Jeroen Berrevoets

Jeroen Berrevoets, Krzysztof Kacprzyk, Zhaozhi Qian et al.

Causal deep learning (CDL) is a new and important research area in the larger field of machine learning. With CDL, researchers aim to structure and encode causal knowledge in the extremely flexible representation space of deep learning models. Doing so will lead to more informed, robust, and general predictions and inference -- which is important! However, CDL is still in its infancy. For example, it is not clear how we ought to compare different methods as they are so different in their output, the way they encode causal knowledge, or even how they represent this knowledge. This is a living paper that categorises methods in causal deep learning beyond Pearl's ladder of causation. We refine the rungs in Pearl's ladder, while also adding a separate dimension that categorises the parametric assumptions of both input and representation, arriving at the map of causal deep learning. Our map covers machine learning disciplines such as supervised learning, reinforcement learning, generative modelling and beyond. Our paradigm is a tool which helps researchers to: find benchmarks, compare methods, and most importantly: identify research gaps. With this work we aim to structure the avalanche of papers being published on causal deep learning. While papers on the topic are being published daily, our map remains fixed. We open-source our map for others to use as they see fit: perhaps to offer guidance in a related works section, or to better highlight the contribution of their paper.

Jeroen Berrevoets, Krzysztof Kacprzyk, Zhaozhi Qian et al.

Causality has the potential to truly transform the way we solve a large number of real-world problems. Yet, so far, its potential largely remains to be unlocked as causality often requires crucial assumptions which cannot be tested in practice. To address this challenge, we propose a new way of thinking about causality -- we call this causal deep learning. Our causal deep learning framework spans three dimensions: (1) a structural dimension, which incorporates partial yet testable causal knowledge rather than assuming either complete or no causal knowledge among the variables of interest; (2) a parametric dimension, which encompasses parametric forms that capture the type of relationships among the variables of interest; and (3) a temporal dimension, which captures exposure times or how the variables of interest interact (possibly causally) over time. Causal deep learning enables us to make progress on a variety of real-world problems by leveraging partial causal knowledge (including independencies among variables) and quantitatively characterising causal relationships among variables of interest (possibly over time). Our framework clearly identifies which assumptions are testable and which ones are not, such that the resulting solutions can be judiciously adopted in practice. Using our formulation we can combine or chain together causal representations to solve specific problems without losing track of which assumptions are required to build these solutions, pushing real-world impact in healthcare, economics and business, environmental sciences and education, through causal deep learning.

Jeroen Berrevoets, Nabeel Seedat, Fergus Imrie et al.

Directed acyclic graphs (DAGs) encode a lot of information about a particular distribution in their structure. However, compute required to infer these structures is typically super-exponential in the number of variables, as inference requires a sweep of a combinatorially large space of potential structures. That is, until recent advances made it possible to search this space using a differentiable metric, drastically reducing search time. While this technique -- named NOTEARS -- is widely considered a seminal work in DAG-discovery, it concedes an important property in favour of differentiability: transportability. To be transportable, the structures discovered on one dataset must apply to another dataset from the same domain. We introduce D-Struct which recovers transportability in the discovered structures through a novel architecture and loss function while remaining fully differentiable. Because D-Struct remains differentiable, our method can be easily adopted in existing differentiable architectures, as was previously done with NOTEARS. In our experiments, we empirically validate D-Struct with respect to edge accuracy and structural Hamming distance in a variety of settings.

Christopher Bockel-Rickermann, Toon Vanderschueren, Jeroen Berrevoets et al.

