arXiv subjects

Tiago Brogueira

Publications and source records attributed to Tiago Brogueira.

3 recordsLinked to original sources

arXiv2026

Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach

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.

cs.LG↗

arXiv2026

Rethinking Bivariate Causal Discovery Through the Lens of Exchangeability

Causal discovery methods have traditionally been developed under two different modeling assumptions: independent and identically distributed (i.i.d.) data and time series data. In this paper, we focus on the i.i.d. setting, arguing that it should be reframed in terms of exchangeability, a strictly more general symmetry principle. For that goal, we propose an exchangeable hierarchical model that builds upon the recent Causal de Finetti theorem. Using this model, we show that both the uncertainty regarding the causal mechanism and the uncertainty in the distribution of latent variables are better captured under the broader assumption of exchangeability. In fact, we argue that this is most often the case with real data, as supported by an in-depth analysis of the Tübingen dataset. Exploiting this insight, we introduce a novel synthetic dataset that mimics the generation process induced by the proposed exchangeable hierarchical model. We show that our exchangeable synthetic dataset mirrors the statistical and causal structure of the Tübingen dataset more closely than other i.i.d. synthetic datasets. Furthermore, we introduce SynthNN, a neural-network-based causal-discovery method trained exclusively on the proposed synthetic dataset. The fact that SynthNN performs competitively with other state-of-the-art methods on the real-world Tübingen dataset provides strong evidence for the realism of the underlying exchangeable generative model.

cs.LG↗

arXiv2025

LxCIM: a new rank-based binary classifier performance metric invariant to local exchange of classes

Binary classification is one of the oldest, most prevalent, and studied problems in machine learning. However, the metrics used to evaluate model performance have received comparatively little attention. The area under the receiver operating characteristic curve (AUROC) has long been a standard choice for model comparison. Despite its advantages, AUROC is not always ideal, particularly for problems that are invariant to local exchange of classes (LxC), a new form of metric invariance introduced in this work. To address this limitation, we propose LxCIM (LxC-invariant metric), which is not only rank-based and invariant under local exchange of classes, but also intuitive, logically consistent, and always computable, while enabling more detailed analysis through the cumulative accuracy-decision rate curve. Moreover, LxCIM exhibits clear theoretical connections to AUROC, accuracy, and the area under the accuracy-decision rate curve (AUDRC). These relationships allow for multiple complementary interpretations: as a symmetric form of AUROC, a rank-based analogue of accuracy, or a more representative and more interpretable variant of AUDRC. Finally, we demonstrate the direct applicability of LxCIM to the bivariate causal discovery problem (which exhibits invariance to local exchange of classes) and show how it addresses the acknowledged limitations of existing metrics used in this field. All code and implementation details are publicly available at github.com/tiagobrogueira/Causal-Discovery-In-Exchangeable-Data.

stat.ML↗