Abstract
Many biological systems perform computations on inputs that have very large dimensionality. Determining the relevant input combinations for a particular computation is often key to understanding its function. A common way to find the relevant input dimensions is to examine the difference in variance between the input distribution and the distribution of inputs associated with certain outputs. In systems neuroscience, the corresponding method is known as spike-triggered covariance (STC). This method has been highly successful in characterizing relevant input dimensions for neurons in a variety of sensory systems. So far, most studies used the STC method with weakly correlated Gaussian inputs. However, it is also important to use this method with inputs that have long range correlations typical of the natural sensory environment. In such cases, the stimulus covariance matrix has one (or more) outstanding eigenvalues that cannot be easily equalized because of sampling variability. Such outstanding modes interfere with analyses of statistical significance of candidate input dimensions that modulate neuronal outputs. In many cases, these modes obscure the significant dimensions. We show that the sensitivity of the STC method in the regime of strongly correlated inputs can be improved by an order of magnitude or more. This can be done by evaluating the significance of dimensions in the subspace orthogonal to the outstanding mode(s). Analyzing the responses of retinal ganglion cells probed with Gaussian noise, we find that taking into account outstanding modes is crucial for recovering relevant input dimensions for these neurons.
Highlights
How do neurons encode sensory stimuli? One of the primary difficulties in answering this long-standing problem is the fact that sensory stimuli have high dimensionality
We show that to use spike-triggered covariance (STC) with strongly correlated, 1=f -type inputs, one has to take into account that the covariance matrix of random samples from this distribution has a complex structure, with one or more outstanding modes
We use simulations on model neurons as well as an analysis of the responses of retinal neurons to demonstrate that taking the presence of these outstanding modes into account improves the sensitivity of the STC method by more than an order of magnitude
Summary
How do neurons encode sensory stimuli? One of the primary difficulties in answering this long-standing problem is the fact that sensory stimuli have high dimensionality. To detect the presence of certain features in the environment over a range of distances and light conditions, one needs to disambiguate the presence of this feature at a weak contrast from the presence of a similar, but different feature presented at a higher contrast This can only be achieved with nonlinear functions that depend on multiple input components, such as the presence of an edge of correct orientation and the absence of the edge orthogonal to it [1]. In support of these arguments, the responses of neurons in different sensory modalities are found to be sensitive to multiple input combinations. Finding either the linear input dimensions that modulate the spike probability (we will refer to these dimensions as relevant) or quadratic forms of inputs [14,15,16] is the focus of much of the current research in the field
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