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Abstract:
The representation of the nonlinear response properties of a neuron by a Wiener series expansion has enjoyed
a certain popularity in the past, but its application has been limited to rather low-dimensional and weakly
nonlinear systems due to the exponential growth of the number of terms that have to be estimated. A recently
developed estimation method [1] utilizes the kernel techniques widely used in the machine learning
community to implicitly represent the Wiener series as an element of an abstract dot product space. In contrast
to the classical estimation methods for the Wiener series, the estimation complexity of the implicit
representation is linear in the input dimensionality and independent of the degree of nonlinearity.
From the neural system identification point of view, the proposed estimation method has several advantages:
1. Due to the linear dependence of the estimation complexity on input dimensionality, system identification
can be also done for systems acting on high-dimensional inputs such as images or video sequences.
2. Compared to classical cross-correlation techniques (such as spike-triggered average or covariance
estimates), similar accuracies can be achieved with a considerably smaller amount of data.
3. The new technique does not need white noise as input, but works for arbitrary classes of input signals such
as, e.g., natural image patches.
4. Regularisation concepts from machine learning to identify systems with noise-contaminated output signals.
We present an application of the implicit Wiener series to find the low-dimensional stimulus subspace which
accounts for most of the neuron's activity. We approximate the second-order term of a full Wiener series
model with a set of parallel cascades consisting of a linear receptive field and a static nonlinearity. This type
of approximation is known as reduced set technique in machine learning. We compare our results on
simulated and physiological datasets to existing identification techniques in terms of prediction performance
and accuracy of the obtained subspaces.
