Density Ratio-based Causal Discovery from Bivariate Continuous-Discrete Data

This paper proposes a causal discovery method for mixed bivariate data consisting of one continuous and one discrete variable. Existing constraint-based approaches are ineffective in the bivariate setting, as they rely on conditional independence tests that are not suited to bivariate data. Score-based methods either impose strong distributional assumptions or face challenges in fairly comparing causal directions between variables of different types, due to differences in their information content. We introduce a novel approach that determines causal direction by analyzing the monotonicity of the conditional density ratio of the continuous variable, conditioned on different values of the discrete variable. Our theoretical analysis shows that the conditional density ratio exhibits monotonicity when the continuous variable causes the discrete variable, but not in the reverse direction. This property provides a principled basis for comparing causal directions between variables of different types, free from strong distributional assumptions and bias arising from differences in their information content. We demonstrate its effectiveness through experiments on both synthetic and real-world datasets, showing superior accuracy compared to existing methods.

Classification from Positive and Biased Negative Data with Skewed Labeled Posterior Probability

The binary classification problem has a situation where only biased data are observed in one of the classes. In this paper, we propose a new method to approach the positive and biased negative (PbN) classification problem, which is a weakly supervised learning method to learn a binary classifier from positive data and negative data with biased observations. We incorporate a method to correct the negative impact due to skewed confidence, which represents the posterior probability that the observed data are positive. This reduces the distortion of the posterior probability that the data are labeled, which is necessary for the empirical risk minimization of the PbN classification problem. We verified the effectiveness of the proposed method by numerical experiments and real data analysis.