Correction: C-HDNet: Hyperdimensional Computing for Causal Effect Estimation from Observational Data Under Network Interference (Social Network Analysis and Mining, (2025), 15, 1, (97), 10.1007/s13278-025-01502-2)

In this article, the title and the introduction section has to be updated and it should be as given below. The title should be C-HDNet: Hyperdimensional Computing for Causal Effect Estimation from Observational Data Under Network Interference And the introduction section should be Estimation of causal effects from observational data is a central concern in many disciplines, including epidemiology, economics, and social sciences, where randomized controlled experiments are often impractical or downright unethical. Hence, there is great interest in methods for drawing valid inferences about the consequences of interventions or exposures in such settings. Unlike associations, which describe statistical relationships, causal inference aims to address counterfactual questions, e.g., would the economy have recovered in the absence of an interest rate cut? The fundamental problem of causal inference is that while we can observe the factual outcome for a given individual under one treatment assignment, the counterfactual, the outcome under any other treatment assignment, is not observed by definition Pearl (2000) and Neal (2020). A variety of techniques have been proposed to estimate causal effects from observational data. The simplest of such methods estimate the counterfactual outcome for an individual of interest (the target individual) from the observed outcome(s) of other individual(s) that are identical to the target individual in nearly every respect except the treatment status using matching techniques Stuart (2010). When the covariates that describe the individuals are high-dimensional, simple matching techniques break down because of the curse of dimensionality. A variety of methods, ranging from simple dimensionality reduction to sophisticated representation learning techniques that leverage modern deep learning methods have been developed (TARNET, Dragonnet, CFRnet, neuralmatching), see Igelström et al. (2022) for reviews. Traditional methods for causal effect estimation from observational data typically assume independence between individuals, which is violated in settings where individuals are not independent, for example, when they are connected by social ties which introduce network interference. Consider for example, a city or country that is experiencing an outbreak of a contagious disease. Social connections between individuals can be represented by a network. Suppose we want to understand how vaccination impacts the disease spread. Such understanding is crucial for creating tailored intervention strategies, such as vaccination or isolation, to mitigate the spread of the disease within the population. However, in the presence of social ties, the decision of an individual to get vaccinated is likely to be influenced by the decisions of his or her friends, i.e., the network of social ties Taie and Kadry (2017), as a result of network interference. The presence of network interference presents several challenges in estimating causal effects in such settings. The most significant challenge is that an individual's outcome can be directly or indirectly influenced by the treatment status of their network neighbors. Unobserved factors that affect both individual treatment and outcomes can create spurious correlations, making it difficult to isolate the true causal effect. Networks can exhibit complex interaction patterns, including direct effects (between neighbors) and indirect effects (through multiple hops in the network). Hence, much recent work has focused on methods for estimating causal effect from networked observational data. Almost all such methods are variants of deep learning methods for causal effect estimation from observational data that attempt to account for network interference by exploiting the knowledge of network structure (Guo et al. 2020b, a, c; Veitch et al. 2019). However, deep learning techniques are computationally expensive, include many tunable hyperparameters, and require a large amount of training data to be effective (Thompson 2021). This paper aims to explore computationally efficient alternatives to deep learning methods for causal effect estimation from observational data in the presence of network interference.Our approach leverages recent advances in hyperdimensional (HD) computing (Kanerva 1992, 2009). HD computing does not require iterative optimization for training and instead relies on simple, fast, operations in a high-dimensional space. Each data sample is represented using hyperdimensional bipolar vectors in {−1, 1}^β, or as multi-bit vectors, where the dimensionality is typically β ≈ 10,000. Our recent work has demonstrated the effectiveness of HD computing for causal effect estimation from observational data in the simpler setting where there is no network interference and hence the data samples are independent. In this work, we propose C-HDNet: a Causal HD computing technique for effect estimation from Network observational data. To the best of our knowledge, this is the first application of hyperdimensional computing for causal effect estimation from observational data in the presence of network interference. The key novelty of C-HDNet lies in the design of the hyperdimensional representation of the covariates that describe the individuals (network nodes) and the relationships that link them to other individuals (network links) into HD vectors; and an efficient algorithm for matching the individuals based on their HD representations. The matched pairs of individuals with similar covariates that appear in similar network contexts but have differ in treatment status can then be used to estimate the individual treatment effect. The primary advantage of our approach over deep learning based methods for causal effect estimation in the presence of network interference (Guo et al. 2020b, a, c; Veitch et al. 2019) is that it requires no iterative optimization and operates as a one-pass learning algorithm—i.e., it involves computing specific steps without the need for repetitive training. Hence, C-HDNet offers a computationally efficient alternative to deep learning. The results of our extensive experiments demonstrate that the efficiency gains are realized without sacrificing accuracy of causal effect estimation relative to the state-of-the-art deep learning methods. The rest of the paper is organized as follows. Section 2, provides background information on causal inference and HD computing. Section 3 provides precise problem formulation. Section 4 describes our proposed algorithm. Section 5 presents results of experiments that compare our algorithm against state-of-the-art baselines. Finally, section 6 concludes the paper. The original article has been corrected.