Roman A Sandler1, Samuel A Deadwyler2, Robert E Hampson2, Dong Song3, Theodore W Berger3, Vasilis Z Marmarelis3. 1. Department of Biomedical Engineering, University of Southern California, Los Angeles, CA, USA. Electronic address: rsandler@usc.edu. 2. Department of Physiology & Pharmacology, Wake Forest School of Medicine, Winston-Salem, NC, USA. 3. Department of Biomedical Engineering, University of Southern California, Los Angeles, CA, USA.
Abstract
BACKGROUND: Neural information processing involves a series of nonlinear dynamical input/output transformations between the spike trains of neurons/neuronal ensembles. Understanding and quantifying these transformations is critical both for understanding neural physiology such as short-term potentiation and for developing cognitive neural prosthetics. NEW METHOD: A novel method for estimating Volterra kernels for systems with point-process inputs and outputs is developed based on elementary probability theory. These Probability Based Volterra (PBV) kernels essentially describe the probability of an output spike given q input spikes at various lags t1, t2, …, tq. RESULTS: The PBV kernels are used to estimate both synthetic systems where ground truth is available and data from the CA3 and CA1 regions rodent hippocampus. The PBV kernels give excellent predictive results in both cases. Furthermore, they are shown to be quite robust to noise and to have good convergence and overfitting properties. Through a slight modification, the PBV kernels are shown to also deal well with correlated point-process inputs. COMPARISON WITH EXISTING METHODS: The PBV kernels were compared with kernels estimated through least squares estimation (LSE) and through the Laguerre expansion technique (LET). The LSE kernels were shown to fair very poorly with real data due to the large amount of input noise. Although the LET kernels gave the best predictive results in all cases, they require prior parameter estimation. It was shown how the PBV and LET methods can be combined synergistically to maximize performance. CONCLUSIONS: The PBV kernels provide a novel and intuitive method of characterizing point-process input-output nonlinear systems.
BACKGROUND: Neural information processing involves a series of nonlinear dynamical input/output transformations between the spike trains of neurons/neuronal ensembles. Understanding and quantifying these transformations is critical both for understanding neural physiology such as short-term potentiation and for developing cognitive neural prosthetics. NEW METHOD: A novel method for estimating Volterra kernels for systems with point-process inputs and outputs is developed based on elementary probability theory. These Probability Based Volterra (PBV) kernels essentially describe the probability of an output spike given q input spikes at various lags t1, t2, …, tq. RESULTS: The PBV kernels are used to estimate both synthetic systems where ground truth is available and data from the CA3 and CA1 regions rodent hippocampus. The PBV kernels give excellent predictive results in both cases. Furthermore, they are shown to be quite robust to noise and to have good convergence and overfitting properties. Through a slight modification, the PBV kernels are shown to also deal well with correlated point-process inputs. COMPARISON WITH EXISTING METHODS: The PBV kernels were compared with kernels estimated through least squares estimation (LSE) and through the Laguerre expansion technique (LET). The LSE kernels were shown to fair very poorly with real data due to the large amount of input noise. Although the LET kernels gave the best predictive results in all cases, they require prior parameter estimation. It was shown how the PBV and LET methods can be combined synergistically to maximize performance. CONCLUSIONS: The PBV kernels provide a novel and intuitive method of characterizing point-process input-output nonlinear systems.
Authors: Robert E Hampson; Greg A Gerhardt; Vasilis Marmarelis; Dong Song; Ioan Opris; Lucas Santos; Theodore W Berger; Sam A Deadwyler Journal: J Neural Eng Date: 2012-09-13 Impact factor: 5.379
Authors: Vasilis Z Marmarelis; Dae C Shin; Dong Song; Robert E Hampson; Sam A Deadwyler; Theodore W Berger Journal: J Comput Neurosci Date: 2012-07-20 Impact factor: 1.621
Authors: Roman A Sandler; Dong Song; Robert E Hampson; Sam A Deadwyler; Theodore W Berger; Vasilis Z Marmarelis Journal: J Neural Eng Date: 2015-09-10 Impact factor: 5.379
Authors: Philippe G Schyns; Jiayu Zhan; Rachael E Jack; Robin A A Ince Journal: Philos Trans R Soc Lond B Biol Sci Date: 2020-04-06 Impact factor: 6.237
Authors: Roman A Sandler; Dustin Fetterhoff; Robert E Hampson; Sam A Deadwyler; Vasilis Z Marmarelis Journal: PLoS Comput Biol Date: 2017-07-07 Impact factor: 4.475