How to recognise whether an observed person walks or runs? We consider a dynamic environment where observations (e.g. the posture of a person) are caused by different dynamic processes (walking or running) which are active one at a time and which may transition from one to another at any time. For this setup, switching dynamic models have been suggested previously, mostly, for linear and nonlinear dynamics in discrete time. Motivated by basic principles of computations in the brain (dynamic, internal models) we suggest a model for switching nonlinear differential equations. The switching process in the model is implemented by a Hopfield network and we use parametric dynamic movement primitives to represent arbitrary rhythmic motions. The model generates observed dynamics by linearly interpolating the primitives weighted by the switching variables and it is constructed such that standard filtering algorithms can be applied. In two experiments with synthetic planar motion and a human motion capture data set we show that inference with the unscented Kalman filter can successfully discriminate several dynamic processes online.
In @cite_22 , the authors derive a smoothing algorithm based on variational inference for an Ornstein-Uhlenbeck (OU) process which is switched by a random telegraph process. Thus, this model can only switch between two constant drifts. Similarly, @cite_0 @cite_20 propose Markov chain Monte Carlo inference for a switched OU process where the number of different parameter sets as well as the parameter values are automatically determined from the data. However, these parameters are limited to the constant drift and diffusion parameters of the OU process which cannot implement generic nonlinear dynamics. In contrast to these models, we approximate a change point process using our continuous-valued switching dynamics which allows us to maintain a coherent continuous framework and apply standard filtering algorithms.
@cite_0 @cite_22 @cite_20
2098657931 2109462896 2221871399
We consider the problem of Bayesian inference for continuous-time multi-stable stochastic systems which can change both their diffusion and drift parameters at discrete times. We propose exact inference and sampling methodologies for two specific cases where the discontinuous dynamics is given by a Poisson process and a two-state Markovian switch. We test the methodology on simulated data, and apply it to two real data sets in finance and systems biology. Our experimental results show that the approach leads to valid inferences and non-trivial insights. We present a novel approach to inference in conditionally Gaussian continuous time stochastic processes, where the latent process is a Markovian jump process. We first consider the case of jump-diffusion processes, where the drift of a linear stochastic differential equation can jump at arbitrary time points. We derive partial differential equations for exact inference and present a very efficient mean field approximation. By introducing a novel lower bound on the free energy, we then generalise our approach to Gaussian processes with arbitrary covariance, such as the non-Markovian RBF covariance. We present results on both simulated and real data, showing that the approach is very accurate in capturing latent dynamics and can be useful in a number of real data modelling tasks. We study a model of a stochastic process with unobserved parameters which suddenly change at random times. The possible parameter values are assumed to be from a finite but unknown set. Using a Chinese restaurant process prior over parameters we develop an efficient MCMC procedure for Bayesian inference. We demonstrate the significance of our approach with an application to systems biology data.