Jake Fawkes

Jake Fawkes, Robert Hu, Robin J. Evans et al.

With the widespread application of causal inference, it is increasingly important to have tools which can test for the presence of causal effects in a diverse array of circumstances. In this vein we focus on the problem of testing for \emph{distributional} causal effects, where the treatment affects not just the mean, but also higher order moments of the distribution, as well as multidimensional or structured outcomes. We build upon a previously introduced framework, Counterfactual Mean Embeddings, for representing causal distributions within Reproducing Kernel Hilbert Spaces (RKHS) by proposing new, improved, estimators for the distributional embeddings. These improved estimators are inspired by doubly robust estimators of the causal mean, using a similar form within the kernel space. We analyse these estimators, proving they retain the doubly robust property and have improved convergence rates compared to the original estimators. This leads to new permutation based tests for distributional causal effects, using the estimators we propose as tests statistics. We experimentally and theoretically demonstrate the validity of our tests.

Shahine Bouabid, Jake Fawkes, Dino Sejdinovic

A directed acyclic graph (DAG) provides valuable prior knowledge that is often discarded in regression tasks in machine learning. We show that the independences arising from the presence of collider structures in DAGs provide meaningful inductive biases, which constrain the regression hypothesis space and improve predictive performance. We introduce collider regression, a framework to incorporate probabilistic causal knowledge from a collider in a regression problem. When the hypothesis space is a reproducing kernel Hilbert space, we prove a strictly positive generalisation benefit under mild assumptions and provide closed-form estimators of the empirical risk minimiser. Experiments on synthetic and climate model data demonstrate performance gains of the proposed methodology.

Jake Fawkes, Robin J. Evans

In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major question surrounding counterfactual invariance, how does it relate to conditional independence? We show that whilst counterfactual invariance implies conditional independence, conditional independence does not give any implications about the degree or likelihood of satisfying counterfactual invariance. Furthermore, we show that for discrete causal models counterfactually invariant functions are often constrained to be functions of particular variables, or even constant.

Jake Fawkes, Nic Fishman, Mel Andrews et al.

Fairness metrics are a core tool in the fair machine learning literature (FairML), used to determine that ML models are, in some sense, "fair". Real-world data, however, are typically plagued by various measurement biases and other violated assumptions, which can render fairness assessments meaningless. We adapt tools from causal sensitivity analysis to the FairML context, providing a general framework which (1) accommodates effectively any combination of fairness metric and bias that can be posed in the "oblivious setting"; (2) allows researchers to investigate combinations of biases, resulting in non-linear sensitivity; and (3) enables flexible encoding of domain-specific constraints and assumptions. Employing this framework, we analyze the sensitivity of the most common parity metrics under 3 varieties of classifier across 14 canonical fairness datasets. Our analysis reveals the striking fragility of fairness assessments to even minor dataset biases. We show that causal sensitivity analysis provides a powerful and necessary toolkit for gauging the informativeness of parity metric evaluations. Our repository is available here: https://github.com/Jakefawkes/fragile_fair.

Jake Fawkes, Michael O'Riordan, Athanasios Vlontzos et al.

Observational data is often readily available in large quantities, but can lead to biased causal effect estimates due to the presence of unobserved confounding. Recent works attempt to remove this bias by supplementing observational data with experimental data, which, when available, is typically on a smaller scale due to the time and cost involved in running a randomised controlled trial. In this work, we prove a theorem that places fundamental limits on this ``best of both worlds'' approach. Using the framework of impossible inference, we show that although it is possible to use experimental data to \emph{falsify} causal effect estimates from observational data, in general it is not possible to \emph{validate} such estimates. Our theorem proves that while experimental data can be used to detect bias in observational studies, without additional assumptions on the smoothness of the correction function, it can not be used to remove it. We provide a practical example of such an assumption, developing a novel Gaussian Process based approach to construct intervals which contain the true treatment effect with high probability, both inside and outside of the support of the experimental data. We demonstrate our methodology on both simulated and semi-synthetic datasets and make the \href{https://github.com/Jakefawkes/Obs_and_exp_data}{code available}.

Omri Ben-Dov, Jake Fawkes, Samira Samadi et al.

Collective action in machine learning is the study of the control that a coordinated group can have over machine learning algorithms. While previous research has concentrated on assessing the impact of collectives against Bayes (sub-)optimal classifiers, this perspective is limited in that it does not account for the choice of learning algorithm. Since classifiers seldom behave like Bayes classifiers and are influenced by the choice of learning algorithms along with their inherent biases, in this work we initiate the study of how the choice of the learning algorithm plays a role in the success of a collective in practical settings. Specifically, we focus on distributionally robust optimization (DRO), popular for improving a worst group error, and on the ubiquitous stochastic gradient descent (SGD), due to its inductive bias for "simpler" functions. Our empirical results, supported by a theoretical foundation, show that the effective size and success of the collective are highly dependent on properties of the learning algorithm. This highlights the necessity of taking the learning algorithm into account when studying the impact of collective action in machine learning.

Erdun Gao, Jake Fawkes, Dino Sejdinovic

Estimating the Conditional Average Treatment Effect (CATE) is often constrained by the high cost of obtaining outcome measurements, making active learning essential. However, conventional active learning strategies suffer from a fundamental objective mismatch. They are designed to reduce uncertainty in model parameters or in observable factual outcomes, failing to directly target the unobservable causal quantities that are the true objects of interest. To address this misalignment, we introduce the principle of causal objective alignment, which posits that acquisition functions should target unobservable causal quantities, such as the potential outcomes and the CATE, rather than indirect proxies. We operationalize this principle through the Causal-EPIG framework, which adapts the information-theoretic criterion of Expected Predictive Information Gain (EPIG) to explicitly quantify the value of a query in terms of reducing uncertainty about unobservable causal quantities. From this unified framework, we derive two distinct strategies that embody a fundamental trade-off: a comprehensive approach that robustly models the full causal mechanisms via the joint potential outcomes, and a focused approach that directly targets the CATE estimand for maximum sample efficiency. Extensive experiments demonstrate that our strategies consistently outperform standard baselines, and crucially, reveal that the optimal strategy is context-dependent, contingent on the base estimator and data complexity. Our framework thus provides a principled guide for sample-efficient CATE estimation in practice.

Jake Fawkes, Robin Evans, Dino Sejdinovic

In this paper we look at popular fairness methods that use causal counterfactuals. These methods capture the intuitive notion that a prediction is fair if it coincides with the prediction that would have been made if someone's race, gender or religion were counterfactually different. In order to achieve this, we must have causal models that are able to capture what someone would be like if we were to counterfactually change these traits. However, we argue that any model that can do this must lie outside the particularly well behaved class that is commonly considered in the fairness literature. This is because in fairness settings, models in this class entail a particularly strong causal assumption, normally only seen in a randomised controlled trial. We argue that in general this is unlikely to hold. Furthermore, we show in many cases it can be explicitly rejected due to the fact that samples are selected from a wider population. We show this creates difficulties for counterfactual fairness as well as for the application of more general causal fairness methods.