# A Unified Probabilistic Model for Learning Latent Factors and Their Connectivities from High-Dimensional Data

arXiv: https://arxiv.org/abs/1805.09567 · HTML: https://mlsanity.com/paper/1805.09567/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2018.

## Built on by (most cited first, 4 of 4)

- [Identifiability of latent-variable and structural-equation models: from linear to nonlinear](https://mlsanity.com/paper/2302.02672/) (2023)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Causal Representation Learning in Temporal Data via Single-Parent Decoding](https://mlsanity.com/paper/2410.07013/) (2024)
- [Denoising Score Matching with Random Fourier Features](https://mlsanity.com/paper/2101.05239/) (2021)

## Abstract (arXiv)

Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation. Another practical challenge is that we may have data from multiple related classes (e.g., multiple subjects or conditions) and wish to incorporate constraints on the similarities across classes. We propose a probabilistic model which simultaneously performs both a grouping of variables (i.e., detecting community structure) and estimation of connectivities between the groups which correspond to latent variables. The model is essentially a factor analysis model where the factors are allowed to have arbitrary correlations, while the factor loading matrix is constrained to express a community structure. The model can be applied on multiple classes so that the connectivities can be different between the classes, while the community structure is the same for all classes. We propose an efficient estimation algorithm based on score matching, and prove the identifiability of the model. Finally, we present an extension to directed (causal) connectivities over latent variables. Simulations and experiments on fMRI data validate the practical utility of the method.