Jixue Liu

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.

Ziqi Xu, Debo Cheng, Jiuyong Li et al.

An essential and challenging problem in causal inference is causal effect estimation from observational data. The problem becomes more difficult with the presence of unobserved confounding variables. The front-door adjustment is a practical approach for dealing with unobserved confounding variables. However, the restriction for the standard front-door adjustment is difficult to satisfy in practice. In this paper, we relax some of the restrictions by proposing the concept of conditional front-door (CFD) adjustment and develop the theorem that guarantees the causal effect identifiability of CFD adjustment. Furthermore, as it is often impossible for a CFD variable to be given in practice, it is desirable to learn it from data. By leveraging the ability of deep generative models, we propose CFDiVAE to learn the representation of the CFD adjustment variable directly from data with the identifiable Variational AutoEncoder and formally prove the model identifiability. Extensive experiments on synthetic datasets validate the effectiveness of CFDiVAE and its superiority over existing methods. The experiments also show that the performance of CFDiVAE is less sensitive to the causal strength of unobserved confounding variables. We further apply CFDiVAE to a real-world dataset to demonstrate its potential application.

Debo Cheng, Jiuyong Li, Lin Liu et al.

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 paper, 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.

Ziqi Xu, Jixue Liu, Debo Cheng et al.

Much research has been devoted to the problem of learning fair representations; however, they do not explicitly the relationship between latent representations. In many real-world applications, there may be causal relationships between latent representations. Furthermore, most fair representation learning methods focus on group-level fairness and are based on correlations, ignoring the causal relationships underlying the data. In this work, we theoretically demonstrate that using the structured representations enable downstream predictive models to achieve counterfactual fairness, and then we propose the Counterfactual Fairness Variational AutoEncoder (CF-VAE) to obtain structured representations with respect to domain knowledge. The experimental results show that the proposed method achieves better fairness and accuracy performance than the benchmark fairness methods.

Ziqi Xu, Debo Cheng, Jiuyong Li et al.

Estimating direct and indirect causal effects from observational data is crucial to understanding the causal mechanisms and predicting the behaviour under different interventions. Causal mediation analysis is a method that is often used to reveal direct and indirect effects. Deep learning shows promise in mediation analysis, but the current methods only assume latent confounders that affect treatment, mediator and outcome simultaneously, and fail to identify different types of latent confounders (e.g., confounders that only affect the mediator or outcome). Furthermore, current methods are based on the sequential ignorability assumption, which is not feasible for dealing with multiple types of latent confounders. This work aims to circumvent the sequential ignorability assumption and applies the piecemeal deconfounding assumption as an alternative. We propose the Disentangled Mediation Analysis Variational AutoEncoder (DMAVAE), which disentangles the representations of latent confounders into three types to accurately estimate the natural direct effect, natural indirect effect and total effect. Experimental results show that the proposed method outperforms existing methods and has strong generalisation ability. We further apply the method to a real-world dataset to show its potential application.

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.

Ziqi Xu, Debo Cheng, Jiuyong Li et al.

An essential problem in causal inference is estimating causal effects from observational data. The problem becomes more challenging with the presence of unobserved confounders. When there are unobserved confounders, the commonly used back-door adjustment is not applicable. Although the instrumental variable (IV) methods can deal with unobserved confounders, they all assume that the treatment directly affects the outcome, and there is no mediator between the treatment and the outcome. This paper aims to use the front-door criterion to address the challenging problem with the presence of unobserved confounders and mediators. In practice, it is often difficult to identify the set of variables used for front-door adjustment from data. By leveraging the ability of deep generative models in representation learning, we propose FDVAE to learn the representation of a Front-Door adjustment set with a Variational AutoEncoder, instead of trying to search for a set of variables for front-door adjustment. Extensive experiments on synthetic datasets validate the effectiveness of FDVAE and its superiority over existing methods. The experiments also show that the performance of FDVAE is not sensitive to the causal strength of unobserved confounders and is feasible in the case of dimensionality mismatch between learned representations and the ground truth. We further apply the method to three real-world datasets to demonstrate its potential applications.

