EEG-GRAPH: A Factor-Graph-Based Model for Capturing Spatial, Temporal, and Observational Relationships in Electroencephalograms
This paper presents a probabilistic-graphical model that can be used to infer characteristics of instantaneous brain activity by jointly analyzing spatial and temporal dependencies observed in electroencephalograms (EEG). Specifically, we describe a factor-graph-based model with customized factor-functions defined based on domain knowledge, to infer pathologic brain activity with the goal of identifying seizure-generating brain regions in epilepsy patients. We utilize an inference technique based on the graph-cut algorithm to exactly solve graph inference in polynomial time. We validate the model by using clinically collected intracranial EEG data from 29 epilepsy patients to show that the model correctly identifies seizure-generating brain regions. Our results indicate that our model outperforms two conventional approaches used for seizure-onset localization (5-7% better AUC: 0.72, 0.67, 0.65) and that the proposed inference technique provides 3-10% gain in AUC (0.72, 0.62, 0.69) compared to sampling-based alternatives.
SUMMARY:
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The authors propose a probabilistic model and MAP inference for localizing seizure onset zones (SOZ) using intracranial EEG data.  The proposed model captures spatial correlations across EEG channels as well as temporal correlations within a channel.  The authors claim that modeling these correlations leads to improved predictions when compared to detection methods that ignore temporal and spatial dependency.
PROS:
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This is a fairly solid applications paper, well-written, well-motivated, and an interesting application.  
CONS:
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The proof of Prop. 1 is not totally clear, for example the energy in Eq. (4) includes a penalty for label disagreement across channels, which is absent in the the graph cut energy provided by the proof. The relationship between min-cut/max-flow and submodular pairwise energies is well established, and the authors should cite this literature (e.g. Kolmogorov and Zabih, PAMI 2004).  Note that the higher-order temporal consistency term can be decomposed into pairwise terms for every pair of temporal states.  It is unclear why this approach is not a valid one for showing optimality of min-cut and the authors should include an explanation.
What do the authors mean by "dynamic graph" (L:103)?  Also, the edge set $E_n$ is indexed by epoch, suggesting graph structure is adjusted over time.  It is not discussed anywhere how these edges are determined and whether they in fact change across epochs.
This estimate of SOZ probability is motivated in Eq. (5) as an MLE.  It isn't clear that (5) is a likelihood as it is not a function of the data, only the latent states.  The estimated probability of a location being an SOZ is given as an average over states across epochs, which is a valid estimator, and connections to MLE are unclear beyond that.
Generalizability claims of the approach (L:92-93) are weak.  The extent to which this is a general model is simply that the model incorporates spatio-temporal dependencies.  Specifying the factors encoding such dependencies in any factor graph will always require domain knowledge.
Some detailed comments:
  * Are there really no free parameters in the model to scale energy weights?  This seems surprising since the distance parameter in the spatial energy would need to be rescaled depending on the units used.
  * Authors claim no other work incorporates spatio-temporal EEG constraints but a recent paper suggests otherwise: Martinez-Vargas et al., "Improved localization of seizure onset zones using spatiotemporal constraints and time-varying source connectivity.", Frontiers in Neuroscience (2017).  Please cite relevant material.
  * Lines in plots of Fig. 3 are too thin and do not appear on a printed version