Decentralized and incomplete data sources are prevalent in real-world applications, posing a formidable challenge for causal inference. These sources cannot be consolidated into a single entity owing to privacy constraints, and the presence of missing values within them can potentially introduce bias to the causal estimands. We introduce a new approach for federated causal inference from incomplete data, enabling the estimation of causal effects from multiple decentralized and incomplete data sources. Our approach disentangles the loss function into multiple components, each corresponding to a specific data source with missing values. Our approach accounts for the missing data under the missing at random assumption, while also estimating higher-order statistics of the causal estimands. Our method recovers the conditional distribution of missing confounders given the observed confounders from the decentralized data sources to identify causal effects. Our framework estimates heterogeneous causal effects without the sharing of raw training data among sources, which helps to mitigate privacy risks. The efficacy of our approach is demonstrated through a collection of simulated and real-world instances, illustrating its potential and practicality.

Causal inference is to estimate the causal effect in a causal relationship when intervention is applied. Precisely, in a causal model with binary interventions, i.e., control and treatment, the causal effect is simply the difference between the factual and counterfactual. The difficulty is that the counterfactual may never been obtained which has to be estimated and so the causal effect could only be an estimate. The key challenge for estimating the counterfactual is to identify confounders which effect both outcomes and treatments. A typical approach is to formulate causal inference as a supervised learning problem and so counterfactual could be predicted. Including linear regression and deep learning models, recent machine learning methods have been adapted to causal inference. In this paper, we propose a method to estimate Causal Effect by using Variational Information Bottleneck (CEVIB). The promising point is that VIB is able to naturally distill confounding variables from the data, which enables estimating causal effect by using observational data. We have compared CEVIB to other methods by applying them to three data sets showing that our approach achieved the best performance. We also experimentally showed the robustness of our method.

The do-calculus is a set of inference directives that helps the transformation of these interventions into more interpretable Estimating causal effects from observational data informs us about probabilistic sentences, and as such, enables an user to derive or which factors are important in an autonomous system, and enables confirm causal claims about interventions [14]. Results inferred us to take better decisions. This is important because it has applications from do-calculus is well understood on the whole but its application in selecting a treatment in medical systems or making is still questionable [10]. This is because do-calculus assumes that better strategies in industries or making better policies for our the distributions being used are error-free, but in practice, we do not government or even the society. Unavailability of complete data, have sufficient samples to confirm that. In case of limited samples, coupled with high cardinality of data, makes this estimation task a popular criterion, namely back-door criterion, is employed to computationally intractable.

Estimation of causal effects is fundamental in situations were the underlying system will be subject to active interventions. Part of building a causal inference engine is defining how variables relate to each other, that is, defining the functional relationship between variables given conditional dependencies. In this paper, we deviate from the common assumption of linear relationships in causal models by making use of neural autoregressive density estimators and use them to estimate causal effects within the Pearl's do-calculus framework. Using synthetic data, we show that the approach can retrieve causal effects from non-linear systems without explicitly modeling the interactions between the variables.