Score-based causal learning in additive noise models

By Christopher Nowzohour, Peter Buhlmann. 2013

35 citations recorded by the source corpus.

Given data sampled from a number of variables, one is often interested in the underlying causal relationships in the form of a directed acyclic graph. In the general case, without interventions on some of the variables it is only possible to identify the graph up to its Markov equivalence class. However, in some situations one can find the true causal graph just from observational data, for example, in structural equation models with additive noise and nonlinear edge functions. Most current methods for achieving this rely on nonparametric independence tests. One of the problems there is that the null hypothesis is independence, which is what one would like to get evidence for. We take a different approach in our work by using a penalized likelihood as a score for model selection. This is practically feasible in many settings and has the advantage of yielding a natural ranking of the candidate models. When making smoothness assumptions on the probability density space, we prove consistency of the penalized maximum likelihood estimator. We also present empirical results for simulated scenarios and real two-dimensional data sets (cause–effect pairs) where we obtain similar results as other state-of-the-art methods.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, methodology): “2 Entropy-based Scores Instead of explicitly testing for independence of residuals and inputs, one can use the sum of their differential entropies as a score function (e.g., Kpotufe et al., 2014; Nowzohour and Bühlmann, 2015).”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, methodology): “Kpotufe et al. (2014); Nowzohour and Bühlmann (2015) proposed to use as a score the sum of the estimated differential entropies of inputs and residuals and proved consistency of that procedure.”
Causal inference in partially linear structural equation models (2016, methodology): “equivalent if one of the nonlinear functions is replaced by a linear function [17, Example 26]. Various estimation methods have been introduced for additive nonlinear SEMs to infer the underlying DAG [17,24,14]. In particular, a restricted maximum likelihood estimation method called CAM, which is co”