Related papers: Results on Counterfactual Invariance
In this paper we investigate the notion of conditional independence and prove several information inequalities for conditionally independent random variables.
We show that one can perform causal inference in a natural way for continuous-time scenarios using tools from stochastic analysis. This provides new alternatives to the positivity condition for inverse probability weighting. The probability…
Confounding of three binary-variables counterfactual model is discussed in this paper. According to the effect between the control variable and the covariate variable, we investigate three counterfactual models: the control variable is…
We show that the ability to consider counterfactual situations is a necessary assumption of Bell's theorem, and that, to allow Bell inequality violations while maintaining all other assumptions, we just require certain measurement choices…
It is well known that while the independence of random variables implies zero correlation, the opposite is not true. Namely, uncorrelated random variables are not necessarily independent. In this note we show that the implication could be…
Heckerman (1993) defined causal independence in terms of a set of temporal conditional independence statements. These statements formalized certain types of causal interaction where (1) the effect is independent of the order that causes are…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
This note provides additional interpretation for the counterfactual outcome distribution and corresponding unconditional quantile "effects" defined and estimated by Firpo, Fortin, and Lemieux (2009) and Chernozhukov, Fern\'andez-Val, and…
Notions of counterfactual invariance (CI) have proven essential for predictors that are fair, robust, and generalizable in the real world. We propose graphical criteria that yield a sufficient condition for a predictor to be…
Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption,…
In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…
What is the difference of a prediction that is made with a causal model and a non-causal model? Suppose we intervene on the predictor variables or change the whole environment. The predictions from a causal model will in general work as…
In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…
We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional…
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions…
Diffeomorphism invariance is sometimes taken to be a criterion of background independence. This claim is commonly accompanied by a second, that the genuine physical magnitudes (the "observables") of background-independent theories and those…
In this expository paper, we consider the problem of causal inference and efficient estimation for the counterfactual survivor function. This problem has previously been considered in the literature in several papers, each relying on the…
Investigation of the reversibility of the directional hierarchy in the interdependency among the notions of conditional independence, conditional mean independence, and zero conditional covariance, for two random variables X and Y given a…
Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel…