Deconstructing multivariate decoding for the study of brain function

Highlights

• We highlight two sources of confusion that affect the interpretation of multivariate decoding results.

• Confusion 1: The dual use of multivariate decoding for real-world predictions and interpretation in terms of brain function.

• Confusion 2: A mixture of statistical and conceptual frameworks of classical univariate analysis and multivariate decoding.

• We show six differences between univariate analysis and multivariate decoding and a different meaning of signal and noise.

• We use four illustrative examples to reveal these confusions and the assumptions of multivariate decoding for interpretation.

Abstract

Multivariate decoding methods were developed originally as tools to enable accurate predictions in real-world applications. The realization that these methods can also be employed to study brain function has led to their widespread adoption in the neurosciences. However, prior to the rise of multivariate decoding, the study of brain function was firmly embedded in a statistical philosophy grounded on univariate methods of data analysis. In this way, multivariate decoding for brain interpretation grew out of two established frameworks: multivariate decoding for predictions in real-world applications, and classical univariate analysis based on the study and interpretation of brain activation. We argue that this led to two confusions, one reflecting a mixture of multivariate decoding for prediction or interpretation, and the other a mixture of the conceptual and statistical philosophies underlying multivariate decoding and classical univariate analysis. Here we attempt to systematically disambiguate multivariate decoding for the study of brain function from the frameworks it grew out of. After elaborating these confusions and their consequences, we describe six, often unappreciated, differences between classical univariate analysis and multivariate decoding. We then focus on how the common interpretation of what is signal and noise changes in multivariate decoding. Finally, we use four examples to illustrate where these confusions may impact the interpretation of neuroimaging data. We conclude with a discussion of potential strategies to help resolve these confusions in interpreting multivariate decoding results, including the potential departure from multivariate decoding methods for the study of brain function.

Introduction

Multivariate decoding¹ has become a central method for the analysis of neuroscientific data. It is being employed commonly in fMRI (Haynes, 2015, Haynes and Rees, 2006, Norman et al., 2006, Tong and Pratte, 2012), but also neurophysiology in non-human primates (Quian Quiroga and Panzeri, 2009) and humans (Contini et al., 2017). The approach grew rapidly in popularity in the neuroimaging community when it became clear that it was not only useful for classification related to real-world applications such as brain-computer interfaces, but also for studying brain function. Now, in many domains classical univariate methods have been replaced by multivariate decoding, in part owing to the higher sensitivity afforded by these techniques (Haynes and Rees, 2006, Norman et al., 2006). In this way, multivariate decoding for brain interpretation grew out two established approaches: multivariate decoding for predictions in real-world applications, and classical univariate analysis for the study of brain function.

In this article, we argue that rather than being part of a consistent and independent statistical framework, multivariate decoding for brain interpretation often reflects a mixture of the philosophies it originated from (Fig. 1A), one activation-based and the other information-based. As a consequence, this mixture of philosophies creates a lot of potential for confusion in the interpretation of results derived from multivariate decoding methods. The aim of this article is to provide a systematic understanding of multivariate decoding for the study of brain function and the assumptions and limitations of this approach in the interpretation of multivariate decoding results.

First, we describe the two sources of confusion: i) the mixture of multivariate decoding for prediction and multivariate decoding for interpretation, and ii) the mixture of the statistical and conceptual philosophies underlying classical univariate analysis and multivariate decoding. Next, we illustrate six methodological and interpretational changes that – explicitly or implicitly – are adopted when shifting from classical univariate methods to multivariate decoding. This discussion is important, because it shows how multifaceted the differences between these approaches are and why they have been so difficult to characterize. Moving to a purely multivariate description of data, we then describe how the meaning of signal and noise is different in the statistical frameworks underlying classical univariate analysis and multivariate decoding. Finally, using four illustrative examples we demonstrate how the sources of confusion can affect the interpretation of multivariate decoding results.

Throughout the article, we use functional MRI as an example, where multivariate data are multiple voxels measured at different time points, and where predicted variables are experimental conditions.² However, this discussion applies equally to other modalities (e.g. structural MRI, MEG/EEG, connectivity measures) whenever multivariate decoding is used as a method of data analysis. In addition, we focus our discussion of multivariate decoding on multivariate classification, although our arguments may apply equally to multivariate regression in a decoding setting.