A Gaussian mixture model based cost function for parameter estimation of chaotic biological systems

• A new cost function is proposed for parameter estimation of chaotic systems.
• Attractor of real system is modeled by a Gaussian mixture model in state space.
• Cost function defined based on likelihood score which comes from GMM computations.
• The method is applied in parameter estimation of chaotic biological systems.
• Two important biological systems, neuron and cardiac pacemaker, are investigated.

As we know, many biological systems such as neurons or the heart can exhibit chaotic behavior. Conventional methods for parameter estimation in models of these systems have some limitations caused by sensitivity to initial conditions. In this paper, a novel cost function is proposed to overcome those limitations by building a statistical model on the distribution of the real system attractor in state space. This cost function is defined by the use of a likelihood score in a Gaussian mixture model (GMM) which is fitted to the observed attractor generated by the real system. Using that learned GMM, a similarity score can be defined by the computed likelihood score of the model time series. We have applied the proposed method to the parameter estimation of two important biological systems, a neuron and a cardiac pacemaker, which show chaotic behavior. Some simulated experiments are given to verify the usefulness of the proposed approach in clean and noisy conditions. The results show the adequacy of the proposed cost function.