Abstract
Adaptive estimation methods based on general Kalman filter are powerful tools to investigate brain networks dynamics given the non-stationary nature of neural signals. These methods rely on two parameters, the model order p and adaptation constant c, which determine the resolution and smoothness of the time-varying multivariate autoregressive estimates. A sub-optimal filtering may present consistent biases in the frequency domain and temporal distortions, leading to fallacious interpretations. Thus, the performance of these methods heavily depends on the accurate choice of these two parameters in the filter design. In this work, we sought to define an objective criterion for the optimal choice of these parameters. Since residual- and information-based criteria are not guaranteed to reach an absolute minimum, we propose to study the partial derivatives of these functions to guide the choice of p and c. To validate the performance of our method, we used a dataset of human visual evoked potentials during face perception where the generation and propagation of information in the brain is well understood and a set of simulated data where the ground truth is available.
Highlights
In the field of neuroscience, the interest in studying the dynamical causal interactions that characterize rest- or taskrelated brain networks has led to a remarkable increase in the application of adaptive estimation algorithms
While adaptive filtering allows dealing with time-varying multivariate timeseries, the interpretation and test of direct causal influences strictly depends upon the optimal choice of parameters in the filter settings
In time-varying multivariate autoregressive models based on the general Kalman filter [4], these two aspects need to be taken into account as a mandatory step during the filter design: a suboptimal filter that is unable to track the true dynamics of a system can increase the risk of wrong causality inference
Summary
In the field of neuroscience, the interest in studying the dynamical causal interactions that characterize rest- or taskrelated brain networks has led to a remarkable increase in the application of adaptive estimation algorithms. In time-varying multivariate autoregressive (tv-MVAR) models based on the general Kalman filter [4], these two aspects need to be taken into account as a mandatory step during the filter design: a suboptimal filter that is unable to track the true dynamics of a system can increase the risk of wrong causality inference. For this reason, it is imperative to rely on objective criteria for the selection of the two key Kalman parameters that determine the structure and speed of the estimated causal influences. The model order & indicates the number of lags to be considered during modeling, and the adaptation constant ' is the tuning parameter that controls the tracking speed and smoothness of the tv-MVAR estimates [5] [6]
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