Causal inference on a population of units connected through a network often presents technical challenges, including how to account for interference. In the presence of local interference, for instance, potential outcomes of a unit depend on its treatment as well as on the treatments of other local units, such as its neighbors according to the network. In observational studies, a further complication is that the typical unconfoundedness assumption must be extended - say, to include the treatment of neighbors, and individual and neighborhood covariates - to guarantee identification and valid inference. Here, we derive analytical expressions for the bias of a naive estimator that wrongly assumes away interference. The bias depends on the level of interference but also on the degree of association between individual and neighborhood treatments. We propose an extended unconfoundedness assumption that accounts for interference, and we develop new covariate-adjustment methods that lead to valid estimates of treatment and interference effects in observational studies on networks. Valid estimation is based on a generalized propensity score that balances individual and neighborhood covariates across units under different levels of individual treatment and of exposure to neighbors' treatment. We illustrate how the proposed approach improves over alternative methods in a simulation study, leveraging Add-Health network and covariate data.
On the other hand, work on causal inference for observational network data is still in its infancy. @cite_0 extend these IPW estimators in the presence of general forms of interference on networks. They focus on direct and indirect effects based on Bernoulli allocation strategies similar to those defined by . Although their estimators allows for general forms of interference, their estimator and their asymptotic results are proved under partial interference and clustered data. and then propose a TMLE estimator for similar treatment and spillover effects and prove asymptotic results under IID assumptions. Finally extend this TMLE estimator to allow for dependence due to both contagion and homophily and derive asymptotic results that allow the number of ties per node to increase as the network grows.
@cite_0
2036443429 1850984366 1804927206 2930033329
Recently, there has been increasing interest in making causal inference when interference is possible. In the presence of interference, treatment may have several types of effects. In this article, we consider inference about such effects when the population consists of groups of individuals where interference is possible within groups but not between groups. A two-stage randomization design is assumed where in the first stage groups are randomized to different treatment allocation strategies and in the second stage individuals are randomized to treatment or control conditional on the strategy assigned to their group in the first stage. For this design, the asymptotic distributions of estimators of the causal effects are derived when either the number of individuals per group or the number of groups grows large. Under certain homogeneity assumptions, the asymptotic distributions provide justification for Wald-type confidence intervals (CIs) and tests. Empirical results demonstrate that the Wald CIs have good coverage in finite samples and are narrower than CIs based on either the Chebyshev or Hoeffding inequalities provided the number of groups is not too small. The methods are illustrated by two examples which consider the effects of cholera vaccination and an intervention to encourage voting. The discovery of causal relationships from purely observational data is a fundamental problem in science. The most elementary form of such a causal discovery problem is to decide whether X causes Y or, alternatively, Y causes X, given joint observations of two variables X,Y. An example is to decide whether altitude causes temperature, or vice versa, given only joint measurements of both variables. Even under the simplifying assumptions of no confounding, no feedback loops, and no selection bias, such bivariate causal discovery problems are challenging. Nevertheless, several approaches for addressing those problems have been proposed in recent years. We review two families of such methods: methods based on Additive Noise Models (ANMs) and Information Geometric Causal Inference (IGCI). We present the benchmark CAUSEEFFECTPAIRS that consists of data for 100 different causee ffect pairs selected from 37 data sets from various domains (e.g., meteorology, biology, medicine, engineering, economy, etc.) and motivate our decisions regarding the "ground truth" causal directions of all pairs. We evaluate the performance of several bivariate causal discovery methods on these real-world benchmark data and in addition on artificially simulated data. Our empirical results on real-world data indicate that certain methods are indeed able to distinguish cause from effect using only purely observational data, although more benchmark data would be needed to obtain statistically significant conclusions. One of the best performing methods overall is the method based on Additive Noise Models that has originally been proposed by (2009), which obtains an accuracy of 63 ± 10 and an AUC of 0.74 ± 0.05 on the real-world benchmark. As the main theoretical contribution of this work we prove the consistency of that method. We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We investigate phase transitions in graph structure as the relative weighting of these two components of the attachment rule is varied. Previous work of one of the authors showed that when the geometric component is weak, the limiting degree sequence of the resulting graph coincides with that of the standard Barab 'asi--Albert preferential attachment model. We show that at the other extreme, in the case of a sufficiently strong geometric component, the limiting degree sequence coincides with that of a purely geometric model, the on-line nearest-neighbour graph, which is of interest in its own right and for which we prove some extensions of known results. We also show the presence of an intermediate regime, in which the behaviour differs significantly from both the on-line nearest-neighbour graph and the Barab 'asi--Albert model; in this regime, we obtain a stretched exponential upper bound on the degree sequence. Our results lend some mathematical support to simulation studies of Manna and Sen, while proving that the power law to stretched exponential phase transition occurs at a different point from the one conjectured by those authors. We consider inference about a scalar parameter under a non-parametric model based on a one-step estimator computed as a plug in estimator plus the empirical mean of an estimator of the parameter's influence function. We focus on a class of parameters that have influence function which depends on two infinite dimensional nuisance functions and such that the bias of the one-step estimator of the parameter of interest is the expectation of the product of the estimation errors of the two nuisance functions. Our class includes many important treatment effect contrasts of interest in causal inference and econometrics, such as ATE, ATT, an integrated causal contrast with a continuous treatment, and the mean of an outcome missing not at random. We propose estimators of the target parameter that entertain approximately sparse regression models for the nuisance functions allowing for the number of potential confounders to be even larger than the sample size. By employing sample splitting, cross-fitting and @math -regularized regression estimators of the nuisance functions based on objective functions whose directional derivatives agree with those of the parameter's influence function, we obtain estimators of the target parameter with two desirable robustness properties: (1) they are rate doubly-robust in that they are root-n consistent and asymptotically normal when both nuisance functions follow approximately sparse models, even if one function has a very non-sparse regression coefficient, so long as the other has a sufficiently sparse regression coefficient, and (2) they are model doubly-robust in that they are root-n consistent and asymptotically normal even if one of the nuisance functions does not follow an approximately sparse model so long as the other nuisance function follows an approximately sparse model with a sufficiently sparse regression coefficient.