Disentangling signal and noise in neural responses through generative modeling

Measurements of neural responses to identically repeated experimental events often exhibit large amounts of variability. This noise is distinct from signal, operationally defined as the average expected response across repeated trials for each given event. Accurately distinguishing signal from noise is important, as each is a target that is worthy of study (many believe noise reflects important aspects of brain function) and it is important not to confuse one for the other. Here, we describe a principled modeling approach in which response measurements are explicitly modeled as the sum of samples from multivariate signal and noise distributions. In our proposed method—termed Generative Modeling of Signal and Noise (GSN)—the signal distribution is estimated by subtracting the estimated noise distribution from the estimated data distribution. Importantly, GSN improves estimates of the signal distribution, but does not provide improved estimates of responses to individual events. We validate GSN using ground-truth simulations and show that it compares favorably with related methods. We also demonstrate the application of GSN to empirical fMRI data to illustrate a simple consequence of GSN: by disentangling signal and noise components in neural responses, GSN denoises principal components analysis and improves estimates of dimensionality. We end by discussing other situations that may benefit from GSN’s characterization of signal and noise, such as estimation of noise ceilings for computational models of neural activity. A code toolbox for GSN is provided with both MATLAB and Python implementations.Author summary: The neural response to a given experimental manipulation typically exhibits high degree of variability from trial to trial. This ‘noise’ is ubiquitous and may play an important role in brain computation (though its precise role is not yet clear). At the same time, neuroscientists are also interested in studying what is consistent across trials, known as the ‘signal’. In this work, we tackle the challenge of separating signal and noise in neural response measurements. We introduce a statistical framework, termed Generative Modeling of Signal and Noise (GSN), in which the data are modeled as a sum of samples from an underlying signal distribution and underlying noise distribution. After providing an algorithm to estimate the parameters of this model, we show how GSN delivers benefits such as denoising the results of principal components analysis and improving estimates of dimensionality. To make it easy to apply GSN, we also provide a code toolbox implementing the method.