Estimating a unit's responses to interventions with an associated dose, the "conditional average dose response" (CADR), is relevant in a variety of domains, from healthcare to business, economics, and beyond. Such a response typically needs to be estimated from observational data, which introduces several challenges. That is why the machine learning (ML) community has proposed several tailored CADR estimators. Yet, the proposal of most of these methods requires strong assumptions on the distribution of data and the assignment of interventions, which go beyond the standard assumptions in causal inference. Whereas previous works have so far focused on smooth shifts in covariate distributions across doses, in this work, we will study estimating CADR from clustered data and where different doses are assigned to different segments of a population. On a novel benchmarking dataset, we show the impacts of clustered data on model performance and propose an estimator, CBRNet, that learns cluster-agnostic and hence dose-agnostic covariate representations through representation balancing for unbiased CADR inference. We run extensive experiments to illustrate the workings of our method and compare it with the state of the art in ML for CADR estimation.

Daan Caljon, Jente Van Belle, Jeroen Berrevoets et al.

In Influence Maximization (IM), the objective is to -- given a budget -- select the optimal set of entities in a network to target with a treatment so as to maximize the total effect. For instance, in marketing, the objective is to target the set of customers that maximizes the total response rate, resulting from both direct treatment effects on targeted customers and indirect, spillover, effects that follow from targeting these customers. Recently, new methods to estimate treatment effects in the presence of network interference have been proposed. However, the issue of how to leverage these models to make better treatment allocation decisions has been largely overlooked. Traditionally, in Uplift Modeling (UM), entities are ranked according to estimated treatment effect, and the top entities are allocated treatment. Since, in a network context, entities influence each other, the UM ranking approach will be suboptimal. The problem of finding the optimal treatment allocation in a network setting is \textcolor{red}{NP-hard,} and generally has to be solved heuristically. To fill the gap between IM and UM, we propose OTAPI: Optimizing Treatment Allocation in the Presence of Interference to find solutions to the IM problem using treatment effect estimates. OTAPI consists of two steps. First, a causal estimator is trained to predict treatment effects in a network setting. Second, this estimator is leveraged to identify an optimal treatment allocation by integrating it into classic IM algorithms. We demonstrate that this novel method outperforms classic IM and UM approaches on both synthetic and semi-synthetic datasets.

Jeroen Berrevoets, Julianna Piskorz, Robert Davis et al.

Estimating treatment effects (TE) from observational data is a critical yet complex task in many fields, from healthcare and economics to public policy. While recent advances in machine learning and causal inference have produced powerful estimation techniques, their adoption remains limited due to the need for deep expertise in causal assumptions, adjustment strategies, and model selection. In this paper, we introduce CATE-B, an open-source co-pilot system that uses large language models (LLMs) within an agentic framework to guide users through the end-to-end process of treatment effect estimation. CATE-B assists in (i) constructing a structural causal model via causal discovery and LLM-based edge orientation, (ii) identifying robust adjustment sets through a novel Minimal Uncertainty Adjustment Set criterion, and (iii) selecting appropriate regression methods tailored to the causal structure and dataset characteristics. To encourage reproducibility and evaluation, we release a suite of benchmark tasks spanning diverse domains and causal complexities. By combining causal inference with intelligent, interactive assistance, CATE-B lowers the barrier to rigorous causal analysis and lays the foundation for a new class of benchmarks in automated treatment effect estimation.

Jeroen Berrevoets, Sam Verboven, Wouter Verbeke

Applying causal inference models in areas such as economics, healthcare and marketing receives great interest from the machine learning community. In particular, estimating the individual-treatment-effect (ITE) in settings such as precision medicine and targeted advertising has peaked in application. Optimising this ITE under the strong-ignorability-assumption -- meaning all confounders expressing influence on the outcome of a treatment are registered in the data -- is often referred to as uplift modeling (UM). While these techniques have proven useful in many settings, they suffer vividly in a dynamic environment due to concept drift. Take for example the negative influence on a marketing campaign when a competitor product is released. To counter this, we propose the uplifted contextual multi-armed bandit (U-CMAB), a novel approach to optimise the ITE by drawing upon bandit literature. Experiments on real and simulated data indicate that our proposed approach compares favourably against the state-of-the-art. All our code can be found online at https://github.com/vub-dl/u-cmab.

