Leonard Waldmann

We present a consistent and highly scalable local approach to learn the causal structure of a linear Gaussian polytree using data from interventional experiments with known intervention targets. Our methods first learn the skeleton of the polytree and then orient its edges. The output is a CPDAG representing the interventional equivalence class of the polytree of the true underlying distribution. The skeleton and orientation recovery procedures we use rely on second order statistics and low-dimensional marginal distributions. We assess the performance of our methods under different scenarios in synthetic data sets and apply our algorithm to learn a polytree in a gene expression interventional data set. Our simulation studies demonstrate that our approach is fast, has good accuracy in terms of structural Hamming distance, and handles problems with thousands of nodes.

Objective: Understanding fluctuations in seizure severity within individuals is important for determining treatment outcomes and responses to therapy, as well as assessing novel treatments for epilepsy. Current methods for grading seizure severity rely on qualitative interpretations from patients and clinicians. Quantitative measures of seizure severity would complement existing approaches to electroencephalographic (EEG) monitoring, outcome monitoring, and seizure prediction. Therefore, we developed a library of quantitative EEG markers that assess the spread and intensity of abnormal electrical activity during and after seizures. Methods: We analyzed intracranial EEG (iEEG) recordings of 1009 seizures from 63 patients. For each seizure, we computed 16 markers of seizure severity that capture the signal magnitude, spread, duration, and postictal suppression of seizures. Results: Quantitative EEG markers of seizure severity distinguished focal versus subclinical seizures across patients. In individual patients, 53% had a moderate to large difference (rank sum r>.3, p<.05) between focal and subclinical seizures in three or more markers. Circadian and longer term changes in severity were found for the majority of patients. Significance: We demonstrate the feasibility of using quantitative iEEG markers to measure seizure severity. Our quantitative markers distinguish between seizure types and are therefore sensitive to established qualitative differences in seizure severity. Our results also suggest that seizure severity is modulated over different timescales. We envisage that our proposed seizure severity library will be expanded and updated in collaboration with the epilepsy research community to include more measures and modalities.

We give a brief literature review on the main concepts of robustness in deep learning and more detailed information on robust out-of-distribution detection and robustness to semantic perturbations. We do not aim to present the topics in their full depth, but to present the main concepts and provide references for further reading. This reports is written for a graduate student to quickly familiarize themselves with the topic

The edges of a directed acyclic graph (DAG) can be interpreted as cause-effect relations from parent to child node. Linear structural equation models (LSEM) are sets of matrices of distributions that quantify these cause-effect relations by describing a node through a linear function of its parents and some additive independent noise term. Given the LSEM of an unknown DAG, previous results have shown that the underlying DAG can only be identified up to the well-known Markov equivalence classes. Under the additional assumption that all error terms have identical variance, it has been proven that the graph can be identified uniquely. The goal of this thesis is to explore these so-called covariance equivalence classes in the general setting of an arbitrary partition of the nodes into groups with equal error variances. The main result of this thesis is the computation of covariance equivalence classes of DAGs with three and four nodes under arbitrary groups of equal error variances with the aid of the computational algebra software Macaulay2 and Maple. Based on these results, a conjecture on the case of arbitrary number of nodes that entails the two known equal error variance settings and explains the computational results is stated. Assuming that the conjecture holds true, the distribution of the sizes of covariance equivalence classes of DAGs up to six nodes is explored. Moreover, the algorithm is extended to allow cyclic graphs, however, it cannot be ensured that these results correspond to covariance equivalence classes of directed cyclic graphs. All code is available for further investigations.