We consider testing and learning problems on causal Bayesian networks as defined by Pearl (Pearl, 2009). Given a causal Bayesian network $\mathcal{M}$ on a graph with $n$ discrete variables and bounded in-degree and bounded `confounded components', we show that $O(\log n)$ interventions on an unknown causal Bayesian network $\mathcal{X}$ on the same graph, and $\tilde{O}(n/ε^2)$ samples per intervention, suffice to efficiently distinguish whether $\mathcal{X}=\mathcal{M}$ or whether there exists some intervention under which $\mathcal{X}$ and $\mathcal{M}$ are farther than $ε$ in total variation distance. We also obtain sample/time/intervention efficient algorithms for: (i) testing the identity of two unknown causal Bayesian networks on the same graph; and (ii) learning a causal Bayesian network on a given graph. Although our algorithms are non-adaptive, we show that adaptivity does not help in general: $Ω(\log n)$ interventions are necessary for testing the identity of two unknown causal Bayesian networks on the same graph, even adaptively. Our algorithms are enabled by a new subadditivity inequality for the squared Hellinger distance between two causal Bayesian networks.
Robustness of decision rules to shifts in the data-generating process is crucial to the successful deployment of decision-making systems. Such shifts can be viewed as interventions on a causal graph, which capture (possibly hypothetical) changes in the data-generating process, whether due to natural reasons or by the action of an adversary. We consider causal Bayesian networks and formally define the interventional robustness problem, a novel model-based notion of robustness for decision functions that measures worst-case performance with respect to a set of interventions that denote changes t…
In many real-world scenarios, such as gene knockout experiments, targeted interventions are often accompanied by unknown interventions at off-target sites. Moreover, different units can get randomly exposed to different unknown interventions, thereby creating a mixture of interventions. Identifying different components of this mixture can be very valuable in some applications. Motivated by such situations, in this work, we study the problem of identifying all components present in a mixture of interventions on a given causal Bayesian Network. We construct an example to show that, in general, t…
University of Massachusetts（马萨诸塞大学）；Massachusetts Institute of Technology（麻省理工学院）
Causal inference can be formalized as Bayesian inference that combines a prior distribution over causal models and likelihoods that account for both observations and interventions. We show that it is possible to implement this approach using a sufficiently expressive probabilistic programming language. Priors are represented using probabilistic programs that generate source code in a domain specific language. Interventions are represented using probabilistic programs that edit this source code to modify the original generative process. This approach makes it straightforward to incorporate data…
Adobe Research（Adobe研究院）；Technion Israel Institute of Technology（以色列理工学院）
We study the problem of determining the best intervention in a Causal Bayesian Network (CBN) specified only by its causal graph. We model this as a stochastic multi-armed bandit (MAB) problem with side-information, where the interventions correspond to the arms of the bandit instance. First, we propose a simple regret minimization algorithm that takes as input a semi-Markovian causal graph with atomic interventions and possibly unobservable variables, and achieves $\tilde{O}(\sqrt{M/T})$ expected simple regret, where $M$ is dependent on the input CBN and could be very small compared to the num…
University of Warwick（华威大学）；The Alan Turing Institute（阿兰·图灵研究所）；Microsoft Research Cambridge（微软剑桥研究院）
This paper studies the problem of performing a sequence of optimal interventions in a causal dynamical system where both the target variable of interest and the inputs evolve over time. This problem arises in a variety of domains e.g. system biology and operational research. Dynamic Causal Bayesian Optimization (DCBO) brings together ideas from sequential decision making, causal inference and Gaussian process (GP) emulation. DCBO is useful in scenarios where all causal effects in a graph are changing over time. At every time step DCBO identifies a local optimal intervention by integrating both…
This report summarises the outcomes of a systematic literature search to identify Bayesian network models used to support decision making in healthcare. After describing the search methodology, the selected research papers are briefly reviewed, with the view to identify publicly available models and datasets that are well suited to analysis using the causal interventional analysis software tool developed in Wang B, Lyle C, Kwiatkowska M (2021). Finally, an experimental evaluation of applying the software on a selection of models is carried out and preliminary results are reported.
Deep neural networks excel at comprehending complex visual signals, delivering on par or even superior performance to that of human experts. However, ad-hoc visual explanations of model decisions often reveal an alarming level of reliance on exploiting non-causal visual cues that strongly correlate with the target label in training data. As such, deep neural nets suffer compromised generalization to novel inputs collected from different sources, and the reverse engineering of their decision rules offers limited interpretability. To overcome these limitations, we present a novel contrastive lea…
The past two decades have seen a growing interest in combining causal information, commonly represented using causal graphs, with machine learning models. Probability trees provide a simple yet powerful alternative representation of causal information. They enable both computation of intervention and counterfactuals, and are strictly more general, since they allow context-dependent causal dependencies. Here we present a Bayesian method for learning probability trees from a combination of interventional and observational data. The method quantifies the expected information gain from an interven…
Georgia Institute of Technology（佐治亚理工学院）；IBM Research（IBM研究院）
Discovering and exploiting the causality in deep neural networks (DNNs) are crucial challenges for understanding and reasoning causal effects (CE) on an explainable visual model. "Intervention" has been widely used for recognizing a causal relation ontologically. In this paper, we propose a causal inference framework for visual reasoning via do-calculus. To study the intervention effects on pixel-level features for causal reasoning, we introduce pixel-wise masking and adversarial perturbation. In our framework, CE is calculated using features in a latent space and perturbed prediction from a D…
We consider recovering a causal graph in presence of latent variables, where we seek to minimize the cost of interventions used in the recovery process. We consider two intervention cost models: (1) a linear cost model where the cost of an intervention on a subset of variables has a linear form, and (2) an identity cost model where the cost of an intervention is the same, regardless of what variables it is on, i.e., the goal is just to minimize the number of interventions. Under the linear cost model, we give an algorithm to identify the ancestral relations of the underlying causal graph, achi…
We study the problem of learning the causal relationships between a set of observed variables in the presence of latents, while minimizing the cost of interventions on the observed variables. We assume access to an undirected graph $G$ on the observed variables whose edges represent either all direct causal relationships or, less restrictively, a superset of causal relationships (identified, e.g., via conditional independence tests or a domain expert). Our goal is to recover the directions of all causal or ancestral relations in $G$, via a minimum cost set of interventions. It is known that co…
National University of Singapore（新加坡国立大学）；Stanford University（斯坦福大学）
We study two problems related to recovering causal graphs from interventional data: (i) $\textit{verification}$, where the task is to check if a purported causal graph is correct, and (ii) $\textit{search}$, where the task is to recover the correct causal graph. For both, we wish to minimize the number of interventions performed. For the first problem, we give a characterization of a minimal sized set of atomic interventions that is necessary and sufficient to check the correctness of a claimed causal graph. Our characterization uses the notion of $\textit{covered edges}$, which enables us to …
