Human lesion studies offer one of the most direct routes to investigating the causal relations between brain regions and behavioral outcomes in circumstances where experimental interventions are highly restricted. However, these studies face a major challenge in identifying the right level of granularity at which brain regions and behavioral outcomes should be analyzed to identify the association between lesions to specific brain regions and specific behavioral outcomes. Here we showcase a novel data-driven approach, Causal Feature Learning (CFL), that learns the appropriate level of analysis and the relation between lesion and cognitive impairment at the same time. The method avoids specifying brain regions and specific outcome measures a priori, allowing for the discovery of new cross-cutting lesion-behavior maps. We show that CFL robustly recovers lesion behavior maps in a simulated dataset where Canonical Correlation Analysis fails to provide interpretable results. We then show that CFL recovers known lesion-behavior maps for language deficits and visuospatial processing using a large dataset of lesion subjects, and finally we illustrate how CFL can be used to identify new groupings of outcomes when mapping lesions to depression symptoms.

Advances in data availability and statistical inference techniques have given rise to the possibility of a stronger empirical foundation for macroeconomic concepts. Such techniques offer an independent test of macroeconomic theory and enable the systematic discovery of new macroeconomic factors. Using as example the Economic Complexity Index (ECI) proposed by Hidalgo Hausmann (2009), we investigate the evidential standards used to empirically confirm and justify new macroeconomic quantities. We compare ECI to a purely data-driven index derived using the tools of causal representation learning and show that ECI can easily be out-performed using its standard. However, this standard (within sample predictive accuracy) is dubious, both when aiming at predictive success or when the aim is policy guidance. A more careful assessment shows that ECI has poor out-of-sample performance and that its policy advice is matched by a simple principal component model. While our assessment of ECI is largely negative, the techniques and standards we develop provide a general framework to systematically assess and empirically justify new macroeconomic quantities.

We propose a new optimization-based method for learning causal structures from observational data, a process known as causal discovery. Our method takes as input observational data over a set of variables and returns a graph in which causal relations are specified by directed edges. We consider a highly general search space that accommodates latent confounders and feedback cycles, which few extant methods do. We formulate the discovery problem as an integer program, and propose a solution technique that exploits the conditional independence structure in the data to identify promising edges for inclusion in the output graph. In the large-sample limit, our method recovers a graph that is (Markov) equivalent to the true data-generating graph. Computationally, our method is competitive with the state-ofthe-art, and can solve in minutes instances that are intractable for alternative causal discovery methods. We leverage our method to develop a procedure for investigating the validity of an instrumental variable and demonstrate it on the influential quarter-of-birth and proximity-tocollege instruments for estimating the returns to education. In particular, our procedure complements existing instrument tests by revealing the precise causal pathways that undermine instrument validity, highlighting the unique merits of the graphical perspective on causality.

A person is directly racially discriminated against only if her race caused her worse treatment. This implies that race is an attribute sufficiently separable from other attributes to isolate its causal role. But race is embedded in a nexus of social factors that resist isolated treatment. If race is socially constructed, in what sense can it cause worse treatment? Some propose that the perception of race, rather than race itself, causes worse treatment. Others suggest that since causal models require modularity, i.e. the ability to isolate causal effects, attempts to causally model discrimination are misguided. This paper addresses the problem differently. We introduce a framework for reasoning about discrimination, in which race is a high-level abstraction of lower-level features. In this framework, race can be modeled as itself causing worse treatment. Modularity is ensured by allowing assumptions about social construction to be precisely and explicitly stated, via an alignment between race and its constituents. Such assumptions can then be subjected to normative and empirical challenges, which lead to different views of when discrimination occurs. By distinguishing constitutive and causal relations, the abstraction framework pinpoints disagreements in the current literature on modeling discrimination, while preserving a precise causal account of discrimination.

Unmeasured confounding is a major challenge for identifying causal relationships from non-experimental data. Here, we propose a method that can accommodate unmeasured discrete confounding. Extending recent identifiability results in deep latent variable models, we show theoretically that confounding can be detected and corrected under the assumption that the observed data is a piecewise affine transformation of a latent Gaussian mixture model and that the identity of the mixture components is confounded. We provide a flow-based algorithm to estimate this model and perform deconfounding. Experimental results on synthetic and real-world data provide support for the effectiveness of our approach.

