10 research outputs found
Mitigating the effects of measurement noise on Granger causality
Computing Granger causal relations among bivariate experimentally observed
time series has received increasing attention over the past few years. Such
causal relations, if correctly estimated, can yield significant insights into
the dynamical organization of the system being investigated. Since experimental
measurements are inevitably contaminated by noise, it is thus important to
understand the effects of such noise on Granger causality estimation. The first
goal of this paper is to provide an analytical and numerical analysis of this
problem. Specifically, we show that, due to noise contamination, (1) spurious
causality between two measured variables can arise and (2) true causality can
be suppressed. The second goal of the paper is to provide a denoising strategy
to mitigate this problem. Specifically, we propose a denoising algorithm based
on the combined use of the Kalman filter theory and the
Expectation-Maximization (EM) algorithm. Numerical examples are used to
demonstrate the effectiveness of the denoising approach.Comment: 16 pages, 7 figure
Effect of measurement noise on Granger causality
Most of the signals recorded in experiments are inevitably contaminated by measurement noise. Hence, it is important to understand the effect of such noise on estimating causal relations between such signals. A primary tool for estimating causality is Granger causality. Granger causality can be computed by modeling the signal using a bivariate autoregressive (AR) process. In this paper, we greatly extend the previous analysis of the effect of noise by considering a bivariate AR process of general order p. From this analysis, we analytically obtain the dependence of Granger causality on various noise-dependent system parameters. In particular, we show that measurement noise can lead to spurious Granger causality and can suppress true Granger causality. These results are verified numerically. Finally, we show how true causality can be recovered numerically using the Kalman expectation maximization algorithm
Denoising neural data with state-space smoothing: method and application
Neural data are inevitably contaminated by noise. When such noisy data are subjected to statistical analysis, misleading conclusions can be reached. Here we attempt to address this problem by applying a state-space smoothing method, based on the combined use of the Kalman filter theory and the Expectation-Maximization algorithm, to denoise two datasets of local field potentials recorded from monkeys performing a visuomotor task. For the first dataset, it was found that the analysis of the high gamma band (60-90 Hz) neural activity in the prefrontal cortex is highly susceptible to the effect of noise, and denoising leads to markedly improved results that were physiologically interpretable. For the second dataset, Granger causality between primary motor and primary somatosensory cortices was not consistent across two monkeys and the effect of noise was suspected. After denoising, the discrepancy between the two subjects was significantly reduced
Denoising neural data with state-space smoothing: Method and application
Neural data are inevitably contaminated by noise. When such noisy data are subjected to statistical analysis, misleading conclusions can be reached. Here we attempt to address this problem by applying a state-space smoothing method, based on the combined use of the Kalman filter theory and the Expectation–Maximization algorithm, to denoise two datasets of local field potentials recorded from monkeys performing a visuomotor task. For the first dataset, it was found that the analysis of the high gamma band (60–90 Hz) neural activity in the prefrontal cortex is highly susceptible to the effect of noise, and denoising leads to markedly improved results that were physiologically interpretable. For the second dataset, Granger causality between primary motor and primary somatosensory cortices was not consistent across two monkeys and the effect of noise was suspected. After denoising, the discrepancy between the two subjects was significantly reduced
Fast robust pattern classification algorithms for real time neuro-motor prosthetic applications
In this paper, we give a brief review of pattern classification algorithms based on discriminant analysis. We then apply these algorithms to classify movement direction based on multivariate local field potentials recorded from a microelectrode array in the primary motor cortex of a monkey performing a reaching task. We obtain prediction accuracies between 55% and 90% using different methods which are significantly above the chance level of 12.5%