# Linked Causal Variational Autoencoder for Inferring Paired Spillover Effects

arXiv: https://arxiv.org/abs/1808.03333 · HTML: https://mlsanity.com/paper/1808.03333/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2018.

## Built on by (most cited first, 16 of 16)

- [Learning Causal Effects on Hypergraphs](https://mlsanity.com/paper/2207.04049/) (2022)
- [A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Models](https://mlsanity.com/paper/2102.06648/) (2021)
- [Estimating Average Treatment Effects via Orthogonal Regularization](https://mlsanity.com/paper/2101.08490/) (2021)
- [Evaluation Methods and Measures for Causal Learning Algorithms](https://mlsanity.com/paper/2202.02896/) (2022)
- [VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2110.14690/) (2021)
- [Exploring Causal Learning through Graph Neural Networks: An In-depth Review](https://mlsanity.com/paper/2311.14994/) (2023)
- [Estimating Treatment Effects Under Heterogeneous Interference](https://mlsanity.com/paper/2309.13884/) (2023)
- [Causal Inference from Text: Unveiling Interactions between Variables](https://mlsanity.com/paper/2311.05286/) (2023)
- [Enhancing Treatment Effect Estimation via Active Learning: A Counterfactual Covering Perspective](https://mlsanity.com/paper/2505.05242/) (2025)
- [Deep Causal Reasoning for Recommendations](https://mlsanity.com/paper/2201.02088/) (2022)
- [Active and Passive Causal Inference Learning](https://mlsanity.com/paper/2308.09248/) (2023)
- [Treatment-Aware Hyperbolic Representation Learning for Causal Effect Estimation with Social Networks](https://mlsanity.com/paper/2401.06557/) (2024)
- [Adaptive Multi-Source Causal Inference](https://mlsanity.com/paper/2105.14877/) (2021)
- [AI Assurance using Causal Inference: Application to Public Policy](https://mlsanity.com/paper/2112.00591/) (2021)
- [Identifiable Latent Bandits: Leveraging observational data for personalized decision-making](https://mlsanity.com/paper/2407.16239/) (2024)
- [Treatment Effect Estimation with Differentiated Networked Effect on Graph Data](https://mlsanity.com/paper/2605.24358/) (2026)

## Abstract (arXiv)

Modeling spillover effects from observational data is an important problem in economics, business, and other fields of research. % It helps us infer the causality between two seemingly unrelated set of events. For example, if consumer spending in the United States declines, it has spillover effects on economies that depend on the U.S. as their largest export market. In this paper, we aim to infer the causation that results in spillover effects between pairs of entities (or units), we call this effect as textitpaired spillover. To achieve this, we leverage the recent developments in variational inference and deep learning techniques to propose a generative model called Linked Causal Variational Autoencoder (LCVA). Similar to variational autoencoders (VAE), LCVA incorporates an encoder neural network to learn the latent attributes and a decoder network to reconstruct the inputs. However, unlike VAE, LCVA treats the textitlatent attributes as confounders that are assumed to affect both the treatment and the outcome of units. Specifically, given a pair of units u and baru, their individual treatment and outcomes, the encoder network of LCVA samples the confounders by conditioning on the observed covariates of u, the treatments of both u and baru and the outcome of u. Once inferred, the latent attributes (or confounders) of u captures the spillover effect of baru on u. Using a network of users from job training dataset (LaLonde (1986)) and co-purchase dataset from Amazon e-commerce domain, we show that LCVA is significantly more robust than existing methods in capturing spillover effects.