Causal inference plays an important role in understanding the underlying mechanisation of the data generation process across various domains. It is challenging to estimate the average causal effect and individual causal effects from observational data with high-dimensional covariates due to the curse of dimension and the problem of data sufficiency. The existing matching methods can not effectively estimate individual causal effect or solve the problem of dimension curse in causal inference. To address this challenge, in this work, we prove that the reduced set by sufficient dimension reduction (SDR) is a balance score for confounding adjustment. Under the theorem, we propose to use an SDR method to obtain a reduced representation set of the original covariates and then the reduced set is used for the matching method. In detail, a non-parametric model is used to learn such a reduced set and to avoid model specification errors. The experimental results on real-world datasets show that the proposed method outperforms the compared matching methods. Moreover, we conduct an experiment analysis and the results demonstrate that the reduced representation is enough to balance the imbalance between the treatment group and control group individuals.

Matching Using Sufficient Dimension Reduction for Heterogeneity Causal Effect Estimation

In causal inference, it is a fundamental task to estimate the causal effect from observational data. However, latent confounders pose major challenges in causal inference in observational data, for example, confounding bias and M-bias. Recent data-driven causal effect estimators tackle the confounding bias problem via balanced representation learning, but assume no M-bias in the system, thus they fail to handle the M-bias. In this paper, we identify a challenging and unsolved problem caused by a variable that leads to confounding bias and M-bias simultaneously. To address this problem with co-occurring M-bias and confounding bias, we propose a novel Disentangled Latent Representation learning framework for learning latent representations from proxy variables for unbiased Causal effect Estimation (DLRCE) from observational data. Specifically, DLRCE learns three sets of latent representations from the measured proxy variables to adjust for the confounding bias and M-bias. Extensive experiments on both synthetic and three real-world datasets demonstrate that DLRCE significantly outperforms the state-of-the-art estimators in the case of the presence of both confounding bias and M-bias.

Disentangled Latent Representation Learning for Tackling the Confounding M-Bias Problem in Causal Inference

Recently, interest has grown in the use of proxy variables of unobserved confounding for inferring the causal effect in the presence of unmeasured confounders from observational data. One difficulty inhibiting the practical use is finding valid proxy variables of unobserved confounding to a target causal effect of interest. These proxy variables are typically justified by background knowledge. In this paper, we investigate the estimation of causal effects among multiple treatments and a single outcome, all of which are affected by unmeasured confounders, within a linear causal model, without prior knowledge of the validity of proxy variables. To be more specific, we first extend the existing proxy variable estimator, originally addressing a single unmeasured confounder, to accommodate scenarios where multiple unmeasured confounders exist between the treatments and the outcome. Subsequently, we present two different sets of precise identifiability conditions for selecting valid proxy variables of unmeasured confounders, based on the second-order statistics and higher-order statistics of the data, respectively. Moreover, we propose two data-driven methods for the selection of proxy variables and for the unbiased estimation of causal effects. Theoretical analysis demonstrates the correctness of our proposed algorithms. Experimental results on both synthetic and real-world data show the effectiveness of the proposed approach. 

pdf/automating-the-selection-of-proxy-variables-of-unmeasured-2lwbwtl5p3.pdf

Automating the Selection of Proxy Variables of Unmeasured Confounders

Causal inference is the process of using assumptions, study designs, and estimation strategies to draw conclusions about the causal relationships between variables based on data. This allows researchers to better understand the underlying mechanisms at work in complex systems and make more informed decisions. In many settings, we may not fully observe all the confounders that affect both the treatment and outcome variables, complicating the estimation of causal effects. To address this problem, a growing literature in both causal inference and machine learning proposes to use Instrumental Variables (IV). This paper serves as the first effort to systematically and comprehensively introduce and discuss the IV methods and their applications in both causal inference and machine learning. First, we provide the formal definition of IVs and discuss the identification problem of IV regression methods under different assumptions. Second, we categorize the existing work on IV methods into three streams according to the focus on the proposed methods, including two-stage least squares with IVs, control function with IVs, and evaluation of IVs. For each stream, we present both the classical causal inference methods, and recent developments in the machine learning literature. Then, we introduce a variety of applications of IV methods in real-world scenarios and provide a summary of the available datasets and algorithms. Finally, we summarize the literature, discuss the open problems and suggest promising future research directions for IV methods and their applications. We also develop a toolkit of IVs methods reviewed in this survey at https://github.com/causal-machine-learning-lab/mliv.

