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[2505.08371] Density Ratio-based Causal Discovery from Bivariate Continuous-Discrete Data
Summary
This paper presents a novel method for determining causal direction between continuous and discrete variables using density ratios, demonstrating its effectiveness through theoretical results and experiments.
Why It Matters
Understanding causal relationships between variables is crucial in various fields, including economics, healthcare, and social sciences. This research provides a new approach to causal discovery that could enhance data analysis and decision-making processes in these areas.
Key Takeaways
- Introduces Density Ratio-based Causal Discovery (DRCD) for causal inference.
- Establishes theoretical results on monotonicity of density ratios for causal direction.
- Demonstrates DRCD's superiority over existing methods through empirical testing.
Computer Science > Machine Learning arXiv:2505.08371 (cs) [Submitted on 13 May 2025 (v1), last revised 26 Feb 2026 (this version, v4)] Title:Density Ratio-based Causal Discovery from Bivariate Continuous-Discrete Data Authors:Takashi Nicholas Maeda, Shohei Shimizu, Hidetoshi Matsui View a PDF of the paper titled Density Ratio-based Causal Discovery from Bivariate Continuous-Discrete Data, by Takashi Nicholas Maeda and 2 other authors View PDF HTML (experimental) Abstract:We address the problem of inferring the causal direction between a continuous variable $X$ and a discrete variable $Y$ from observational data. For the model $X \to Y$, we adopt the threshold model used in prior work. For the model $Y \to X$, we consider two cases: (1) the conditional distributions of $X$ given different values of $Y$ form a location-shift family, and (2) they are mixtures of generalized normal distributions with independently parameterized components. We establish identifiability of the causal direction through three theoretical results. First, we prove that under $X \to Y$, the density ratio of $X$ conditioned on different values of $Y$ is monotonic. Second, we establish that under $Y \to X$ with non-location-shift conditionals, monotonicity of the density ratio holds only on a set of Lebesgue measure zero in the parameter space. Third, we show that under $X \to Y$, the conditional distributions forming a location-shift family requires a precise coordination between the causal mechanism ...