This article is an attempt to provide an example that illustrates Hans Reichenbach’s concept of coordination. Throughout Reichenbach’s career the concept of coordination played an important role in his understanding of the connection between reality and how it is scientifically described. Reichenbach never fully specified what coordination is and how exactly it works. Instead, we are left with a variety of hints and gestures, many not entirely consistent with each other and several that are subject to change over the course of his career. Using the example of how to discover and construct causal variables, I will show that most of the features of coordination that Reichenbach described can be instantiated together and formulated precisely.

Causal Feature Learning (CFL) is a domain-general framework that learns macro-level causes and effects from micro-level data. In contrast to traditional coarsening methods, CFL bases its aggregation on the relation between two micro-variables, providing macro-level representations of each variable with respect to it’s relationship with the other. Here, we implement a CFL software package that aims to reduce the barriers to running CFL. With customizable models, thorough documentation, and helper methods to interpret results, CFL makes it possible for researchers to easily analyze and identify potentially relevant features in their data.

We provide a critical assessment of the account of causal emergence presented in Erik Hoel’s 2017 article “When the map is better than the territory”. The account integrates causal and information theoretic concepts to explain under what circumstances there can be causal descriptions of a system at multiple scales of analysis. We show that the causal macro variables implied by this account result in interventions with significant ambiguity, and that the operations of marginalization and abstraction do not commute. Both of these are desiderata that, we argue, any account of multi-scale causal analysis should be sensitive to. The problems we highlight in Hoel’s definition of causal emergence derive from the use of various averaging steps and the introduction of a maximum entropy distribution that is extraneous to the system under investigation.

We propose a new method for learning causal structures from observational data, a process known as causal discovery. Our method takes as input observational data over a set of variables and returns a graph in which causal relations are specified by directed edges. We consider a highly general search space that accommodates latent confounders and feedback cycles, which few extant methods do. We formulate the discovery problem as an integer program, and propose a solution technique that leverages the conditional independence structure in the data to identify promising edges for inclusion in the output graph. In the large-sample limit, our method recovers a graph that is equivalent to the true data-generating graph. Computationally, our method is competitive with the state-of-the-art, and can solve in minutes instances that are intractable for alternative causal discovery methods. We demonstrate our approach by showing how it can be used to examine the validity of instrumental variables, which are widely used for causal inference. In particular, we analyze US Census data from the seminal paper on the returns to education by Angrist and Krueger (1991), and find that the causal structures uncovered by our method are consistent with the literature.

Human and animal behaviour exhibits complex but regular patterns over time, often referred to as expressions of personality. Yet it remains unclear what personality really is: is it just the behavioural patterns themselves, something in the brain, in the genes or perhaps all of these? Here we offer a set of causal hypotheses about the role of personality, integrating psychological and neuroscientific approaches to personality in a testable framework. These hypotheses clarify the causal and constitutive relations that personality has with genes, environment, brain, mind and behaviour, and we suggest specific experiments that can adjudicate amongst the different hypotheses. We focus on a set of models that propose that personality is instantiated in the brain, distally caused by genes and environment and, in turn, causing the overt behaviours from which it is often inferred. We argue that articulating and testing such models will be essential in a mature science of personality.

The cause-effect pair challenges focused on the development of inference methods to determine the causal relation between two variables. It is natural to then ask how such methods could generalize beyond the two variable case to settings that either involve more variables—such as is the case in graph learning—or to settings where the relationship between the candidate variables does not fall into one of the classes defined by the challenges. This chapter explores the extension of the proposed methods to such cases. It comes to the conclusion that such extensions are not likely to naturally evolve from the approaches that won the pair challenge.

In recent years the possibility of relaxing the so-called Faithfulness assumption in automated causal discovery has been investigated. The investigation showed (1) that the Faithfulness assumption can be weakened in various ways that in an important sense preserve its power, and (2) that weakening of Faithfulness may help to speed up methods based on Answer Set Programming. However, this line of work has so far only considered the discovery of causal models without latent variables. In this paper, we study weakenings of Faithfulness for constraint-based discovery of semi-Markovian causal models, which accommodate the possibility of latent variables, and show that both (1) and (2) remain the case in this more realistic setting.

