Thuc Duy Le

Debo Cheng, Jiuyong Li, Lin Liu et al.

In many fields of scientific research and real-world applications, unbiased estimation of causal effects from non-experimental data is crucial for understanding the mechanism underlying the data and for decision-making on effective responses or interventions. A great deal of research has been conducted to address this challenging problem from different angles. For estimating causal effect in observational data, assumptions such as Markov condition, faithfulness and causal sufficiency are always made. Under the assumptions, full knowledge such as, a set of covariates or an underlying causal graph, is typically required. A practical challenge is that in many applications, no such full knowledge or only some partial knowledge is available. In recent years, research has emerged to use search strategies based on graphical causal modelling to discover useful knowledge from data for causal effect estimation, with some mild assumptions, and has shown promise in tackling the practical challenge. In this survey, we review these data-driven methods on causal effect estimation for a single treatment with a single outcome of interest and focus on the challenges faced by data-driven causal effect estimation. We concisely summarise the basic concepts and theories that are essential for data-driven causal effect estimation using graphical causal modelling but are scattered around the literature. We identify and discuss the challenges faced by data-driven causal effect estimation and characterise the existing methods by their assumptions and the approaches to tackling the challenges. We analyse the strengths and limitations of the different types of methods and present an empirical evaluation to support the discussions. We hope this review will motivate more researchers to design better data-driven methods based on graphical causal modelling for the challenging problem of causal effect estimation.

Debo Cheng, Ziqi Xu, Jiuyong Li et al.

The instrumental variable (IV) approach is a widely used way to estimate the causal effects of a treatment on an outcome of interest from observational data with latent confounders. A standard IV is expected to be related to the treatment variable and independent of all other variables in the system. However, it is challenging to search for a standard IV from data directly due to the strict conditions. The conditional IV (CIV) method has been proposed to allow a variable to be an instrument conditioning on a set of variables, allowing a wider choice of possible IVs and enabling broader practical applications of the IV approach. Nevertheless, there is not a data-driven method to discover a CIV and its conditioning set directly from data. To fill this gap, in this paper, we propose to learn the representations of the information of a CIV and its conditioning set from data with latent confounders for average causal effect estimation. By taking advantage of deep generative models, we develop a novel data-driven approach for simultaneously learning the representation of a CIV from measured variables and generating the representation of its conditioning set given measured variables. Extensive experiments on synthetic and real-world datasets show that our method outperforms the existing IV methods.

Debo Cheng, Ziqi Xu, Jiuyong Li et al.

This paper studies the challenging problem of estimating causal effects from observational data, in the presence of unobserved confounders. The two-stage least square (TSLS) method and its variants with a standard instrumental variable (IV) are commonly used to eliminate confounding bias, including the bias caused by unobserved confounders, but they rely on the linearity assumption. Besides, the strict condition of unconfounded instruments posed on a standard IV is too strong to be practical. To address these challenging and practical problems of the standard IV method (linearity assumption and the strict condition), in this paper, we use a conditional IV (CIV) to relax the unconfounded instrument condition of standard IV and propose a non-linear CIV regression with Confounding Balancing Representation Learning, CBRL.CIV, for jointly eliminating the confounding bias from unobserved confounders and balancing the observed confounders, without the linearity assumption. We theoretically demonstrate the soundness of CBRL.CIV. Extensive experiments on synthetic and two real-world datasets show the competitive performance of CBRL.CIV against state-of-the-art IV-based estimators and superiority in dealing with the non-linear situation.

Debo Cheng, Ziqi Xu, Jiuyong Li et al.

