Two Optimal Strategies for Active Learning of Causal Models from Interventional Data

From observational data alone, a causal DAG is only identifiable up to Markov equivalence. Interventional data generally improves identifiability; however, the gain of an intervention strongly depends on the intervention target, that is, the intervened variables. We present active learning (that is, optimal experimental design) strategies calculating optimal interventions for two different learning goals. The first one is a greedy approach using single-vertex interventions that maximizes the number of edges that can be oriented after each intervention. The second one yields in polynomial time a minimum set of targets of arbitrary size that guarantees full identifiability. This second approach proves a conjecture of Eberhardt (2008) indicating the number of unbounded intervention targets which is sufficient and in the worst case necessary for full identifiability. In a simulation study, we compare our two active learning approaches to random interventions and an existing approach, and analyze the influence of estimation errors on the overall performance of active learning

LazyIter: A Fast Algorithm for Counting Markov Equivalent DAGs and Designing Experiments

The causal relationships among a set of random variables are commonly represented by a Directed Acyclic Graph (DAG), where there is a directed edge from variable $X$ to variable $Y$ if $X$ is a direct cause of $Y$. From the purely observational data, the true causal graph can be identified up to a Markov Equivalence Class (MEC), which is a set of DAGs with the same conditional independencies between the variables. The size of an MEC is a measure of complexity for recovering the true causal graph by performing interventions. We propose a method for efficient iteration over possible MECs given intervention results. We utilize the proposed method for computing MEC sizes and experiment design in active and passive learning settings. Compared to previous work for computing the size of MEC, our proposed algorithm reduces the time complexity by a factor of $O(n)$ for sparse graphs where $n$ is the number of variables in the system. Additionally, integrating our approach with dynamic programming, we design an optimal algorithm for passive experiment design. Experimental results show that our proposed algorithms for both computing the size of MEC and experiment design outperform the state of the art.Comment: 11 pages, 2 figures, ICM

Two optimal strategies for active learning of causal models from interventions

Abstract From observational data alone, a causal DAG is in general only identifiable up to Markov equivalence. Interventional data generally improves identifiability; however, the gain of an intervention strongly depends on the intervention target, i.e., the intervened variables. We present active learning strategies calculating optimal interventions for two different learning goals. The first one is a greedy approach using single-vertex interventions that maximizes the number of edges that can be oriented after each intervention. The second one yields in polynomial time a minimum set of targets of arbitrary size that guarantees full identifiability. This second approach proves a conjecture of Eberhard

Trust Your ∇\nabla: Gradient-based Intervention Targeting for Causal Discovery

Inferring causal structure from data is a challenging task of fundamental importance in science. Observational data are often insufficient to identify a system's causal structure uniquely. While conducting interventions (i.e., experiments) can improve the identifiability, such samples are usually challenging and expensive to obtain. Hence, experimental design approaches for causal discovery aim to minimize the number of interventions by estimating the most informative intervention target. In this work, we propose a novel Gradient-based Intervention Targeting method, abbreviated GIT, that 'trusts' the gradient estimator of a gradient-based causal discovery framework to provide signals for the intervention acquisition function. We provide extensive experiments in simulated and real-world datasets and demonstrate that GIT performs on par with competitive baselines, surpassing them in the low-data regime

Experiment Selection for Causal Discovery

Randomized controlled experiments are often described as the most reliable tool available to scientists for discovering causal relationships among quantities of interest. However, it is often unclear how many and which different experiments are needed to identify the full (possibly cyclic) causal structure among some given (possibly causally insufficient) set of variables. Recent results in the causal discovery literature have explored various identifiability criteria that depend on the assumptions one is able to make about the underlying causal process, but these criteria are not directly constructive for selecting the optimal set of experiments. Fortunately, many of the needed constructions already exist in the combinatorics literature, albeit under terminology which is unfamiliar to most of the causal discovery community. In this paper we translate the theoretical results and apply them to the concrete problem of experiment selection. For a variety of settings we give explicit constructions of the optimal set of experiments and adapt some of the general combinatorics results to answer questions relating to the problem of experiment selection

Learning Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity

We study causal representation learning, the task of recovering high-level latent variables and their causal relationships in the form of a causal graph from low-level observed data (such as text and images), assuming access to observations generated from multiple environments. Prior results on the identifiability of causal representations typically assume access to single-node interventions which is rather unrealistic in practice, since the latent variables are unknown in the first place. In this work, we provide the first identifiability results based on data that stem from general environments. We show that for linear causal models, while the causal graph can be fully recovered, the latent variables are only identified up to the surrounded-node ambiguity (SNA) \citep{varici2023score}. We provide a counterpart of our guarantee, showing that SNA is basically unavoidable in our setting. We also propose an algorithm, \texttt{LiNGCReL} which provably recovers the ground-truth model up to SNA, and we demonstrate its effectiveness via numerical experiments. Finally, we consider general non-parametric causal models and show that the same identification barrier holds when assuming access to groups of soft single-node interventions.Comment: 42 page