# SILVar: Single Index Latent Variable Models

arXiv: https://arxiv.org/abs/1705.03536 · HTML: https://mlsanity.com/paper/1705.03536/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2017.

## Built on by (most cited first, 7 of 7)

- [Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noise](https://mlsanity.com/paper/2312.05974/) (2023)
- [Joint inference of multiple graphs with hidden variables from stationary graph signals](https://mlsanity.com/paper/2110.03666/) (2021)
- [Recovering the Graph Underlying Networked Dynamical Systems under Partial Observability: A Deep Learning Approach](https://mlsanity.com/paper/2208.04405/) (2022)
- [LegendreTron: Uprising Proper Multiclass Loss Learning](https://mlsanity.com/paper/2301.11695/) (2023)
- [Network Topology Inference from Smooth Signals Under Partial Observability](https://mlsanity.com/paper/2410.05707/) (2024)
- [Inferring the Graph of Networked Dynamical Systems under Partial Observability and Spatially Colored Noise](https://mlsanity.com/paper/2312.11324/) (2023)
- [SKI to go Faster: Accelerating Toeplitz Neural Networks via Asymmetric Kernels](https://mlsanity.com/paper/2305.09028/) (2023)

## Abstract (arXiv)

A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows joint estimation of certain non-linearities in the system, the direct interactions between measured variables, and the effects of unmodeled elements on the observed system. The particular form of the model adopted is justified, and learning is posed as a regularized empirical risk minimization. This leads to classes of structured convex optimization problems with a "sparse plus low-rank" flavor. Relations between the proposed model and several common model paradigms, such as those of Robust Principal Component Analysis (PCA) and Vector Autoregression (VAR), are established. Particularly in the VAR setting, the low-rank contributions can come from broad trends exhibited in the time series. Details of the algorithm for learning the model are presented. Experiments demonstrate the performance of the model and the estimation algorithm on simulated and real data.