One of the fundamental challenges in causal inference is to estimate the causal effect of a treatment on its outcome of interest from observational data. However, causal effect estimation often suffers from the impacts of confounding bias caused by unmeasured confounders that affect both the treatment and the outcome. The instrumental variable (IV) approach is a powerful way to eliminate the confounding bias from latent confounders. However, the existing IV-based estimators require a nominated IV, and for a conditional IV (CIV) the corresponding conditioning set too, for causal effect estimation. This limits the application of IV-based estimators. In this paper, by leveraging the advantage of disentangled representation learning, we propose a novel method, named DVAE.CIV, for learning and disentangling the representations of CIV and the representations of its conditioning set for causal effect estimations from data with latent confounders. Extensive experimental results on both synthetic and real-world datasets demonstrate the superiority of the proposed DVAE.CIV method against the existing causal effect estimators.

Jiuyong Li, Ha Xuan Tran, Thuc Duy Le et al.

This paper studies the problem of estimating the contributions of features to the prediction of a specific instance by a machine learning model and the overall contribution of a feature to the model. The causal effect of a feature (variable) on the predicted outcome reflects the contribution of the feature to a prediction very well. A challenge is that most existing causal effects cannot be estimated from data without a known causal graph. In this paper, we define an explanatory causal effect based on a hypothetical ideal experiment. The definition brings several benefits to model agnostic explanations. First, explanations are transparent and have causal meanings. Second, the explanatory causal effect estimation can be data driven. Third, the causal effects provide both a local explanation for a specific prediction and a global explanation showing the overall importance of a feature in a predictive model. We further propose a method using individual and combined variables based on explanatory causal effects for explanations. We show the definition and the method work with experiments on some real-world data sets.

Wentao Gao, Jiuyong Li, Debo Cheng et al.

Global Climate Models (GCMs) are crucial for predicting future climate changes by simulating the Earth systems. However, the GCM Outputs exhibit systematic biases due to model uncertainties, parameterization simplifications, and inadequate representation of complex climate phenomena. Traditional bias correction methods, which rely on historical observation data and statistical techniques, often neglect unobserved confounders, leading to biased results. This paper proposes a novel bias correction approach to utilize both GCM and observational data to learn a factor model that captures multi-cause latent confounders. Inspired by recent advances in causality based time series deconfounding, our method first constructs a factor model to learn latent confounders from historical data and then applies them to enhance the bias correction process using advanced time series forecasting models. The experimental results demonstrate significant improvements in the accuracy of precipitation outputs. By addressing unobserved confounders, our approach offers a robust and theoretically grounded solution for climate model bias correction.

Wentao Gao, Ziqi Xu, Jiuyong Li et al.

As the growing demand for long sequence time-series forecasting in real-world applications, such as electricity consumption planning, the significance of time series forecasting becomes increasingly crucial across various domains. This is highlighted by recent advancements in representation learning within the field. This study introduces a novel multi-view approach for time series forecasting that innovatively integrates trend and seasonal representations with an Independent Component Analysis (ICA)-based representation. Recognizing the limitations of existing methods in representing complex and high-dimensional time series data, this research addresses the challenge by combining TS (trend and seasonality) and ICA (independent components) perspectives. This approach offers a holistic understanding of time series data, going beyond traditional models that often miss nuanced, nonlinear relationships. The efficacy of TSI model is demonstrated through comprehensive testing on various benchmark datasets, where it shows superior performance over current state-of-the-art models, particularly in multivariate forecasting. This method not only enhances the accuracy of forecasting but also contributes significantly to the field by providing a more in-depth understanding of time series data. The research which uses ICA for a view lays the groundwork for further exploration and methodological advancements in time series forecasting, opening new avenues for research and practical applications.

Jiuyong Li, Lin Liu, Ziqi Xu et al.

A predictive model makes outcome predictions based on some given features, i.e., it estimates the conditional probability of the outcome given a feature vector. In general, a predictive model cannot estimate the causal effect of a feature on the outcome, i.e., how the outcome will change if the feature is changed while keeping the values of other features unchanged. This is because causal effect estimation requires interventional probabilities. However, many real world problems such as personalised decision making, recommendation, and fairness computing, need to know the causal effect of any feature on the outcome for a given instance. This is different from the traditional causal effect estimation problem with a fixed treatment variable. This paper first tackles the challenge of estimating the causal effect of any feature (as the treatment) on the outcome w.r.t. a given instance. The theoretical results naturally link a predictive model to causal effect estimations and imply that a predictive model is causally interpretable when the conditions identified in the paper are satisfied. The paper also reveals the robust property of a causally interpretable model. We use experiments to demonstrate that various types of predictive models, when satisfying the conditions identified in this paper, can estimate the causal effects of features as accurately as state-of-the-art causal effect estimation methods. We also show the potential of such causally interpretable predictive models for robust predictions and personalised decision making.

