Thesis defense Hans-Christian Ruiz (Donders series 329)
3 July 2018
Promotor: prof. dr. H. Kappen
Particle Smoothing and Latent Process Estimation in Neuroscience
Parameter estimation in time-series models is a challenging task, especially when a hidden process is involved. Then, the estimation of parameters within the Expectation-Maximization (EM) algorithm requires gradient estimates with respect to the posterior distribution over the latent process, which is in general intractable. There exist many different methods to approximate the posterior distribution, for instance Kalman-type methods and particle methods. The later involve sampling from the posterior distribution, which is very challenging and inefficient because most samples have zero contribution to the posterior estimates. In this thesis, we develop and apply an alternative method to sample adaptively from the joint posterior distribution. This method, called controlled particle smoothing, relies on the Path Integral theory to compute parameterized controllers that maximize the likelihood of the sampled processes. As a consequence, the number of effective samples contributing to the estimates increases, making our approach many orders of magnitude more efficient than the state-of-the-art methods. In addition, we apply this framework to address the causal connectivity estimation problem from fMRI time-series. First, we estimate the hidden neuronal activity from fMRI data obtained during a reaction time experiment. This is done without any assumption on the input to the brain region under consideration. We show that it is possible to estimate the stimulus and reaction timing from the inferred neuronal activity with an accuracy well below the typical BOLD time scale and even below the TR. Then, we combine our method with the EM-algorithm to infer causal connections from synthetic data using the standard biologically plausible model similar to Dynamic Causal Modelling. We show that our approach find precise points estimates of the directed connectivity structure. Moreover, our approach is robust against random initializations of the connectivity structure. In addition, we examine the effects that the neural time scale has on the BOLD signal and the connectivity estimates. We conclude, first, that faster time scales make the BOLD signal insensitive against changes in the connectivity and thus, more and better quality data is required. Second, assuming the wrong neuronal time scale biases the connectivity estimates dramatically such that any attempt in retrieving the causal structure fails completely.