Despitethis noble goal, it has been acknowledged in the literature that statistical tests based ontheEOareoblivious totheunderlying causal mechanisms thatgenerated the disparity in the first place (Hardt et al. 2016).

We then apply the framework to the challenging practical setting where confounding factors (that induce spurious correlations) are observable only on asmall fraction of data.

We incorporate an exogenous variable in the SCM that is learned and utilised for reasoning about interventionsintheobservation.

Causal inference is a key research area in machine learning, yet confusion reigns over the tools needed to tackle it. There are prevalent claims in the machine learning literature that you need a bespoke causal framework or notation to answer causal questions. In this paper, we want to make it clear that you \emph{can} answer any causal inference question within the realm of probabilistic modelling and inference, without causal-specific tools or notation. Through concrete examples, we demonstrate how causal questions can be tackled by writing down the probability of everything. Lastly, we reinterpret causal tools as emerging from standard probabilistic modelling and inference, elucidating their necessity and utility.

Counterfactual inference aims to answer retrospective what if questions and thus belongs to the most fine-grained type of inference in Pearl's causality ladder. Existing methods for counterfactual inference with continuous outcomes aim at point identification and thus make strong and unnatural assumptions about the underlying structural causal model. In this paper, we relax these assumptions and aim at partial counterfactual identification of continuous outcomes, i.e., when the counterfactual query resides in an ignorance interval with informative bounds. We prove that, in general, the ignorance interval of the counterfactual queries has non-informative bounds, already when functions of structural causal models are continuously differentiable. As a remedy, we propose a novel sensitivity model called Curvature Sensitivity Model.

We consider the linear causal representation learning setting where we observe a linear mixing of $d$ unknown latent factors, which follow a linear structural causal model. Recent work has shown that it is possible to recover the latent factors as well as the underlying structural causal model over them, up to permutation and scaling, provided that we have at least $d$ environments, each of which corresponds to perfect interventions on a single latent node (factor). After this powerful result, a key open problem faced by the community has been to relax these conditions: allow for coarser than perfect single-node interventions, and allow for fewer than $d$ of them, since the number of latent factors $d$ could be very large. In this work, we consider precisely such a setting, where we allow a smaller than $d$ number of environments, and also allow for very coarse interventions that can very coarsely \textit{change the entire causal graph over the latent factors}. On the flip side, we relax what we wish to extract to simply the \textit{list of nodes that have shifted between one or more environments}. We provide a surprising identifiability result that it is indeed possible, under some very mild standard assumptions, to identify the set of shifted nodes. Our identifiability proof moreover is a constructive one: we explicitly provide necessary and sufficient conditions for a node to be a shifted node, and show that we can check these conditions given observed data. Our algorithm lends itself very naturally to the sample setting where instead of just interventional distributions, we are provided datasets of samples from each of these distributions. We corroborate our results on both synthetic experiments as well as an interesting psychometric dataset.

This manuscript contributes a general and practical framework for casting a Markov process model of a system at equilibrium as a structural causal model, and carrying out counterfactual inference. Markov processes mathematically describe the mechanisms in the system, and predict the system's equilibrium behavior upon intervention, but do not support counterfactual inference. In contrast, structural causal models support counterfactual inference, but do not identify the mechanisms.

Let $X$ and $Y$ denote the instance and clean label, respectively. When $Y$ is a cause of $X$, according to which many datasets have been constructed, e.g., \textit{SVHN} and \textit{CIFAR}, the distributions of $P(X)$ and $P(Y|X)$ are generally entangled. This means that the unsupervised instances are helpful to learn the classifier and thus reduce the side effect of label noise. However, it remains elusive on how to exploit the causal information to handle the label-noise problem. We propose to model and make use of the causal process in order to correct the label-noise effect.Empirically, the proposed method outperforms all state-of-the-art methods on both synthetic and real-world label-noise datasets.