Xiaojing Du, Jiuyong Li, Lin Liu et al.

In many networked systems, interventions applied to one group of units can induce substantial causal effects on another group through cross-group interference pathways. Despite its practical importance in domains such as public health, digital marketing, and social policy, the problem of identifying which intervention subset in a source group maximizes the benefit on a target group remains largely unaddressed. We formalize this problem as cross-group causal influence estimation and introduce the core-to-group causal effect (Co2G), a formally defined causal estimand that quantifies the contrast in target-group outcomes under intervention versus non-intervention on a candidate source subset. We establish the nonparametric identifiability of Co2G from observational network data using do-calculus under standard causal assumptions, and develop a graph neural network-based estimator that captures cross-group interference patterns. To navigate the combinatorial search space of candidate subsets, we propose CauMax, an uncertainty-aware causal effect maximization framework with two scalable selection algorithms: (i)CauMax-G, an iterative greedy search with Monte Carlo dropout--based lower confidence bounds, and (ii)CauMax-D, a differentiable gradient-based optimization via Gumbel-Softmax relaxation. Extensive experiments on two real-world social networks demonstrate that CauMax achieves an order-of-magnitude reduction in regret compared with structural heuristics and diffusion-based baselines, and that moderate uncertainty penalization consistently improves subset selection quality.

Debo Cheng, Ziqi Xu, Jiuyong Li et al.

Causal inference from longitudinal observational data is a challenging problem due to the difficulty in correctly identifying the time-dependent confounders, especially in the presence of latent time-dependent confounders. Instrumental variable (IV) is a powerful tool for addressing the latent confounders issue, but the traditional IV technique cannot deal with latent time-dependent confounders in longitudinal studies. In this work, we propose a novel Time-dependent Instrumental Factor Model (TIFM) for time-varying causal effect estimation from data with latent time-dependent confounders. At each time-step, the proposed TIFM method employs the Recurrent Neural Network (RNN) architecture to infer latent IV, and then uses the inferred latent IV factor for addressing the confounding bias caused by the latent time-dependent confounders. We provide a theoretical analysis for the proposed TIFM method regarding causal effect estimation in longitudinal data. Extensive evaluation with synthetic datasets demonstrates the effectiveness of TIFM in addressing causal effect estimation over time. We further apply TIFM to a climate dataset to showcase the potential of the proposed method in tackling real-world problems.

Debo Cheng, Jiuyong Li, Lin Liu et al.

Latent confounders are a fundamental challenge for inferring causal effects from observational data. The instrumental variable (IV) approach is a practical way to address this challenge. Existing IV based estimators need a known IV or other strong assumptions, such as the existence of two or more IVs in the system, which limits the application of the IV approach. In this paper, we consider a relaxed requirement, which assumes there is an IV proxy in the system without knowing which variable is the proxy. We propose a Variational AutoEncoder (VAE) based disentangled representation learning method to learn an IV representation from a dataset with latent confounders and then utilise the IV representation to obtain an unbiased estimation of the causal effect from the data. Extensive experiments on synthetic and real-world data have demonstrated that the proposed algorithm outperforms the existing IV based estimators and VAE-based estimators.

Wentao Gao, Jiuyong Li, Lin Liu et al.

