Tiago Brogueira

Tiago Brogueira, Mário A. T. Figueiredo

Approaches to bivariate causal discovery based on the minimum description length (MDL) principle approximate the (uncomputable) Kolmogorov complexity of the models in each causal direction, selecting the one with the lower total complexity. The premise is that nature's mechanisms are simpler in their true causal order. Inherently, the description length (complexity) in each direction includes the description of the cause variable and that of the causal mechanism. In this work, we argue that current state-of-the-art MDL-based methods do not correctly address the problem of estimating the description length of the cause variable, effectively leaving the decision to the description length of the causal mechanism. Based on rate-distortion theory, we propose a new way to measure the description length of the cause, corresponding to the minimum rate required to achieve a distortion level representative of the underlying distribution. This distortion level is deduced using rules from histogram-based density estimation, while the rate is computed using the related concept of information dimension, based on an asymptotic approximation. Combining it with a traditional approach for the causal mechanism, we introduce a new bivariate causal discovery method, termed rate-distortion MDL (RDMDL). We show experimentally that RDMDL achieves competitive performance on the Tübingen dataset. All the code and experiments are publicly available at github.com/tiagobrogueira/Causal-Discovery-In-Exchangeable-Data.

Tiago Brogueira, Mário Figueiredo

Causal discovery methods have traditionally been developed under two distinct regimes: independent and identically distributed (i.i.d.) and timeseries data, each governed by separate modelling assumptions. In this paper, we argue that the i.i.d. setting can and should be reframed in terms of exchangeability, a strictly more general symmetry principle. We present the implications of this reframing, alongside two core arguments: (1) a conceptual argument, based on extending the dependency of experimental causal inference on exchangeability to causal discovery; and (2) an empirical argument, showing that many existing i.i.d. causal-discovery methods are predicated on exchangeability assumptions, and that the sole extensive widely-used real-world "i.i.d." benchmark (the Tübingen dataset) consists mainly of exchangeable (and not i.i.d.) examples. Building on this insight, we introduce a novel synthetic dataset that enforces only the exchangeability assumption, without imposing the stronger i.i.d. assumption. We show that our exchangeable synthetic dataset mirrors the statistical structure of the real-world "i.i.d." dataset more closely than all other i.i.d. synthetic datasets. Furthermore, we demonstrate the predictive capability of this dataset by proposing a neural-network-based causal-discovery algorithm trained exclusively on our synthetic dataset, and which performs similarly to other state-of-the-art i.i.d. methods on the real-world benchmark.