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.

Oscar Blessed Deho, Michael Bewong, Selasi Kwashie et al.

Over the last few decades, machine learning (ML) applications have grown exponentially, yielding several benefits to society. However, these benefits are tempered with concerns of discriminatory behaviours exhibited by ML models. In this regard, fairness in machine learning has emerged as a priority research area. Consequently, several fairness metrics and algorithms have been developed to mitigate against discriminatory behaviours that ML models may possess. Yet still, very little attention has been paid to the problem of naturally occurring changes in data patterns (\textit{aka} data distributional drift), and its impact on fairness algorithms and metrics. In this work, we study this problem comprehensively by analyzing 4 fairness-unaware baseline algorithms and 7 fairness-aware algorithms, carefully curated to cover the breadth of its typology, across 5 datasets including public and proprietary data, and evaluated them using 3 predictive performance and 10 fairness metrics. In doing so, we show that (1) data distributional drift is not a trivial occurrence, and in several cases can lead to serious deterioration of fairness in so-called fair models; (2) contrary to some existing literature, the size and direction of data distributional drift is not correlated to the resulting size and direction of unfairness; and (3) choice of, and training of fairness algorithms is impacted by the effect of data distributional drift which is largely ignored in the literature. Emanating from our findings, we synthesize several policy implications of data distributional drift on fairness algorithms that can be very relevant to stakeholders and practitioners.

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.

Sha Lu, Jixue Liu, Stefan Peters et al.

Anomaly detection in tabular data is challenging due to high dimensionality, complex feature dependencies, and heterogeneous noise. Many existing methods rely on proximity-based cues and may miss anomalies caused by violations of complex feature dependencies. Dependency-based anomaly detection provides a principled alternative by identifying anomalies as violations of dependencies among features. However, existing methods often struggle to model such dependencies robustly and to scale to high-dimensional data with complex dependency structures. To address these challenges, we propose uLEAD-TabPFN, a dependency-based anomaly detection framework built on Prior-Data Fitted Networks (PFNs). uLEAD-TabPFN identifies anomalies as violations of conditional dependencies in a learned latent space, leveraging frozen PFNs for dependency estimation. Combined with uncertainty-aware scoring, the proposed framework enables robust and scalable anomaly detection. Experiments on 57 tabular datasets from ADBench show that uLEAD-TabPFN achieves particularly strong performance in medium- and high-dimensional settings, where it attains the top average rank. On high-dimensional datasets, uLEAD-TabPFN improves the average ROC-AUC by nearly 20\% over the average baseline and by approximately 2.8\% over the best-performing baseline, while maintaining overall superior performance compared to state-of-the-art methods. Further analysis shows that uLEAD-TabPFN provides complementary anomaly detection capability, achieving strong performance on datasets where many existing methods struggle.

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.

Debo Cheng, Yang Xie, Ziqi Xu et al.

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.

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.

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.

Jixue Liu, Jiuyong Li, Stefan Peters et al.

Many studies have been done to detect smokes from satellite imagery. However, these prior methods are not still effective in detecting various smokes in complex backgrounds. Smokes present challenges in detection due to variations in density, color, lighting, and backgrounds such as clouds, haze, and/or mist, as well as the contextual nature of thin smoke. This paper addresses these challenges by proposing a new segmentation model called VTrUNet which consists of a virtual band construction module to capture spectral patterns and a transformer boosted UNet to capture long range contextual features. The model takes imagery of six bands: red, green, blue, near infrared, and two shortwave infrared bands as input. To show the advantages of the proposed model, the paper presents extensive results for various possible model architectures improving UNet and draws interesting conclusions including that adding more modules to a model does not always lead to a better performance. The paper also compares the proposed model with very recently proposed and related models for smoke segmentation and shows that the proposed model performs the best and makes significant improvements on prediction performances

Debo Cheng, Jiuyong Li, Lin Liu et al.