Zero-inflated data pose significant challenges in precipitation forecasting due to the predominance of zeros with sparse non-zero events. To address this, we propose the Zero Inflation Diffusion Framework (ZIDF), which integrates Gaussian perturbation for smoothing zero-inflated distributions, Transformer-based prediction for capturing temporal patterns, and diffusion-based denoising to restore the original data structure. In our experiments, we use observational precipitation data collected from South Australia along with synthetically generated zero-inflated data. Results show that ZIDF demonstrates significant performance improvements over multiple state-of-the-art precipitation forecasting models, achieving up to 56.7\% reduction in MSE and 21.1\% reduction in MAE relative to the baseline Non-stationary Transformer. These findings highlight ZIDF's ability to robustly handle sparse time series data and suggest its potential generalizability to other domains where zero inflation is a key challenge.

Xiaojing Du, Jiuyong Li, Lin Liu et al.

Estimating peer causal effects within complex real-world networks such as social networks is challenging, primarily due to simultaneous feedback between peers and unobserved confounders. Existing methods either address unobserved confounders while ignoring the simultaneous feedback, or account for feedback but under restrictive linear assumptions, thus failing to obtain accurate peer effect estimation. In this paper, we propose DIG2RSI, a novel Deep learning framework which leverages I-G transformation (matrix operation) and 2SRI (an instrumental variable or IV technique) to address both simultaneous feedback and unobserved confounding, while accommodating complex, nonlinear and high-dimensional relationships. DIG2RSI first applies the I-G transformation to disentangle mutual peer influences and eliminate the bias due to the simultaneous feedback. To deal with unobserved confounding, we first construct valid IVs from network data. In stage 1 of 2RSI, we train a neural network on these IVs to predict peer exposure, and extract residuals as proxies for the unobserved confounders. In the stage 2, we fit a separate neural network augmented by an adversarial discriminator that incorporates these residuals as a control function and enforces the learned representation to contain no residual confounding signal. The expressive power of deep learning models in capturing complex non-linear relationships and adversarial debiasing enhances the effectiveness of DIG2RSI in eliminating bias from both feedback loops and hidden confounders. We prove consistency of our estimator under standard regularity conditions, ensuring asymptotic recovery of the true peer effect. Empirical results on two semi-synthetic benchmarks and a real-world dataset demonstrate that DIG2RSI outperforms existing approaches.

Debo Cheng, Ziqi Xu, Jiuyong Li et al.

Intervention intuition is often used in model explanation where the intervention effect of a feature on the outcome is quantified by the difference of a model prediction when the feature value is changed from the current value to the baseline value. Such a model intervention effect of a feature is inherently association. In this paper, we will study the conditions when an intuitive model intervention effect has a causal interpretation, i.e., when it indicates whether a feature is a direct cause of the outcome. This work links the model intervention effect to the causal interpretation of a model. Such an interpretation capability is important since it indicates whether a machine learning model is trustworthy to domain experts. The conditions also reveal the limitations of using a model intervention effect for causal interpretation in an environment with unobserved features. Experiments on semi-synthetic datasets have been conducted to validate theorems and show the potential for using the model intervention effect for model interpretation.

Sha Lu, Lin Liu, Kui Yu et al.

Anomaly detection is crucial for understanding unusual behaviors in data, as anomalies offer valuable insights. This paper introduces Dependency-based Anomaly Detection (DepAD), a general framework that utilizes variable dependencies to uncover meaningful anomalies with better interpretability. DepAD reframes unsupervised anomaly detection as supervised feature selection and prediction tasks, which allows users to tailor anomaly detection algorithms to their specific problems and data. We extensively evaluate representative off-the-shelf techniques for the DepAD framework. Two DepAD algorithms emerge as all-rounders and superior performers in handling a wide range of datasets compared to nine state-of-the-art anomaly detection methods. Additionally, we demonstrate that DepAD algorithms provide new and insightful interpretations for detected anomalies.

Debo Cheng, Jiuyong Li, Lin Liu et al.

