Jakub Wornbard

The PhD will focus on developing novel statistical methods related to questions in machine learning, emphasising causal learning, domain adaptation, and kernel-based approaches. One key area could be designing algorithms that leverage causal structures to improve transfer learning, e.g., by identifying covariates whose effect on the predicted response is unaffected by the changes in the data generating mechanisms. Another likely focus is developing nonparametric hypothesis tests, particularly for conditional independence. Given recent hardness results showing the non-existence of uniformly valid conditional independence tests, the goal would be to design methods with performance guarantees for restricted scenarios. Advancements of this kind could benefit fields like causal discovery. While the specific applications remain open, potential areas of interest include neuroscience and Earth system science. For example, in the former, there is interest in developing causal models of brain activity, e.g., determining whether the correlated activity of two brain regions results from one affecting the other, the existence of a third region which activates both, or some combination of these factors. Meanwhile, in Earth system science, the developed methods could be used for predicting parameters such as photosynthesis intensity, across a broader region, based on locally measured flows of carbon, water, and energy. The variable temporal and spatial availability of data across continents and climate zones suggests that in order to do it efficiently in regions with little data, one may need to utilise that coming from different continents or biomes, hence necessitating the use of methods which are robust to domain shift.