Machine learning models have had discernible achievements in a myriad of applications. However, most of these models are black-boxes, and it is obscure how the decisions are made by them. This makes the models unreliable and untrustworthy. To provide insights into the decision making processes of these models, a variety of traditional interpretable models have been proposed. Moreover, to generate more humanfriendly explanations, recent work on interpretability tries to answer questions related to causality such as "Why does this model makes such decisions?" or "Was it a specific feature that caused the decision made by the model?". In this work, models that aim to answer causal questions are referred to as causal interpretable models. The existing surveys have covered concepts and methodologies of traditional interpretability. In this work, we present a comprehensive survey on causal interpretable models from the aspects of the problems and methods. In addition, this survey provides in-depth insights into the existing evaluation metrics for measuring interpretability, which can help practitioners understand for what scenarios each evaluation metric is suitable.

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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 paired 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 latent attributes as confounders that are assumed to affect both the treatment and the outcome of units. Specifically, given a pair of units u andū, 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 andū and the outcome of u. Once inferred, the latent attributes (or confounders) of u captures the spillover effect ofū 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. CCS CONCEPTS• Computing methodologies → Supervised learning by regression; • Mathematics of computing → Variational methods; KEYWORDS causal inference; spillover effect; variational autoencoder * Both authors contributed equally to the paper Permission to make digital

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