This paper discusses the problem of causal query in observational data with hidden variables, with the aim of seeking the change of an outcome when "manipulating" a variable while given a set of plausible confounding variables which affect the manipulated variable and the outcome. Such an "experiment on data" to estimate the causal effect of the manipulated variable is useful for validating an experiment design using historical data or for exploring confounders when studying a new relationship. However, existing data-driven methods for causal effect estimation face some major challenges, including poor scalability with high dimensional data, low estimation accuracy due to heuristics used by the global causal structure learning algorithms, and the assumption of causal sufficiency when hidden variables are inevitable in data. In this paper, we develop a theorem for using local search to find a superset of the adjustment (or confounding) variables for causal effect estimation from observational data under a realistic pretreatment assumption. The theorem ensures that the unbiased estimate of causal effect is included in the set of causal effects estimated by the superset of adjustment variables. Based on the developed theorem, we propose a data-driven algorithm for causal query. Experiments show that the proposed algorithm is faster and produces better causal effect estimation than an existing data-driven causal effect estimation method with hidden variables. The causal effects estimated by the proposed algorithm are as accurate as those by the state-of-the-art methods using domain knowledge.

Jiuyong Li, Lin Liu, Shisheng Zhang et al.

In personalised decision making, evidence is required to determine whether an action (treatment) is suitable for an individual. Such evidence can be obtained by modelling treatment effect heterogeneity in subgroups. The existing interpretable modelling methods take a top-down approach to search for subgroups with heterogeneous treatment effects and they may miss the most specific and relevant context for an individual. In this paper, we design a \emph{Treatment effect pattern (TEP)} to represent treatment effect heterogeneity in data. To achieve an interpretable presentation of TEPs, we use a local causal structure around the outcome to explicitly show how those important variables are used in modelling. We also derive a formula for unbiasedly estimating the \emph{Conditional Average Causal Effect (CATE)} using the local structure in our problem setting. In the discovery process, we aim at minimising heterogeneity within each subgroup represented by a pattern. We propose a bottom-up search algorithm to discover the most specific patterns fitting individual circumstances the best for personalised decision making. Experiments show that the proposed method models treatment effect heterogeneity better than three other existing tree based methods in synthetic and real world data sets.

Jixue Liu, Jiuyong Li, Feiyue Ye et al.

Algorithmic discrimination is an important aspect when data is used for predictive purposes. This paper analyzes the relationships between discrimination and classification, data set partitioning, and decision models, as well as correlation. The paper uses real world data sets to demonstrate the existence of discrimination and the independence between the discrimination of data sets and the discrimination of classification models.

Jixue Liu, Jiuyong Li, Lin Liu et al.

Predictive models such as decision trees and neural networks may produce discrimination in their predictions. This paper proposes a method to post-process the predictions of a predictive model to make the processed predictions non-discriminatory. The method considers multiple protected variables together. Multiple protected variables make the problem more challenging than a simple protected variable. The method uses a well-cited discrimination metric and adapts it to allow the specification of explanatory variables, such as position, profession, education, that describe the contexts of the applications. It models the post-processing of predictions problem as a nonlinear optimization problem to find best adjustments to the predictions so that the discrimination constraints of all protected variables are all met at the same time. The proposed method is independent of classification methods. It can handle the cases that existing methods cannot handle: satisfying multiple protected attributes at the same time, allowing multiple explanatory attributes, and being independent of classification model types. An evaluation using four real world data sets shows that the proposed method is as effectively as existing methods, in addition to its extra power.

Saisai Ma, Jiuyong Li, Lin Liu et al.

With the increasing need of personalised decision making, such as personalised medicine and online recommendations, a growing attention has been paid to the discovery of the context and heterogeneity of causal relationships. Most existing methods, however, assume a known cause (e.g. a new drug) and focus on identifying from data the contexts of heterogeneous effects of the cause (e.g. patient groups with different responses to the new drug). There is no approach to efficiently detecting directly from observational data context specific causal relationships, i.e. discovering the causes and their contexts simultaneously. In this paper, by taking the advantages of highly efficient decision tree induction and the well established causal inference framework, we propose the Tree based Context Causal rule discovery (TCC) method, for efficient exploration of context specific causal relationships from data. Experiments with both synthetic and real world data sets show that TCC can effectively discover context specific causal rules from the data.

