MINDS - Research Overview

Modelling of stochastic time series. Stochastic time series, such as speech signals, texts, DNA or protein sequences, are standardly modelled using hidden Markov models (HMMs). A major drawback of HMMs is that the known learning algorithms for them are compuationally very expensive. An alternative approach was developed and explored at MINDS, called observable operator models (OOMs). The OOM formalism is based on modelling stochastic processes by sequences of linear operators and is in many respects similar to the formalism of quantum mechanics. OOMs are more expressive than HMMs, and they give rise to a novel class of learning algorithms which are computationally much cheaper than current HMM algorithms. More...

Modelling of nonlinear dynamical systems. Many nonlinear dynamical system are so complex that they cannot be reasonably described with analytical equation. Examples are brain systems, stock markets, cognitive systems, or mobile robots that maneuvre in rough terrains. Nonetheless one often wants to predict, filter, monitor or control such systems. The only resort are blackbox models: mathematical structures that are derived from empirical observations of the target system by a learning (aka system identification) method. We developed and explore a  method that relies on recurrent neural networks, called echo state networks (ESNs). ESNs give rise to a new class of constructive learning algorithms that are both very accurate and very fast. More...