Betrouwbaar Statistisch Leren voor Regressie en Causale Ontdekking

We are interested in developing statistical learning methods with reliable performance on consistency, convergence, and identifiability. Specifically, we focus on the tasks of regression and causal discovery. For regression, we developed a novel linear model tree method named Piecewise Linear Organic Tree and incorporated it into the random forest. We proved the consistency and fast convergence rate of the proposed model tree and ensemble method. For causal discovery, we introduced the Mixed-type Additive Noise Model, a general structural equation model for mixed-type data involving both continuous and categorical variables which unifies the existing ones. We showed that under mild functional constraints, the causal graph underlying the model is identifiable from the observational distribution and developed a learning method. We further developed a differentiable causal structural learning method NOTIME, which has identifiability guarantees on the Linear Non-Gaussian Additive noise models based on a continuous optimization framework that minimizes a dependence measure.