Abstract
The signal transformations that take place in high-level sensory regions of the brain remain enigmatic because of the many nonlinear transformations that separate responses of these neurons from the input stimuli. One would like to have dimensionality reduction methods that can describe responses of such neurons in terms of operations on a large but still manageable set of relevant input features. A number of methods have been developed for this purpose, but often these methods rely on the expansion of the input space to capture as many relevant stimulus components as statistically possible. This expansion leads to a lower effective sampling thereby reducing the accuracy of the estimated components. Alternatively, so-called low-rank methods explicitly search for a small number of components in the hope of achieving higher estimation accuracy. Even with these methods, however, noise in the neural responses can force the models to estimate more components than necessary, again reducing the methods' accuracy. Here we describe how a flexible regularization procedure, together with an explicit rank constraint, can strongly improve the estimation accuracy compared to previous methods suitable for characterizing neural responses to natural stimuli. Applying the proposed low-rank method to responses of auditory neurons in the songbird brain, we find multiple relevant components making up the receptive field for each neuron and characterize their computations in terms of logical OR and AND computations. The results highlight potential differences in how invariances are constructed in visual and auditory systems.