Abstract
Representational models specify how activity patterns in populations of neurons (or, more generally, in multivariate brain-activity measurements) relate to sensory stimuli, motor responses, or cognitive processes. In an experimental context, representational models can be defined as hypotheses about the distribution of activity profiles across experimental conditions. Currently, three different methods are being used to test such hypotheses: encoding analysis, pattern component modeling (PCM), and representational similarity analysis (RSA). Here we develop a common mathematical framework for understanding the relationship of these three methods, which share one core commonality: all three evaluate the second moment of the distribution of activity profiles, which determines the representational geometry, and thus how well any feature can be decoded from population activity. Using simulated data for three different experimental designs, we compare the power of the methods to adjudicate between competing representational models. PCM implements a likelihood-ratio test and therefore provides the most powerful test if its assumptions hold. However, the other two approaches—when conducted appropriately—can perform similarly. In encoding analysis, the linear model needs to be appropriately regularized, which effectively imposes a prior on the activity profiles. With such a prior, an encoding model specifies a well-defined distribution of activity profiles. In RSA, the unequal variances and statistical dependencies of the dissimilarity estimates need to be taken into account to reach near-optimal power in inference. The three methods render different aspects of the information explicit (e.g. single-response tuning in encoding analysis and population-response representational dissimilarity in RSA) and have specific advantages in terms of computational demands, ease of use, and extensibility. The three methods are properly construed as complementary components of a single data-analytical toolkit for understanding neural representations on the basis of multivariate brain-activity data.
Highlights
The measurement of brain activity is rapidly advancing in terms of spatial and temporal resolution, and in terms of the number of responses that can be measured simultaneously [1]
We show that the multivariate second moment of the activity profiles fully defines the representational geometry and with it all the information that can linearly or nonlinearly decoded
We focused on approaches that characterize the distribution of activity profiles by its second moment
Summary
The measurement of brain activity is rapidly advancing in terms of spatial and temporal resolution, and in terms of the number of responses that can be measured simultaneously [1]. Modern electrode arrays and calcium imaging enable the recording of hundreds of neurons in parallel. Electrophysiological signals that reflect summaries of the population activity can be recorded using both invasive (e.g. the local field potential, LFP) and non-invasive techniques (e.g. scalp electrophysiological measurements) at increasingly high spatial resolution. Modern functional magnetic resonance imaging (fMRI) enables us to measure hemodynamic activity in hundreds of thousands of voxels across the entire human brain at sub-millimeter resolution. In order to translate advances in brain-activity measurement into advances in computational theory [2], researchers increasingly seek to test representational models that capture both what information is represented in a population of neurons, and how it is represented. Knowing the content and format of representations provides strong constraints for computational models of brain information processing.
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