Paper: Bayesian Bi-clustering of Neural Spiking Activity with Latent Structures (ICLR-2024)

Reviewer comment (Writing):
Some typos, e.g., the "cite" doesn't refer to a paper in section 2.3, the figure index should be 2 rather than 3 in section 3, and the figure index should be 3 rather than 4 in section 4.

Author response:
Thanks, just fixed.

Reviewer comment (Theory):
What's the time complexity (concerning the number of iterations, trials, neurons, and time points) of the proposed model with the efficient MCMC algorithm?

Author response:
Thanks for suggestions on studying time complexity more carefully. The simulation is fast, but for this application example, it takes around 1s for each iteration with brute force implement in a i7-8665U CPU @ 1.90GHz 2.11 GHz laptop. To make it scalable for large dataset, besides implementation of computation techniques like parallel, we can instead do variational inference (VI). But before infer model by VI, checking by MCMC is always good :).

Reviewer comment (Novelty):
What kind of desirable neural data could be better analyzed by such spatiotemporal clustering structures rather than LDS-based models (e.g., SLDS, r-SLDS)?

Author response:
The proposed model is also a LDS-based model, and here we use the latent trajectories to define neural and temporal clusters, so that the detected clusters can be interpretaed as "functional". 

    When implementing the mentioned model SLDS, r-SLDS to multiple population, we need to first define appropriate "neural population". This is hard but important (e.g. neither anatomy nor cell type may be appropriate, since neurons may 'cross talk'), and bad definition on "neural population" can mess up estimation of latent trajectoreis. For example, in C.elegens application in population-rSLDS [1], they deal "with different notions of population structure" and they claim that "there are many reasonable definitions of population ". So, it would be interesting to avoid these confusions, and define "functional" group by latent states. (Also, doing everything together can avoid selective inference issue)

Reviewer comment (Novelty):
Could you please discuss the relationship of this method to the PP-Seq model [1]? PP-Seq is an unsupervised non-parametrical model to detect neural sequences in high dimensional neural recordings, which could be considered as a clustering approach to finding spatiotemporal neural patterns.

Author response:
Detecting neural sequence is an interesting problem and PP-Seq works perfectly for this. However, the problems we want to solve are not exactly the same. Basically...

    - PP-Seq tries to detect neural sequence, and the "clustering element" is spikes at each point. Therefore, for each neuron, it can belong to different clusters at different time (red/ blue sequences in PP-Seq paper can be interleaved), and also there will be different group across neuron at the same time.
    - However, here we want to cluster neurons over time and find the synchronous state changes.  We factorize spatial and temporal cluster structure. For subject cluster, the "clustering element" is the whole trajectory, and each neurons consistently belong to only 1 neural cluster. While for temporal cluster, the state is synchronous across all neurons. Figure 1A can give you a better sense of the difference.  
    - The neural sequence defined by PP-Seq based on several "attributes", and attribute like amplitude may not be appropriate in some cases (e.g. firing of pre-neuron may inhibit post-neuron). Here all clustering structure are based on latent trajectories, i.e., the pattern of the waveform, which can have "functional" interpretation. 

    Also thanks for mentioning PP-Seq, and it can be valuable to take seqeuntial response (delay of response) into account when clustering, by modeling the latent factors in a more careful way.

Reviewer comment (Theory):
While some constraints required for identifiability are provided at the end of section 2.1, I am not convinced that these are sufficient conditions. A theoretical proof of the model identifiability along with all necessary conditions seems important here, given the vast number of parameters.

Author response:
The model idetifiability issue has been studied for a long time in factor analysis (FA) model (if we ignore the temporal system equation and do matrix transpose, the model is equivalent to Poisson FA), and we discuss details in appendix A.1.1. Originally, people claim that constraining $1/2p(p-1)$ parameters and using diagonal constrains is enough (reivew in [1]), there are still permutation and sign issue. To further resolve this, we simply search for the signed-permutation that has the closest Euclidean distance to the previous sample. A more "MCMC"-type solution is developed in [2]. Since in our model, we factor the bias $d_i$ out, we need further "centering" constraint. Besides these conceptual and theoretical claims, empirically we don't find problems in our MCMC.

Reviewer comment (Writing):
There are some typos in the paper and some terms undefined, e.g. 
- the distribution \mathcal{S} in equation (4) is only given in the appendix  
- in the first paragraph of Sec 2.1, where \log\mu_{i, t} = d_i + \tilde{c}' \tilde{x}_t^{(z_i)} has missing subscript i in \tilde{c}.

Author response:
Thanks, just fixed.

Reviewer comment (Theory):
The temporal clusters are captured in the temporal dynamic in the AR(1) model. What is the motivation of such modeling from an application perspective, compared to simpler modeling (e.g. directly model temporal clusters of \tilde{X}_t through change points, etc)?

Author response:
Good question! For many problems (although not for this paper), we may be more interested in the transition matrix $A_{\xi_t}$ (maybe also $Q_{\xi_t}$), since it summarizes the interactions between different neural populations. Therefore, clustering based on dynamics parameters $(b_{\xi_t}, A_{\xi_t}, Q_{\xi_t})$ can provide us the dynamics for interactions between neural population. Simpler modeling is good enough for temporal clustering, and I guess the results can be very similar. But we may lose some insights on dynamics for neural population interactions.

Reviewer comment (Novelty):
The authors only reviewed some work in time series clustering. However, the neural spiking activity data is originally a point process and one has to aggregate them using small bins into count time series. There is some existing work on finding clusters in point process literature as well, which in my opinion should be reviewed for relevance. For example, [1], [2], [3], and references therein.

Author response:
Thanks for menioning these methods and providing the refereces. All these methods are very great, but the defined "clusters" may not directly related to underlying mechanisms and may lose some scientific insights. This motivates us to define neuron and temporal states by latent trajectories directly, as latent factors can usually have scientific interpretation (more details in intro & discussion). We reviewed these methods and added several sentences on this at the begining of paragraph 3 in Intro section.

Reviewer comment (Experiments):
In the real data analysis, the authors argue that it is necessary to use the biclustering algorithm. However, no comparison to any existing method is given. Similar to the simulation studies, I suggest comparing the predictive performance of the proposed algorithm to some existing methods.

Author response:
Thanks the reviewer for these constructive suggestions. All these simulation experiements can make our methods more convincing, especially for suggestions on sensitivity of bin size, since selection on bin size is important to balance computation time and resolution in practice. These are very interesting directions for future work, but the main goal here is to illustrate new idea, and extensive study may beyond the scope (and page limit) of this paper.