Elements of information theory
Elements of information theory
The nature of statistical learning theory
The nature of statistical learning theory
Exploiting generative models in discriminative classifiers
Proceedings of the 1998 conference on Advances in neural information processing systems II
Classes of kernels for machine learning: a statistics perspective
The Journal of Machine Learning Research
A tutorial on support vector regression
Statistics and Computing
Online SVR Training by Solving the Primal Optimization Problem
Journal of Signal Processing Systems
Improved similarity measures for small sets of spike trains
Neural Computation
Strictly positive-definite spike train kernels for point-process divergences
Neural Computation
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Inner-product operators, often referred to as kernels in statistical learning, define a mapping from some input space into a feature space. The focus of this letter is the construction of biologically motivated kernels for cortical activities. The kernels we derive, termed Spikernels, map spike count sequences into an abstract vector space in which we can perform various prediction tasks. We discuss in detail the derivation of Spikernels and describe an efficient algorithm for computing their value on any two sequences of neural population spike counts. We demonstrate the merits of our modeling approach by comparing the Spikernel to various standard kernels in the task of predicting hand movement velocities from cortical recordings. All of the kernels that we tested in our experiments outperform the standard scalar product used in linear regression, with the Spikernel consistently achieving the best performance.