Unobserved confounding is the main obstacle to causal effect estimation from observational data. Instrumental variables (IVs) are widely used for causal effect estimation when there exist latent confounders. With the standard IV method, when a given IV is valid, unbiased estimation can be obtained, but the validity requirement on a standard IV is strict and untestable. Conditional IVs have been proposed to relax the requirement of standard IVs by conditioning on a set of observed variables (known as a conditioning set for a conditional IV). However, the criterion for finding a conditioning set for a conditional IV needs a directed acyclic graph (DAG) representing the causal relationships of both observed and unobserved variables. This makes it challenging to discover a conditioning set directly from data. In this paper, by leveraging maximal ancestral graphs (MAGs) for causal inference with latent variables, we study the graphical properties of ancestral IVs, a type of conditional IVs using MAGs, and develop the theory to support data-driven discovery of the conditioning set for a given ancestral IV in data under the pretreatment variable assumption. Based on the theory, we develop an algorithm for unbiased causal effect estimation with a given ancestral IV and observational data. Extensive experiments on synthetic and real-world datasets demonstrate the performance of the algorithm in comparison with existing IV methods.

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.

Zhenlong Xu, Ziqi Xu, Jixue Liu et al.

The increasing application of machine learning techniques in everyday decision-making processes has brought concerns about the fairness of algorithmic decision-making. This paper concerns the problem of collider bias which produces spurious associations in fairness assessment and develops theorems to guide fairness assessment avoiding the collider bias. We consider a real-world application of auditing a trained classifier by an audit agency. We propose an unbiased assessment algorithm by utilising the developed theorems to reduce collider biases in the assessment. Experiments and simulations show the proposed algorithm reduces collider biases significantly in the assessment and is promising in auditing trained classifiers.

Debo Cheng, Jiuyong Li, Lin Liu et al.

Having a large number of covariates can have a negative impact on the quality of causal effect estimation since confounding adjustment becomes unreliable when the number of covariates is large relative to the samples available. Propensity score is a common way to deal with a large covariate set, but the accuracy of propensity score estimation (normally done by logistic regression) is also challenged by large number of covariates. In this paper, we prove that a large covariate set can be reduced to a lower dimensional representation which captures the complete information for adjustment in causal effect estimation. The theoretical result enables effective data-driven algorithms for causal effect estimation. We develop an algorithm which employs a supervised kernel dimension reduction method to search for a lower dimensional representation for the original covariates, and then utilizes nearest neighbor matching in the reduced covariate space to impute the counterfactual outcomes to avoid large-sized covariate set problem. The proposed algorithm is evaluated on two semi-synthetic and three real-world datasets and the results have demonstrated the effectiveness of the algorithm.

Jiuyong Li, Weijia Zhang, Lin Liu et al.

In many applications, there is a need to predict the effect of an intervention on different individuals from data. For example, which customers are persuadable by a product promotion? which patients should be treated with a certain type of treatment? These are typical causal questions involving the effect or the change in outcomes made by an intervention. The questions cannot be answered with traditional classification methods as they only use associations to predict outcomes. For personalised marketing, these questions are often answered with uplift modelling. The objective of uplift modelling is to estimate causal effect, but its literature does not discuss when the uplift represents causal effect. Causal heterogeneity modelling can solve the problem, but its assumption of unconfoundedness is untestable in data. So practitioners need guidelines in their applications when using the methods. In this paper, we use causal classification for a set of personalised decision making problems, and differentiate it from classification. We discuss the conditions when causal classification can be resolved by uplift (and causal heterogeneity) modelling methods. We also propose a general framework for causal classification, by using off-the-shelf supervised methods for flexible implementations. Experiments have shown two instantiations of the framework work for causal classification and for uplift (causal heterogeneity) modelling, and are competitive with the other uplift (causal heterogeneity) modelling methods.

