Alex Markham: A Causal Graph Kernel Embedding via Distance Covariance
Time: Tue 2021-09-21 10.15
Lecturer: Alex Markham (KTH)
We use the distance covariance, a nonlinear measure of dependence introduced by Székely et al. 2007, to define a new kernel capable of measuring the similarity between the generating causal structures underlying different samples. Our kernel can readily be used with existing machine learning methods, allowing them to incorporate causal information to solve a wide variety of tasks (e.g., clustering with kernel k-means, classification with kernel support vector machines, or dimensionality reduction/data visualization with kernel principal component analysis). In this talk, we focus on the theoretical aspects of the kernel, namely on (i) how equivalence classes of ancestral graphs are embedded into a kernel space defined by the distance covariance and (ii) how this facilitates the isometry of distances between sample points and distances between their generating causal models.