Updating Statistical Measures of Causal Strength (original) (raw)
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Probabilistic Measures of Causal Strength
A number of theories of causation posit that causes raise the probability of their effects. In this paper, we survey a number of proposals for analyzing causal strength in terms of probabilities. We attempt to characterize just what each one measures, discuss the relationships between the measures, and discuss a number of properties of each measure.
Annals of Statistics, 2012
Many methods for causal inference generate directed acyclic graphs (DAGs) that formalize causal relations between n variables. Given the joint distribution on all these variables, the DAG contains all information about how intervening on one variable changes the distribution of the other n-1 variables. However, quantifying the causal influence of one variable on another one remains a non-trivial question. Here we propose a set of natural, intuitive postulates that a measure of causal strength should satisfy. We then introduce a communication scenario, where edges in a DAG play the role of channels that can be locally corrupted by interventions. Causal strength is then the relative entropy distance between the old and the new distribution. Many other measures of causal strength have been proposed, including average causal effect, transfer entropy, directed information, and information flow. We explain how they fail to satisfy the postulates on simple DAGs of <= 3 nodes. Finally, we investigate the behavior of our measure on time-series, supporting our claims with experiments on simulated data.Here we propose a measure for causal strength that refers to direct effects and measure the "strength of an arrow" or a set of arrows. It is based on a hypothetical intervention that modifies the joint distribution by cutting the corresponding edge. The causal strength is then the relative entropy distance between the old and the new distribution. We discuss other measures of causal strength like the average causal effect, transfer entropy and information flow and describe their limitations. We argue that our measure is also more appropriate for time series than the known ones. Finally, we discuss conceptual problems in defining the strength of indirect effects.
A Statistic Criterion for Reducing Indeterminacy in Linear Causal Modeling
Inferring causal relationships from observational data is still an open challenge in machine learning. State-ofthe-art approaches often rely on constraint-based algorithms which detect v-structures in triplets of nodes in order to orient arcs. These algorithms are destined to fail when confronted with completely connected triplets. This paper proposes a criterion to deal with arc orientation also in presence of completely linearly connected triplets. This criterion is then used in a Relevance-Causal (RC) algorithm, which combines the original causal criterion with a relevance measure, to infer causal dependencies from observational data. A set of simulated experiments on the inference of the causal structure of linear networks shows the effectiveness of the proposed approach.
Reducing the bias of causality measures
Physical Review E, 2011
Measures of the direction and strength of the interdependence between two time series are evaluated and modified in order to reduce the bias in the estimation of the measures, so that they give zero values when there is no causal effect. For this, point shuffling is employed as used in the frame of surrogate data. This correction is not specific to a particular measure and it is implemented here on measures based on state space reconstruction and information measures. The performance of the causality measures and their modifications is evaluated on simulated uncoupled and coupled dynamical systems and for different settings of embedding dimension, time series length and noise level. The corrected measures, and particularly the suggested corrected transfer entropy, turn out to stabilize at the zero level in the absence of causal effect and detect correctly the direction of information flow when it is present. The measures are also evaluated on electroencephalograms (EEG)
Uniform consistency in causal inference
2003
Abstract There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934). Spirtes (1994), Spirtes et al.(1993) and Pearl & Verma (1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and/or an unknown time order, and that under weak conditions, for certain combinations of directed acyclic graphs and probability distributions, are asymptotically, in sample size, consistent.
A New Look at Causal Independence
Uncertainty Proceedings 1994, 1994
Heckerman (1993) defined causal independence in terms of a set of temporal conditional independence statements. These statements formalized certain types of causal interaction where (1) the effect is independent of the order that causes are introduced and (2) the impact of a single cause on the effect does not depend on what other causes have previously been applied. In this paper, we introduce an equivalent atemporal characterization of causal independence based on a functional representation of the relationship between causes and the effect. In this representation, the interaction between causes and effect can be written as a nested decomposition of functions. Causal independence can be exploited by representing this decomposition in the belief network, resulting in representations that are more efficient for inference than general causal models. We present empirical results showing the benefits of a causal-independence representation for belief-network inference.
Decision-theoretic foundations for statistical causality
arXiv (Cornell University), 2020
We develop a mathematical and interpretative foundation for the enterprise of decision-theoretic statistical causality (DT), which is a straightforward way of representing and addressing causal questions. DT reframes causal inference as "assisted decision-making", and aims to understand when, and how, I can make use of external data, typically observational, to help me solve a decision problem by taking advantage of assumed relationships between the data and my problem. The relationships embodied in any representation of a causal problem require deeper justification, which is necessarily context-dependent. Here we clarify the considerations needed to support applications of the DT methodology. Exchangeability considerations are used to structure the required relationships, and a distinction drawn between intention to treat and intervention to treat forms the basis for the enabling condition of "ignorability". We also show how the DT perspective unifies and sheds light on other popular formalisations of statistical causality, including potential responses and directed acyclic graphs.
A Uniformly Consistent Estimator of Causal Effects under the kkk-Triangle-Faithfulness Assumption
Statistical Science, 2014
Spirtes, Glymour and Scheines [Causation, Prediction, and Search (1993) Springer] described a pointwise consistent estimator of the Markov equivalence class of any causal structure that can be represented by a directed acyclic graph for any parametric family with a uniformly consistent test of conditional independence, under the Causal Markov and Causal Faithfulness assumptions. Robins et al. [Biometrika 90 (2003) 491-515], however, proved that there are no uniformly consistent estimators of Markov equivalence classes of causal structures under those assumptions. Subsequently, Kalisch and Bühlmann [J. Mach. Learn. Res. 8 (2007) 613-636] described a uniformly consistent estimator of the Markov equivalence class of a linear Gaussian causal structure under the Causal Markov and Strong Causal Faithfulness assumptions. However, the Strong Faithfulness assumption may be false with high probability in many domains. We describe a uniformly consistent estimator of both the Markov equivalence class of a linear Gaussian causal structure and the identifiable structural coefficients in the Markov equivalence class under the Causal Markov assumption and the considerably weaker k-Triangle-Faithfulness assumption.