Krzysztof Kacprzyk, Samuel Holt, Jeroen Berrevoets et al.

Inferring unbiased treatment effects has received widespread attention in the machine learning community. In recent years, our community has proposed numerous solutions in standard settings, high-dimensional treatment settings, and even longitudinal settings. While very diverse, the solution has mostly relied on neural networks for inference and simultaneous correction of assignment bias. New approaches typically build on top of previous approaches by proposing new (or refined) architectures and learning algorithms. However, the end result -- a neural-network-based inference machine -- remains unchallenged. In this paper, we introduce a different type of solution in the longitudinal setting: a closed-form ordinary differential equation (ODE). While we still rely on continuous optimization to learn an ODE, the resulting inference machine is no longer a neural network. Doing so yields several advantages such as interpretability, irregular sampling, and a different set of identification assumptions. Above all, we consider the introduction of a completely new type of solution to be our most important contribution as it may spark entirely new innovations in treatment effects in general. We facilitate this by formulating our contribution as a framework that can transform any ODE discovery method into a treatment effects method.

Nicolas Huynh, Jeroen Berrevoets, Nabeel Seedat et al. · cambridge

Identification and appropriate handling of inconsistencies in data at deployment time is crucial to reliably use machine learning models. While recent data-centric methods are able to identify such inconsistencies with respect to the training set, they suffer from two key limitations: (1) suboptimality in settings where features exhibit statistical independencies, due to their usage of compressive representations and (2) lack of localization to pin-point why a sample might be flagged as inconsistent, which is important to guide future data collection. We solve these two fundamental limitations using directed acyclic graphs (DAGs) to encode the training set's features probability distribution and independencies as a structure. Our method, called DAGnosis, leverages these structural interactions to bring valuable and insightful data-centric conclusions. DAGnosis unlocks the localization of the causes of inconsistencies on a DAG, an aspect overlooked by previous approaches. Moreover, we show empirically that leveraging these interactions (1) leads to more accurate conclusions in detecting inconsistencies, as well as (2) provides more detailed insights into why some samples are flagged.

Tennison Liu, Jeroen Berrevoets, Zhaozhi Qian et al.

This paper addresses unsupervised representation learning on tabular data containing multiple views generated by distinct sources of measurement. Traditional methods, which tackle this problem using the multi-view framework, are constrained by predefined assumptions that assume feature sets share the same information and representations should learn globally shared factors. However, this assumption is not always valid for real-world tabular datasets with complex dependencies between feature sets, resulting in localized information that is harder to learn. To overcome this limitation, we propose a data-driven approach that learns feature set dependencies by representing feature sets as graph nodes and their relationships as learnable edges. Furthermore, we introduce LEGATO, a novel hierarchical graph autoencoder that learns a smaller, latent graph to aggregate information from multiple views dynamically. This approach results in latent graph components that specialize in capturing localized information from different regions of the input, leading to superior downstream performance.

Tobias Hatt, Jeroen Berrevoets, Alicia Curth et al.

Estimating heterogeneous treatment effects is an important problem across many domains. In order to accurately estimate such treatment effects, one typically relies on data from observational studies or randomized experiments. Currently, most existing works rely exclusively on observational data, which is often confounded and, hence, yields biased estimates. While observational data is confounded, randomized data is unconfounded, but its sample size is usually too small to learn heterogeneous treatment effects. In this paper, we propose to estimate heterogeneous treatment effects by combining large amounts of observational data and small amounts of randomized data via representation learning. In particular, we introduce a two-step framework: first, we use observational data to learn a shared structure (in form of a representation); and then, we use randomized data to learn the data-specific structures. We analyze the finite sample properties of our framework and compare them to several natural baselines. As such, we derive conditions for when combining observational and randomized data is beneficial, and for when it is not. Based on this, we introduce a sample-efficient algorithm, called CorNet. We use extensive simulation studies to verify the theoretical properties of CorNet and multiple real-world datasets to demonstrate our method's superiority compared to existing methods.

