Additional Feedback: The authors propose a Gibbs sampling algorithm that is mentioned to be very efficient. I would expect the parameters to be very correlated, especially in a three-layer model. Could the authors elaborate on this, efficient in what sense? I assume the Gibbs sampler is rather used as a stochastic optimization algorithm than a way to explore the whole posterior? The link activation variable u_k is essentially a variable that will work on the topic level to give strength to individual topics for the links.

The paper, the reviews, the author response and the ensuing discussion were all taken into consideration. All reviewers considered the work marginally above the acceptance threshold. Novelty was a concern for some but other reviewers appreciated it. Lacking comparisons to GCN and others, evaluation of underlying topics, and consideration of topic modeling prior work were also concerns. However, the paper was generally felt to represent good work, and use of a deep model in this context, design of the model, and convincing experiments were appreciated.

The study of learning causal structure with latent variables has advanced the understanding of the world by uncovering causal relationships and latent factors, e.g., Causal Representation Learning (CRL). However, in real-world scenarios, such as those in climate systems, causal relationships are often nonparametric, dynamic, and exist among both observed variables and latent variables. These challenges motivate us to consider a general setting in which causal relations are nonparametric and unrestricted in their occurrence, which is unconventional to current methods. To solve this problem, with the aid of 3-measurement in temporal structure, we theoretically show that both latent variables and processes can be identified up to minor indeterminacy under mild assumptions. Moreover, we tackle the general nonlinear Causal Discovery (CD) from observations, e.g., temperature, as a specific task of learning independent representation, through the principle of functional equivalence. Based on these insights, we develop an estimation approach simultaneously recovering both the observed causal structure and latent causal process in a nontrivial manner. Simulation studies validate the theoretical foundations and demonstrate the effectiveness of the proposed methodology. In the experiments involving climate data, this approach offers a powerful and in-depth understanding of the climate system.

Traditional approaches to studying decision-making in neuroscience focus on simplified behavioral tasks where animals perform repetitive, stereotyped actions to receive explicit rewards. While informative, these methods constrain our understanding of decision-making to short timescale behaviors driven by explicit goals. In natural environments, animals exhibit more complex, long-term behaviors driven by intrinsic motivations that are often unobservable. Recent works in time-varying inverse reinforcement learning (IRL) aim to capture shifting motivations in long-term, freely moving behaviors. However, a crucial challenge remains: animals make decisions based on their history, not just their current state. To address this, we introduce SWIRL (SWitching IRL), a novel framework that extends traditional IRL by incorporating time-varying, history-dependent reward functions. SWIRL models long behavioral sequences as transitions between short-term decision-making processes, each governed by a unique reward function. SWIRL incorporates biologically plausible history dependency to capture how past decisions and environmental contexts shape behavior, offering a more accurate description of animal decision-making. We apply SWIRL to simulated and real-world animal behavior datasets and show that it outperforms models lacking history dependency, both quantitatively and qualitatively. This work presents the first IRL model to incorporate history-dependent policies and rewards to advance our understanding of complex, naturalistic decision-making in animals. Historically, decision making in neuroscience has been studied using simplified assays where animals perform repetitive, stereotyped actions (such as licks, nose pokes, or lever presses) in response to sensory stimuli to obtain an explicit reward. While this approach has its advantages, it has limited our understanding of decision making to scenarios where animals are instructed to achieve an explicit goal over brief timescales, usually no more than tens of seconds.

Hippocampal formation (HF) can rapidly adapt to varied environments and build flexible working memory (WM). To mirror the HF's mechanism on generalization and WM, we propose a model named Generalization and Associative Temporary Encoding (GATE), which deploys a 3-D multi-lamellar dorsoventral (DV) architecture, and learns to build up internally representation from externally driven information layer-wisely. In each lamella, regions of HF: EC3-CA1-EC5-EC3 forms a re-entrant loop that discriminately maintains information by EC3 persistent activity, and selectively readouts the retained information by CA1 neurons. CA3 and EC5 further provides gating function that controls these processes. After learning complex WM tasks, GATE forms neuron representations that align with experimental records, including splitter, lap, evidence, trace, delay-active cells, as well as conventional place cells. Crucially, DV architecture in GATE also captures information, range from detailed to abstract, which enables a rapid generalization ability when cue, environment or task changes, with learned representations inherited. GATE promises a viable framework for understanding the HF's flexible memory mechanisms and for progressively developing brain-inspired intelligent systems.

Model uncertainty quantification involves measuring and evaluating the uncertainty linked to a model's predictions, helping assess their reliability and confidence. Noise injection is a technique used to enhance the robustness of neural networks by introducing randomness. In this paper, we establish a connection between noise injection and uncertainty quantification from a Bayesian standpoint. We theoretically demonstrate that injecting noise into the weights of a neural network is equivalent to Bayesian inference on a deep Gaussian process. Consequently, we introduce a Monte Carlo Noise Injection (MCNI) method, which involves injecting noise into the parameters during training and performing multiple forward propagations during inference to estimate the uncertainty of the prediction. Through simulation and experiments on regression and classification tasks, our method demonstrates superior performance compared to the baseline model.

There are, of course, many other hybrid methods available for learning Bayesian networks and therefore causal structures.

I found the paper very well presented and enjoyable to read. The basic problem is interesting, and the approach presented as some salient features, notably the fact that one does not have to make parametric assumption on the underlying distribution. The high-level idea of imposing structural assumptions but nonetheless relying on discriminative models was quite elegant. The basic insight in estimating the risk from unlabelled data is that by encoding a certain structural assumption - namely, that the data comprises three independent views - one implicitly gets information about the class-conditional risks by considering the first three moments of the label vectors. This leads to a system of equations which may be solved to infer the class-conditional risks.

I think this paper addresses an important issue and makes valuable contributions, and thus should be published. I have a few concerns, hence my lower rating for the last question above (which I think could be addressed relatively easily, however). I think this is fundamentally *OK* and even perhaps a positive thing. However, I think a bit more discussion needs to be given to how the arguments might be made more formal. For example, in Section 2.1, I think the proof is intended to hold only in the limit of M going to infinity. Please give a stament of what should hold in what limit-- this wasn't clear to me.

The proposed method is very similar to previous work by Nie et al. -- both use k-trees to search for low-treewidth Bayesian networks, both start with a randomly chosen initial clique, and both propose using an A* method for finding the best tree. The differences are that Nie et al. score k-trees using a mutual information score and use BDeu for choosing the final consistent Bayesian network, while this paper proposes using BIC and incrementally building the Bayesian network along with the k-tree, using the BN to score the k-tree. This paper also includes the additional restriction that the complete variable (partial) order is chosen randomly, while in Nie et al. The main justification for these differences is the ability to scale to large treewidths. However, in the experiments, the previous S2 algorithm also can scale to large treewidths.