Paper:
Cross-Spectral Factor Analysis
In neuropsychiatric disorders such as schizophrenia or depression, there is often a disruption in the way that regions of the brain synchronize with one another. To facilitate understanding of network-level synchronization between brain regions, we introduce a novel model of multisite low-frequency neural recordings, such as local field potentials (LFPs) and electroencephalograms (EEGs). The proposed model, named Cross-Spectral Factor Analysis (CSFA), breaks the observed signal into factors defined by unique spatio-spectral properties. These properties are granted to the factors via a Gaussian process formulation in a multiple kernel learning framework. In this way, the LFP signals can be mapped to a lower dimensional space in a way that retains information of relevance to neuroscientists. Critically, the factors are interpretable. The proposed approach empirically allows similar performance in classifying mouse genotype and behavioral context when compared to commonly used approaches that lack the interpretability of CSFA. We also introduce a semi-supervised approach, termed discriminative CSFA (dCSFA). CSFA and dCSFA provide useful tools for understanding neural dynamics, particularly by aiding in the design of causal follow-up experiments.

Review:
The authors propose a factor analysis method called CSFA for modelling LFP data, which is a generative model with the specific assumption that factors, called Elecotomes, are sampled from Gaussian processes with cross-spectral mixture kernel. The generative model is straightforward use of CSM, and the estimation is apparently also a known form (resilient back prop; I never heard of it before). I do like the dCSFA formulation. The proposed method focuses on spectral power and phase relationship across regions, and is claimed to bring both better interpretability and higher predictive power. They also extend CSFA to be discriminative to side information such as genetic and behavioral data by incorporating logistic loss (or the likes of it). The authors applied the proposed method to synthetic and real mouse data, and compared it with PCA.
== issues ==
=== Page limit ===
This paper is 10 pages. (references start at page 8 and goes to page 10)
=== Section 2.1 ===
The authors claim that reduced dimensionality increases the power of hypothesis testing. In general, this is not true. Any dimensionality-reduction decision is made implicitly upon a hypothesis of dimensionality. The hypothesis testing performed after reduction is conditional on it, making the problem more subtle than presented.
=== Section 2.5 ===
lambda in Eq(7) is chosen based on cross-validation of the predictive accuracy. Why was it not chosen by cross-validation of the objective function itself? The authors should report its value along the accuracy in the result section. Would it be extremely large to make the first likelihood term ineffective? 
=== FA or PCA ===
Eq 3 shows that the noise is constant across the diagonal. The main difference between FA and PCA is allowing each dimension of signal to have different amount of noise. This noise formulation is closer to PCA, isn't it? But then I was confused reading sec 3.2. What's the covariance matrix of interest in sec 3.2? Over time? space? factors? frequencies?
=== "Causal" ===
The word 'causal' frequently appears in the first 2 pages of the text, setting high expectations. However, the method itself does not seem to have any explanatory power to discover causal structure or inherent causal hypothesis. Or is the reader supposed to get it from the phase plots?
=== comparison with baseline PCA in frequency domain ===
How was the window of data converted to the "Fourier domain"? Was it simply a DFT or was a more sophisticated spectrum estimator used, e.g., multi-taper methods. I ask this because raw FFT/DFT is a bad estimator for the spectrum (very high variance regardless of the length of time window). Neuroscientists often use packages that support such estimation (e.g., MATLAB package chronux). It would not be fair if those are not taken into account.
=== averaging over 6 mice ===
Was the CSFA/dCSFA for Fig 3 computed to produce common factor across 6 mice? What justifies such approach?
== minor ==
 - L 230, 231: absolute KL div numbers are not useful. At least provide standard error of the estimator. (KL div is often very hard to estimate!!)
 - Subsection 2.1 & 2.3.1 reads like filler texts. (not much content)
 - L 124: $s\tilde B_q$? what's $s$ here?
 - L 228: to to
 - overall writing can be improved