Jeroen Berrevoets, Fergus Imrie, Trent Kyono et al.

Missing data is a systemic problem in practical scenarios that causes noise and bias when estimating treatment effects. This makes treatment effect estimation from data with missingness a particularly tricky endeavour. A key reason for this is that standard assumptions on missingness are rendered insufficient due to the presence of an additional variable, treatment, besides the input (e.g. an individual) and the label (e.g. an outcome). The treatment variable introduces additional complexity with respect to why some variables are missing that is not fully explored by previous work. In our work we introduce mixed confounded missingness (MCM), a new missingness mechanism where some missingness determines treatment selection and other missingness is determined by treatment selection. Given MCM, we show that naively imputing all data leads to poor performing treatment effects models, as the act of imputation effectively removes information necessary to provide unbiased estimates. However, no imputation at all also leads to biased estimates, as missingness determined by treatment introduces bias in covariates. Our solution is selective imputation, where we use insights from MCM to inform precisely which variables should be imputed and which should not. We empirically demonstrate how various learners benefit from selective imputation compared to other solutions for missing data. We highlight that our experiments encompass both average treatment effects and conditional average treatment effects.

Jeroen Berrevoets, Alicia Curth, Ioana Bica et al.

Choosing the best treatment-plan for each individual patient requires accurate forecasts of their outcome trajectories as a function of the treatment, over time. While large observational data sets constitute rich sources of information to learn from, they also contain biases as treatments are rarely assigned randomly in practice. To provide accurate and unbiased forecasts, we introduce the Disentangled Counterfactual Recurrent Network (DCRN), a novel sequence-to-sequence architecture that estimates treatment outcomes over time by learning representations of patient histories that are disentangled into three separate latent factors: a treatment factor, influencing only treatment selection; an outcome factor, influencing only the outcome; and a confounding factor, influencing both. With an architecture that is completely inspired by the causal structure of treatment influence over time, we advance forecast accuracy and disease understanding, as our architecture allows for practitioners to infer which patient features influence which part in a patient's trajectory, contrasting other approaches in this domain. We demonstrate that DCRN outperforms current state-of-the-art methods in forecasting treatment responses, on both real and simulated data.

Boris van Breugel, Trent Kyono, Jeroen Berrevoets et al.

Machine learning models have been criticized for reflecting unfair biases in the training data. Instead of solving for this by introducing fair learning algorithms directly, we focus on generating fair synthetic data, such that any downstream learner is fair. Generating fair synthetic data from unfair data - while remaining truthful to the underlying data-generating process (DGP) - is non-trivial. In this paper, we introduce DECAF: a GAN-based fair synthetic data generator for tabular data. With DECAF we embed the DGP explicitly as a structural causal model in the input layers of the generator, allowing each variable to be reconstructed conditioned on its causal parents. This procedure enables inference time debiasing, where biased edges can be strategically removed for satisfying user-defined fairness requirements. The DECAF framework is versatile and compatible with several popular definitions of fairness. In our experiments, we show that DECAF successfully removes undesired bias and - in contrast to existing methods - is capable of generating high-quality synthetic data. Furthermore, we provide theoretical guarantees on the generator's convergence and the fairness of downstream models.

Yao Zhang, Jeroen Berrevoets, Mihaela van der Schaar

Conditional average treatment effects (CATEs) allow us to understand the effect heterogeneity across a large population of individuals. However, typical CATE learners assume all confounding variables are measured in order for the CATE to be identifiable. This requirement can be satisfied by collecting many variables, at the expense of increased sample complexity for estimating CATEs. To combat this, we propose an energy-based model (EBM) that learns a low-dimensional representation of the variables by employing a noise contrastive loss function. With our EBM we introduce a preprocessing step that alleviates the dimensionality curse for any existing learner developed for estimating CATEs. We prove that our EBM keeps the representations partially identifiable up to some universal constant, as well as having universal approximation capability. These properties enable the representations to converge and keep the CATE estimates consistent. Experiments demonstrate the convergence of the representations, as well as show that estimating CATEs on our representations performs better than on the variables or the representations obtained through other dimensionality reduction methods.