Debo Cheng, Jiuyong Li, Lin Liu et al.

Causal effect estimation from observational data is a crucial but challenging task. Currently, only a limited number of data-driven causal effect estimation methods are available. These methods either provide only a bound estimation of the causal effect of a treatment on the outcome, or generate a unique estimation of the causal effect, but making strong assumptions on data and having low efficiency. In this paper, we identify a practical problem setting and propose an approach to achieving unique and unbiased estimation of causal effects from data with hidden variables. For the approach, we have developed the theorems to support the discovery of the proper covariate sets for confounding adjustment (adjustment sets). Based on the theorems, two algorithms are proposed for finding the proper adjustment sets from data with hidden variables to obtain unbiased and unique causal effect estimation. Experiments with synthetic datasets generated using five benchmark Bayesian networks and four real-world datasets have demonstrated the efficiency and effectiveness of the proposed algorithms, indicating the practicability of the identified problem setting and the potential of the proposed approach in real-world applications.

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.

Jixue Liu, Selasi Kwashie, Jiuyong Li et al.

Entity linking and resolution is a fundamental database problem with applications in data integration, data cleansing, information retrieval, knowledge fusion, and knowledge-base population. It is the task of accurately identifying multiple, differing, and possibly contradicting representations of the same real-world entity in data. In this work, we propose an entity linking and resolution system capable of linking entities across different databases and mentioned-entities extracted from text data. Our entity linking/resolution solution, called Certus, uses a graph model to represent the profiles of entities. The graph model is versatile, thus, it is capable of handling multiple values for an attribute or a relationship, as well as the provenance descriptions of the values. Provenance descriptions of a value provide the settings of the value, such as validity periods, sources, security requirements, etc. This paper presents the architecture for the entity linking system, the logical, physical, and indexing models used in the system, and the general linking process. Furthermore, we demonstrate the performance of update operations of the physical storage models when the system is implemented in two state-of-the-art database management systems, HBase and Postgres.

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.

Jiuyong Li, Lin Liu, Jixue Liu et al.

It is common that a trained classification model is applied to the operating data that is deviated from the training data because of noise. This paper demonstrates that an ensemble classifier, Diversified Multiple Tree (DMT), is more robust in classifying noisy data than other widely used ensemble methods. DMT is tested on three real world biomedical data sets from different laboratories in comparison with four benchmark ensemble classifiers. Experimental results show that DMT is significantly more accurate than other benchmark ensemble classifiers on noisy test data. We also discuss a limitation of DMT and its possible variations.

Jiuyong Li, Thuc Duy Le, Lin Liu et al.

Randomised controlled trials (RCTs) are the most effective approach to causal discovery, but in many circumstances it is impossible to conduct RCTs. Therefore observational studies based on passively observed data are widely accepted as an alternative to RCTs. However, in observational studies, prior knowledge is required to generate the hypotheses about the cause-effect relationships to be tested, hence they can only be applied to problems with available domain knowledge and a handful of variables. In practice, many data sets are of high dimensionality, which leaves observational studies out of the opportunities for causal discovery from such a wealth of data sources. In another direction, many efficient data mining methods have been developed to identify associations among variables in large data sets. The problem is, causal relationships imply associations, but the reverse is not always true. However we can see the synergy between the two paradigms here. Specifically, association rule mining can be used to deal with the high-dimensionality problem while observational studies can be utilised to eliminate non-causal associations. In this paper we propose the concept of causal rules (CRs) and develop an algorithm for mining CRs in large data sets. We use the idea of retrospective cohort studies to detect CRs based on the results of association rule mining. Experiments with both synthetic and real world data sets have demonstrated the effectiveness and efficiency of CR mining. In comparison with the commonly used causal discovery methods, the proposed approach in general is faster and has better or competitive performance in finding correct or sensible causes. It is also capable of finding a cause consisting of multiple variables, a feature that other causal discovery methods do not possess.

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.