Scientific models describe natural phenomena at different levels of abstraction. Abstract descriptions can provide the basis for interventions on the system and explanation of observed phenomena at a level of granularity that is coarser than the most fundamental account of the system. Beckers and Halpern (2019), building on work of Rubenstein et al. (2017), developed an account of abstraction for causal models that is exact. Here we extend this account to the more realistic case where an abstract causal model offers only an approximation of the underlying system. We show how the resulting account handles the discrepancy that can arise between low- and high-level causal models of the same system, and in the process provide an account of how one causal model approximates another, a topic of independent interest. Finally, we extend the account of approximate abstractions to probabilistic causal models, indicating how and where uncertainty can enter into an approximate abstraction.

We present and evaluate the Fast (conditional) Independence Test (FIT) -- a nonparametric conditional independence test. The test is based on the idea that when P(X∣Y,Z)=P(X∣Y), Z is not useful as a feature to predict X, as long as Y is also a regressor. On the contrary, if P(X∣Y,Z)≠P(X∣Y), Z might improve prediction results. FIT applies to thousand-dimensional random variables with a hundred thousand samples in a fraction of the time required by alternative methods. We provide an extensive evaluation that compares FIT to six extant nonparametric independence tests. The evaluation shows that FIT has low probability of making both Type I and Type II errors compared to other tests, especially as the number of available samples grows. Our implementation of FIT is publicly available.

Using the flexibility of recently developed methods for causal discovery based on Boolean satisfiability (SAT) solvers, we encode a variety of assumptions that weaken the Faithfulness assumption. The encoding results in a number of SAT-based algorithms whose asymptotic correctness relies on weaker conditions than are standardly assumed. This implementation of a whole set of assumptions in the same platform enables us to systematically explore the effect of weakening the Faithfulness assumption on causal discovery. An important effect, suggested by simulation results, is that adopting weaker assumptions greatly alleviates the problem of conflicting constraints and substantially shortens solving time. As a result, SAT-based causal discovery is potentially more scalable under weaker assumptions.

This article presents an overview of several known approaches to causal discovery. It is organized by relating the different fundamental assumptions that the methods depend on. The goal is to indicate that for a large variety of different settings the assumptions necessary and sufficient for causal discovery are now well understood.

Emotions involve many cortical and subcortical regions, prominently including the amygdala. It remains unknown how these multiple network components interact, and it remains unknown how they cause the behavioral, autonomic, and experiential effects of emotions. Here we describe a framework for combining a novel technique, concurrent electrical stimulation with fMRI (es-fMRI), together with a novel analysis, inferring causal structure from fMRI data (causal discovery). We outline a research program for investigating human emotion with these new tools, and provide initial findings from two large resting-state datasets as well as case studies in neurosurgical patients with electrical stimulation of the amygdala. The overarching goal is to use causal discovery methods on fMRI data to infer causal graphical models of how brain regions interact, and then to further constrain these models with direct stimulation of specific brain regions and concurrent fMRI. We conclude by discussing limitations and future extensions. The approach could yield anatomical hypotheses about brain connectivity, motivate rational strategies for treating mood disorders with deep brain stimulation, and could be extended to animal studies that use combined optogenetic fMRI.

Causal feature learning (CFL) (Chalupka et al., Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence. AUAI Press, Edinburgh, pp 181–190, 2015) is a causal inference framework rooted in the language of causal graphical models (Pearl J, Reasoning and inference. Cambridge University Press, Cambridge, 2009; Spirtes et al., Causation, Prediction, and Search. Massachusetts Institute of Technology, Massachusetts, 2000), and computational mechanics (Shalizi, PhD thesis, University of Wisconsin at Madison, 2001). CFL is aimed at discovering high-level causal relations from low-level data, and at reducing the experimental effort to understand confounding among the high-level variables. We first review the scientific motivation for CFL, then present a detailed introduction to the framework, laying out the definitions and algorithmic steps. A simple example illustrates the techniques involved in the learning steps and provides visual intuition. Finally, we discuss the limitations of the current framework and list a number of open problems.