Sam Verboven, Muhammad Hafeez Chaudhary, Jeroen Berrevoets et al.

Multi-task learning (MTL) can improve performance on a task by sharing representations with one or more related auxiliary-tasks. Usually, MTL-networks are trained on a composite loss function formed by a constant weighted combination of the separate task losses. In practice, constant loss weights lead to poor results for two reasons: (i) the relevance of the auxiliary tasks can gradually drift throughout the learning process; (ii) for mini-batch based optimisation, the optimal task weights vary significantly from one update to the next depending on mini-batch sample composition. We introduce HydaLearn, an intelligent weighting algorithm that connects main-task gain to the individual task gradients, in order to inform dynamic loss weighting at the mini-batch level, addressing i and ii. Using HydaLearn, we report performance increases on synthetic data, as well as on two supervised learning domains.

Wouter Verbeke, Diego Olaya, Jeroen Berrevoets et al.

Classification is a well-studied machine learning task which concerns the assignment of instances to a set of outcomes. Classification models support the optimization of managerial decision-making across a variety of operational business processes. For instance, customer churn prediction models are adopted to increase the efficiency of retention campaigns by optimizing the selection of customers that are to be targeted. Cost-sensitive and causal classification methods have independently been proposed to improve the performance of classification models. The former considers the benefits and costs of correct and incorrect classifications, such as the benefit of a retained customer, whereas the latter estimates the causal effect of an action, such as a retention campaign, on the outcome of interest. This study integrates cost-sensitive and causal classification by elaborating a unifying evaluation framework. The framework encompasses a range of existing and novel performance measures for evaluating both causal and conventional classification models in a cost-sensitive as well as a cost-insensitive manner. We proof that conventional classification is a specific case of causal classification in terms of a range of performance measures when the number of actions is equal to one. The framework is shown to instantiate to application-specific cost-sensitive performance measures that have been recently proposed for evaluating customer retention and response uplift models, and allows to maximize profitability when adopting a causal classification model for optimizing decision-making. The proposed framework paves the way toward the development of cost-sensitive causal learning methods and opens a range of opportunities for improving data-driven business decision-making.

Sam Verboven, Jeroen Berrevoets, Chris Wuytens et al.

In the majority of executive domains, a notion of normality is involved in most strategic decisions. However, few data-driven tools that support strategic decision-making are available. We introduce and extend the use of autoencoders to provide strategically relevant granular feedback. A first experiment indicates that experts are inconsistent in their decision making, highlighting the need for strategic decision support. Furthermore, using two large industry-provided human resources datasets, the proposed solution is evaluated in terms of ranking accuracy, synergy with human experts, and dimension-level feedback. This three-point scheme is validated using (a) synthetic data, (b) the perspective of data quality, (c) blind expert validation, and (d) transparent expert evaluation. Our study confirms several principal weaknesses of human decision-making and stresses the importance of synergy between a model and humans. Moreover, unsupervised learning and in particular the autoencoder are shown to be valuable tools for strategic decision-making.

Jeroen Berrevoets, Wouter Verbeke

Uplift modeling requires experimental data, preferably collected in random fashion. This places a logistical and financial burden upon any organisation aspiring such models. Once deployed, uplift models are subject to effects from concept drift. Hence, methods are being developed that are able to learn from newly gained experience, as well as handle drifting environments. As these new methods attempt to eliminate the need for experimental data, another approach to test such methods must be formulated. Therefore, we propose a method to simulate environments that offer causal relationships in their parameters.