A Bayesian model for local smoothing in kernel density estimation
Statistics and Computing
Multivariate locally adaptive density estimation
Computational Statistics & Data Analysis
Estimating a state-space model from point process observations
Neural Computation
Differences in spiking patterns among cortical neurons
Neural Computation
A Method for Selecting the Bin Size of a Time Histogram
Neural Computation
Estimating instantaneous irregularity of neuronal firing
Neural Computation
Optimizing time histograms for non-poissonian spike trains
Neural Computation
Random bin for analyzing neuron spike trains
Computational Intelligence and Neuroscience - Special issue on Computational Intelligence in Biomedical Science and Engineering
Information transmission using non-poisson regular firing
Neural Computation
PL-Tree: an efficient indexing method for high-dimensional data
SSTD'13 Proceedings of the 13th international conference on Advances in Spatial and Temporal Databases
Firing-rate models capture essential response dynamics of LGN relay cells
Journal of Computational Neuroscience
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Kernel smoother and a time-histogram are classical tools for estimating an instantaneous rate of spike occurrences. We recently established a method for selecting the bin width of the time-histogram, based on the principle of minimizing the mean integrated square error (MISE) between the estimated rate and unknown underlying rate. Here we apply the same optimization principle to the kernel density estimation in selecting the width or "bandwidth" of the kernel, and further extend the algorithm to allow a variable bandwidth, in conformity with data. The variable kernel has the potential to accurately grasp non-stationary phenomena, such as abrupt changes in the firing rate, which we often encounter in neuroscience. In order to avoid possible overfitting that may take place due to excessive freedom, we introduced a stiffness constant for bandwidth variability. Our method automatically adjusts the stiffness constant, thereby adapting to the entire set of spike data. It is revealed that the classical kernel smoother may exhibit goodness-of-fit comparable to, or even better than, that of modern sophisticated rate estimation methods, provided that the bandwidth is selected properly for a given set of spike data, according to the optimization methods presented here.