Thuc Duy Le, Tao Hoang, Jiuyong Li et al.

Discovering causal relationships from data is the ultimate goal of many research areas. Constraint based causal exploration algorithms, such as PC, FCI, RFCI, PC-simple, IDA and Joint-IDA have achieved significant progress and have many applications. A common problem with these methods is the high computational complexity, which hinders their applications in real world high dimensional datasets, e.g gene expression datasets. In this paper, we present an R package, ParallelPC, that includes the parallelised versions of these causal exploration algorithms. The parallelised algorithms help speed up the procedure of experimenting big datasets and reduce the memory used when running the algorithms. The package is not only suitable for super-computers or clusters, but also convenient for researchers using personal computers with multi core CPUs. Our experiment results on real world datasets show that using the parallelised algorithms it is now practical to explore causal relationships in high dimensional datasets with thousands of variables in a single multicore computer. ParallelPC is available in CRAN repository at https://cran.rproject.org/web/packages/ParallelPC/index.html.

Saisai Ma, Jiuyong Li, Lin Liu et al.

In recent years, many methods have been developed for detecting causal relationships in observational data. Some of them have the potential to tackle large data sets. However, these methods fail to discover a combined cause, i.e. a multi-factor cause consisting of two or more component variables which individually are not causes. A straightforward approach to uncovering a combined cause is to include both individual and combined variables in the causal discovery using existing methods, but this scheme is computationally infeasible due to the huge number of combined variables. In this paper, we propose a novel approach to address this practical causal discovery problem, i.e. mining combined causes in large data sets. The experiments with both synthetic and real world data sets show that the proposed method can obtain high-quality causal discoveries with a high computational efficiency.

Jiuyong Li, Saisai Ma, Thuc Duy Le et al.

Uncovering causal relationships in data is a major objective of data analytics. Causal relationships are normally discovered with designed experiments, e.g. randomised controlled trials, which, however are expensive or infeasible to be conducted in many cases. Causal relationships can also be found using some well designed observational studies, but they require domain experts' knowledge and the process is normally time consuming. Hence there is a need for scalable and automated methods for causal relationship exploration in data. Classification methods are fast and they could be practical substitutes for finding causal signals in data. However, classification methods are not designed for causal discovery and a classification method may find false causal signals and miss the true ones. In this paper, we develop a causal decision tree where nodes have causal interpretations. Our method follows a well established causal inference framework and makes use of a classic statistical test. The method is practical for finding causal signals in large data sets.

Thuc Duy Le, Tao Hoang, Jiuyong Li et al.

Discovering causal relationships from observational data is a crucial problem and it has applications in many research areas. The PC algorithm is the state-of-the-art constraint based method for causal discovery. However, runtime of the PC algorithm, in the worst-case, is exponential to the number of nodes (variables), and thus it is inefficient when being applied to high dimensional data, e.g. gene expression datasets. On another note, the advancement of computer hardware in the last decade has resulted in the widespread availability of multi-core personal computers. There is a significant motivation for designing a parallelised PC algorithm that is suitable for personal computers and does not require end users' parallel computing knowledge beyond their competency in using the PC algorithm. In this paper, we develop parallel-PC, a fast and memory efficient PC algorithm using the parallel computing technique. We apply our method to a range of synthetic and real-world high dimensional datasets. Experimental results on a dataset from the DREAM 5 challenge show that the original PC algorithm could not produce any results after running more than 24 hours; meanwhile, our parallel-PC algorithm managed to finish within around 12 hours with a 4-core CPU computer, and less than 6 hours with a 8-core CPU computer. Furthermore, we integrate parallel-PC into a causal inference method for inferring miRNA-mRNA regulatory relationships. The experimental results show that parallel-PC helps improve both the efficiency and accuracy of the causal inference algorithm.