Towards Bounding Causal Effects under Markov Equivalence

Predicting the effect of unseen interventions is a fundamental research question across the data sciences. It is well established that, in general, such questions cannot be answered definitively from observational data, e.g., as a consequence of unobserved confounding. A generalization of this task is to determine non-trivial bounds on causal effects induced by the data, also known as the task of partial causal identification. In the literature, several algorithms have been developed for solving this problem. Most, however, require a known parametric form or a fully specified causal diagram as input, which is usually not available in practical applications. In this paper, we assume as input a less informative structure known as a Partial Ancestral Graph, which represents a Markov equivalence class of causal diagrams and is learnable from observational data. In this more "data-driven" setting, we provide a systematic algorithm to derive bounds on causal effects that can be computed analytically.

Functional Causal Bayesian Optimization

We propose functional causal Bayesian optimization (fCBO), a method for finding interventions that optimize a target variable in a known causal graph. fCBO extends the CBO family of methods to enable functional interventions, which set a variable to be a deterministic function of other variables in the graph. fCBO models the unknown objectives with Gaussian processes whose inputs are defined in a reproducing kernel Hilbert space, thus allowing to compute distances among vector-valued functions. In turn, this enables to sequentially select functions to explore by maximizing an expected improvement acquisition functional while keeping the typical computational tractability of standard BO settings. We introduce graphical criteria that establish when considering functional interventions allows attaining better target effects, and conditions under which selected interventions are also optimal for conditional target effects. We demonstrate the benefits of the method in a synthetic and in a real-world causal graph.

Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations

Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare by assisting decision-makers to answer ''what-iF'' questions. Existing causal inference approaches typically consider regular, discrete-time intervals between observations and treatment decisions and hence are unable to naturally model irregularly sampled data, which is the common setting in practice. To handle arbitrary observation patterns, we interpret the data as samples from an underlying continuous-time process and propose to model its latent trajectory explicitly using the mathematics of controlled differential equations. This leads to a new approach, the Treatment Effect Neural Controlled Differential Equation (TE-CDE), that allows the potential outcomes to be evaluated at any time point. In addition, adversarial training is used to adjust for time-dependent confounding which is critical in longitudinal settings and is an added challenge not encountered in conventional time-series. To assess solutions to this problem, we propose a controllable simulation environment based on a model of tumor growth for a range of scenarios with irregular sampling reflective of a variety of clinical scenarios. TE-CDE consistently outperforms existing approaches in all simulated scenarios with irregular sampling.

Generalization bounds and algorithms for estimating conditional average treatment effect of dosage

We investigate the task of estimating the conditional average causal effect of treatment-dosage pairs from a combination of observational data and assumptions on the causal relationships in the underlying system. This has been a longstanding challenge for fields of study such as epidemiology or economics that require a treatment-dosage pair to make decisions but may not be able to run randomized trials to precisely quantify their effect and heterogeneity across individuals. In this paper, we extend (Shalit et al, 2017) to give new bounds on the counterfactual generalization error in the context of a continuous dosage parameter which relies on a different approach to defining counterfactuals and assignment bias adjustment. This result then guides the definition of new learning objectives that can be used to train representation learning algorithms for which we show empirically new state-of-the-art performance results across several benchmark datasets for this problem, including in comparison to doubly-robust estimation methods.

MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms

Missing data is an important problem in machine learning practice. Starting from the premise that imputation methods should preserve the causal structure of the data, we develop a regularization scheme that encourages any baseline imputation method to be causally consistent with the underlying data generating mechanism. Our proposal is a causally-aware imputation algorithm (MIRACLE). MIRACLE iteratively refines the imputation of a baseline by simultaneously modeling the missingness generating mechanism, encouraging imputation to be consistent with the causal structure of the data. We conduct extensive experiments on synthetic and a variety of publicly available datasets to show that MIRACLE is able to consistently improve imputation over a variety of benchmark methods across all three missingness scenarios: at random, completely at random, and not at random.

Consistency of mechanistic causal discovery in continuous-time using Neural ODEs

The discovery of causal mechanisms from time series data is a key problem in fields working with complex systems. Most identifiability results and learning algorithms assume the underlying dynamics to be discrete in time. Comparatively few, in contrast, explicitly define causal associations in infinitesimal intervals of time, independently of the scale of observation and of the regularity of sampling. In this paper, we consider causal discovery in continuous-time for the study of dynamical systems. We prove that for vector fields parameterized in a large class of neural networks, adaptive regularization schemes consistently recover causal graphs in systems of ordinary differential equations (ODEs). Using this insight, we propose a causal discovery algorithm based on penalized Neural ODEs that we show to be applicable to the general setting of irregularly-sampled multivariate time series and to strongly outperform the state of the art.

Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding

Unobserved confounding is one of the greatest challenges for causal discovery. The case in which unobserved variables have a potentially widespread effect on many of the observed ones is particularly difficult because most pairs of variables are conditionally dependent given any other subset. In this paper, we show that beyond conditional independencies, unobserved confounding in this setting leaves a characteristic footprint in the observed data distribution that allows for disentangling spurious and causal effects. Using this insight, we demonstrate that a sparse linear Gaussian directed acyclic graph among observed variables may be recovered approximately and propose an adjusted score-based causal discovery algorithm that may be implemented with general-purpose solvers and scales to high-dimensional problems. We find, in addition, that despite the conditions we pose to guarantee causal recovery, performance in practice is robust to large deviations in model assumptions.

Policy Analysis using Synthetic Controls in Continuous-Time

Counterfactual estimation using synthetic controls is one of the most successful recent methodological developments in causal inference. Despite its popularity, the current description only considers time series aligned across units and synthetic controls expressed as linear combinations of observed control units. We propose a continuous-time alternative that models the latent counterfactual path explicitly using the formalism of controlled differential equations. This model is directly applicable to the general setting of irregularly-aligned multivariate time series and may be optimized in rich function spaces -- thereby improving on some limitations of existing approaches.

Generalization and Invariances in the Presence of Unobserved Confounding

The ability to extrapolate, or generalize, from observed to new related environments is central to any form of reliable machine learning, yet most methods fail when moving beyond $i.i.d$ data. In some cases, the reason lies in a misappreciation of the causal structure that governs the observed data. But, in others, it is unobserved data, such as hidden confounders, that drive changes in observed distributions and distort observed correlations. In this paper, we argue that generalization must be defined with respect to a broader class of distribution shifts, irrespective of their origin (arising from changes in observed, unobserved or target variables). We propose a new learning principle from which we may expect an explicit notion of generalization to certain new environments, even in the presence of hidden confounding. This principle leads us to formulate a general objective that may be paired with any gradient-based learning algorithm; algorithms that have a causal interpretation in some cases and enjoy notions of predictive stability in others. We demonstrate the empirical performance of our approach on healthcare data from different modalities, including image and speech data.

Learning Overlapping Representations for the Estimation of Individualized Treatment Effects

The choice of making an intervention depends on its potential benefit or harm in comparison to alternatives. Estimating the likely outcome of alternatives from observational data is a challenging problem as all outcomes are never observed, and selection bias precludes the direct comparison of differently intervened groups. Despite their empirical success, we show that algorithms that learn domain-invariant representations of inputs (on which to make predictions) are often inappropriate, and develop generalization bounds that demonstrate the dependence on domain overlap and highlight the need for invertible latent maps. Based on these results, we develop a deep kernel regression algorithm and posterior regularization framework that substantially outperforms the state-of-the-art on a variety of benchmarks data sets.