pdf/instrumental-variables-in-causal-inference-and-machine-y1qtnwrw.pdf

Instrumental Variables in Causal Inference and Machine Learning: A Survey

Even when the causal graph underlying our data is unknown, we can use observational data to narrow down the possible values that an average treatment effect (ATE) can take by (1) identifying the graph up to a Markov equivalence class; and (2) estimating that ATE for each graph in the class. While the PC algorithm can identify this class under strong faithfulness assumptions, it can be computationally prohibitive. Fortunately, only the local graph structure around the treatment is required to identify the set of possible ATE values, a fact exploited by local discovery algorithms to improve computational efficiency. In this paper, we introduce Local Discovery using Eager Collider Checks (LDECC), a new local causal discovery algorithm that leverages unshielded colliders to orient the treatment's parents differently from existing methods. We show that there exist graphs where LDECC exponentially outperforms existing local discovery algorithms and vice versa. Moreover, we show that LDECC and existing algorithms rely on different faithfulness assumptions, leveraging this insight to weaken the assumptions for identifying the set of possible ATE values.

Local Causal Discovery for Estimating Causal Effects

: Materials with a kagome lattice provide a platform for searching for new electronic phases and investigating the interplay between correlation and topology. Various probes have recently shown that the kagome lattice can host diverse quantum phases with intertwined orders, including charge density wave states, bond density wave states, chiral charge order, and, rarely, superconductivity. However, reports of the coexistence of superconductivity and magnetic order in kagome materials remain elusive. Here we revisit a magnetic superconductor CeRu 2 with a kagome network formed by Ru atoms. Our first-principles calculations revealed a kagome flat band near the Fermi surface, indicative of flat-band magnetism. At ambient pressure, CeRu 2 exhibits a superconducting transition temperature (T c ) up to ~ 6 K and a magnetic order at ~ 40 K. Notably, superconductivity and related behavior can be tuned by adjusting the amount of Ru. We conducted a systematic investigation of the superconductivity and magnetic order in CeRu 2 via magnetic, resistivity, and structural measurements under pressure up to ~ 168 GPa. An unusual phase diagram that suggests an intriguing interplay between the compound’s superconducting order parameters has been constructed. A T c resurgence was observed above pressure of ~ 28 GPa, accompanied by the sudden appearance of a secondary superconducting transition. Our experiments have identified tantalizing phase transitions driven by high pressure and suggest that the superconductivity and magnetism in CeRu 2 are strongly intertwined.

Magnetic Kagome Superconductor CeRu$_2$

Instrumental variable (IV) is a powerful approach to inferring the causal effect of a treatment on an outcome of interest from observational data even when there exist latent confounders between the treatment and the outcome. However, existing IV methods require that an IV is selected and justified with domain knowledge. An invalid IV may lead to biased estimates. Hence, discovering a valid IV is critical to the applications of IV methods. In this article, we study and design a data-driven algorithm to discover valid IVs from data under mild assumptions. We develop the theory based on partial ancestral graphs (PAGs) to support the search for a set of candidate ancestral IVs (AIVs), and for each possible AIV, the identification of its conditioning set. Based on the theory, we propose a data-driven algorithm to discover a pair of IVs from data. The experiments on synthetic and real-world datasets show that the developed IV discovery algorithm estimates accurate estimates of causal effects in comparison with the state-of-the-art IV-based causal effect estimators.

pdf/discovering-ancestral-instrumental-variables-for-causal-33ozdk04.pdf

Discovering Ancestral Instrumental Variables for Causal Inference from Observational Data

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Magnetic Kagome Superconductor CeRu$_2$

Discovering Ancestral Instrumental Variables for Causal Inference from Observational Data