Causal interpretation rules for encoding and decoding models in neuroimaging
Introduction
The question how neural activity gives rise to cognition is arguably one of the most interesting problems in neuroimaging (Hamann, 2001, Ward, 2003, Atlas et al., 2010). Neuroimaging studies per se, however, only provide insights into neuralcorrelates but not into neural causes of cognition (Ward, 2003, Rees et al., 2002). Nevertheless, causal terminology is often introduced in the interpretation of neuroimaging data. For instance, Hamann writes in a review on the neural mechanisms of emotional memory that “Hippocampal activity in this study was correlated with amygdala activity, supporting the view that the amygdala enhances explicit memory by modulating activity in the hippocampus” (Hamann, 2001), and Myers et al. note in a study on working memory that “we tested […] whether pre-stimulus alpha oscillations measured with electroencephalography (EEG) influence the encoding of items into working memory” (Myers et al., 2014) (our emphasis of causal terminology). The apparent contradiction between the prevalent use of causal terminology and the correlational nature of neuroimaging studies gives rise to the following question: which causal statements are and whichones are not supported by empirical evidence?
We argue that the answer to this question depends on the experimental setting and on the type of model used in the analysis of neuroimaging data. Neuroimaging distinguishes between encoding and decoding models (Naselaris et al., 2011), known in machine learning as generative and discriminative models (Jordan, 2002). Encoding models predict brain states, e. g. BOLD activity measured by fMRI or event-related potentials measured by EEG/MEG, from experimental conditions (Friston et al., 1994, Friston et al., 2003, David et al., 2006). Decoding models use machine learning algorithms to quantify the probability of an experimental condition given a brain state feature vector (Mitchell et al., 2004, Pereira et al., 2009). Several recent publications have addressed the interpretation of encoding and decoding models in neuroimaging, discussing topics such as potential confounds (Todd et al., 2013, Woolgar et al., 2014), the dimensionality of the neural code (Davis et al., 2014), and the relation of linear encoding and decoding models (Haufe et al., 2014). We contribute to this discussion by investigating, for each type of model, which causal statements are warranted and which ones are not supported by empirical evidence. Our investigation is based on the seminal work by Pearl (2000) and Spirtes et al. (2000) on causal inference (cf. (Ramsey et al., 2010, Grosse-Wentrup et al., 2011, Waldorp et al., 2011, Mumford and Ramsey, 2014) for applications of this framework in neuroimaging). We find that the distinction between encoding and decoding models is not sufficient for this investigation. It is further necessary to consider whether models work in causal or anti-causal direction, i. e. whether they model the effect of a cause or the cause of an effect (Schölkopf et al., 2012). To accommodate this distinction, we distinguish between stimulus- and response-based paradigms. We then provide causal interpretation rules for each combination of experimental setting (stimulus- or response-based) and model type (encoding or decoding). We find that when considering one model at a time, only encoding models in stimulus-based experimental paradigms support unambiguous causal statements. Also, we demonstrate that by comparing encoding and decoding models trained on the same data, experimentally testable conditions can be identified that provide further insights into causal structure. These results enable us to reinterpret previous work on the relation of encoding and decoding models in a causal framework (Todd et al., 2013, Woolgar et al., 2014, Haufe et al., 2014).
The empirical relevance of our theoretical results is illustrated on EEG data recorded during a visuo-motor learning task. We demonstrate that an encoding model allows us to determine EEG features that are effects of the instruction to rest or to plan a reaching movement, but does not enable us to distinguish between direct and indirect effects. By comparing relevant features in an encoding and a decoding model, we provide empirical evidence that sensorimotor μ- and/or occipital α-rhythms(8–14 Hz) are direct effects, while brain rhythms in higher cortical areas, including precuneus and anterior cingulate cortex, respond to the instruction to plan a reaching movement only as a result of the modulation by other cortical processes.
We note that while we have chosen to illustrate the empirical significance of our results on neuroimaging data, and specifically on EEG recordings, the provided causal interpretation rules apply to any encoding and decoding model trained on experimental data. This provides a guideline to researchers on how (not) to interpret encoding and decoding models when investigating the neural basis of cognition. A preliminary version of this work has been presented in Weichwald et al. (2014).
Section snippets
Methods
We begin this section by introducing the causal framework by Pearl (2000) and Spirtes et al. (2000) that our work is based on (Section 2.1) and demonstrate how it leads to testable predictions for the causal statements cited in the introduction (Section 2.2). We then introduce the distinction between causal and anti-causal encoding and decoding models (Section 2.3) and establish a connection between these models and causal inference (Section 2.4). This connection enables us to present the
Experimental Results
In this section, we demonstrate the empirical significance of our theoretical results on EEG data recorded during a visuo-motor learning task. We investigate the neural basis of planning a reaching movement by training encoding and decoding models on EEG bandpower features derived from trial-periods in which subjects have either been instructed to rest or to plan a reaching movement. We chose this stimulus-based setting to illustrate our theoretical results, as it admits less ambiguous causal
Discussion
The rules presented in this work provide a guideline to researchers which causal statements are and which ones are not supported by empirical data when analyzing encoding and decoding models. In particular, we argued that only encoding models instimulus-based paradigms support unambiguous causal statements. We demonstrated that further causal insights can be derived by combining encoding and decoding models, and illustrated the significance of this theoretical result on experimental data. While
Acknowledgments
The authors want to thank the reviewers for their encouraging, very concise and constructive feedback, which significantly improved this manuscript.
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