In this paper, we propose a variational model, iterative Structural Inference of Directed Graphs (iSIDG), to infer the existence of directed interactions from observational agents' features over a time period in a dynamical system. First, the iterative process in our model feeds the learned interactions back to encourage our model to eliminate indirect interactions and to emphasize directional representation during learning. Second, we show that extra regularization terms in the objective function for smoothness, connectiveness, and sparsity prompt our model to infer a more realistic structure and to further eliminate indirect interactions. We evaluate iSIDG on various datasets including biological networks, simulated fMRI data, and physical simulations to demonstrate that our model is able to precisely infer the existence of interactions, and is significantly superior to baseline models.

Neural Information Processing Systems http://nips.cc/

In dynamical systems, the states of an agent are affected by the interactions, and the states are usually recorded as a set of continuous variables, which make it difficult to uncover the interactions based on the similarity between the agents.

This paper introduces SICSM, a novel structural inference framework that integrates Selective State Space Models (selective SSMs) with Generative Flow Networks (GFNs) to handle the challenges posed by dynamical systems with irregularly sampled trajectories and partial observations. By utilizing the robust temporal modeling capabilities of selective SSMs, our approach learns input-dependent transition functions that adapt to non-uniform time intervals, thereby enhancing the accuracy of structural inference. By aggregating dynamics across diverse temporal dependencies and channeling them into the GFN, the SICSM adeptly approximates the posterior distribution of the system's structure. This process not only enables precise inference of complex interactions within partially observed systems but also ensures the seamless integration of prior knowledge, enhancing the model's accuracy and robustness.Extensive evaluations on sixteen diverse datasets demonstrate that SICSM outperforms existing methods, particularly in scenarios characterized by irregular sampling and incomplete observations, which highlight its potential as a reliable tool for scientific discovery and system diagnostics in disciplines that demand precise modeling of complex interactions.

I'm mainly going to comment on the execution of the paper since I'm currently not very knowledgeable in the computational neuroscience of navigation in the brain: -Although it is easy to understand the paper content at a high level, I found it quite difficult to understand some important details, requiring multiple passes over the text to make sense of them. Examples: i) There are non-bold letters that denote continuous distributions over space (G, P), and boldfaced versions of them that represent "discretized" vectors that are grid and place cell responses. Is this mapping a simple discretization of the support of the probability functions? If not, what is the mapping? I guess this is a discretization at landmark locations for place cells (one landmark per place cell). Is it the same thing for the grid cells?