Causal Dependence Plots

Explaining artificial intelligence or machine learning models is increasingly important. To use such data-driven systems wisely we must understand how they interact with the world, including how they depend causally on data inputs. In this work we develop Causal Dependence Plots (CDPs) to visualize how one variable--an outcome--depends on changes in another variable--a predictor--$\textit{along with any consequent causal changes in other predictor variables}$. Crucially, CDPs differ from standard methods based on holding other predictors constant or assuming they are independent. CDPs make use of an auxiliary causal model because causal conclusions require causal assumptions. With simulations and real data experiments, we show CDPs can be combined in a modular way with methods for causal learning or sensitivity analysis. Since people often think causally about input-output dependence, CDPs can be powerful tools in the xAI or interpretable machine learning toolkit and contribute to applications like scientific machine learning and algorithmic fairness

Sample-Specific Root Causal Inference with Latent Variables

Root causal analysis seeks to identify the set of initial perturbations that induce an unwanted outcome. In prior work, we defined sample-specific root causes of disease using exogenous error terms that predict a diagnosis in a structural equation model. We rigorously quantified predictivity using Shapley values. However, the associated algorithms for inferring root causes assume no latent confounding. We relax this assumption by permitting confounding among the predictors. We then introduce a corresponding procedure called Extract Errors with Latents (EEL) for recovering the error terms up to contamination by vertices on certain paths under the linear non-Gaussian acyclic model. EEL also identifies the smallest sets of dependent errors for fast computation of the Shapley values. The algorithm bypasses the hard problem of estimating the underlying causal graph in both cases. Experiments highlight the superior accuracy and robustness of EEL relative to its predecessors

A Bayesian Nonparametric Conditional Two-sample Test with an Application to Local Causal Discovery

For a continuous random variable $Z$, testing conditional independence $X \perp\!\!\!\perp Y |Z$ is known to be a particularly hard problem. It constitutes a key ingredient of many constraint-based causal discovery algorithms. These algorithms are often applied to datasets containing binary variables, which indicate the 'context' of the observations, e.g. a control or treatment group within an experiment. In these settings, conditional independence testing with $X$ or $Y$ binary (and the other continuous) is paramount to the performance of the causal discovery algorithm. To our knowledge no nonparametric 'mixed' conditional independence test currently exists, and in practice tests that assume all variables to be continuous are used instead. In this paper we aim to fill this gap, as we combine elements of Holmes et al. (2015) and Teymur and Filippi (2020) to propose a novel Bayesian nonparametric conditional two-sample test. Applied to the Local Causal Discovery algorithm, we investigate its performance on both synthetic and real-world data, and compare with state-of-the-art conditional independence tests

On the Lasso for Graphical Continuous Lyapunov Models

Graphical continuous Lyapunov models offer a new perspective on modeling causally interpretable dependence structure in multivariate data by treating each independent observation as a one-time cross-sectional snapshot of a temporal process. Specifically, the models assume that the observations are cross-sections of independent multivariate Ornstein-Uhlenbeck processes in equilibrium. The Gaussian equilibrium exists under a stability assumption on the drift matrix, and the equilibrium covariance matrix is determined by the continuous Lyapunov equation. Each graphical continuous Lyapunov model assumes the drift matrix to be sparse, with a support determined by a directed graph. A natural approach to model selection in this setting is to use an $\ell_1$-regularization technique that, based on a given sample covariance matrix, seeks to find a sparse approximate solution to the Lyapunov equation. We study the model selection properties of the resulting lasso technique to arrive at a consistency result. Our detailed analysis reveals that the involved irrepresentability condition is surprisingly difficult to satisfy. While this may prevent asymptotic consistency in model selection, our numerical experiments indicate that even if the theoretical requirements for consistency are not met, the lasso approach is able to recover relevant structure of the drift matrix and is robust to aspects of model misspecification

Joint Causal Inference from Multiple Contexts

The gold standard for discovering causal relations is by means of experimentation. Over the last decades, alternative methods have been proposed that can infer causal relations between variables from certain statistical patterns in purely observational data. We introduce Joint Causal Inference (JCI), a novel approach to causal discovery from multiple data sets from different contexts that elegantly unifies both approaches. JCI is a causal modeling framework rather than a specific algorithm, and it can be implemented using any causal discovery algorithm that can take into account certain background knowledge. JCI can deal with different types of interventions (e.g., perfect, imperfect, stochastic, etc.) in a unified fashion, and does not require knowledge of intervention targets or types in case of interventional data. We explain how several well-known causal discovery algorithms can be seen as addressing special cases of the JCI framework, and we also propose novel implementations that extend existing causal discovery methods for purely observational data to the JCI setting. We evaluate different JCI implementations on synthetic data and on flow cytometry protein expression data and conclude that JCI implementations can considerably outperform state-of-the-art causal discovery algorithms.Comment: Final version, as published by JML

Causality and independence in perfectly adapted dynamical systems

Perfect adaptation in a dynamical system is the phenomenon that one or more variables have an initial transient response to a persistent change in an external stimulus but revert to their original value as the system converges to equilibrium. The causal ordering algorithm can be used to construct an equilibrium causal ordering graph that represents causal relations and a Markov ordering graph that implies conditional independences from a set of equilibrium equations. Based on this, we formulate sufficient graphical conditions to identify perfect adaptation from a set of first-order differential equations. Furthermore, we give sufficient conditions to test for the presence of perfect adaptation in experimental equilibrium data. We apply our ideas to a simple model for a protein signalling pathway and test its predictions both in simulations and on real-world protein expression data. We demonstrate that perfect adaptation in this model can explain why the presence and orientation of edges in the output of causal discovery algorithms does not always appear to agree with the direction of edges in biological consensus networks.Comment: 32 page