mean-field and Plefka approximations; relations between these, advantages, drawbacks
• alternative approaches

Learning model/network parameters:

• with/without hidden nodes

Learning network structure:

• going beyond correlation information

Workshop website is available here.