Christoph Hofer

University of Salzburg · Department of Computer Science

The problem of (point) forecasting $ \textit{univariate} $ time series is considered. Most approaches, ranging from traditional statistical methods to recent learning-based techniques with neural networks, directly operate on raw time series observations. As an extension, we study whether $\textit{local topological properties}$, as captured via per...

Objective: Differential diagnosis of mild cognitive impairment MCI and temporal lobe epilepsy TLE is a debated issue, specifically because these conditions may coincide in the elderly population. We evaluate automated differential diagnosis based on characteristics derived from structural brain MRI of different brain regions. Methods: In 22 heal...

We study the problem of learning representations with controllable connectivity properties. This is beneficial in situations when the imposed structure can be leveraged upstream. In particular, we control the connectivity of an autoencoder's latent space via a novel type of loss, operating on information from persistent homology. Under mild conditi...

We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this end, we leverage persistent homology computed via a real-valued, learnable, filter function. We establish the t...

Spinal cord injury (SCI) leads to severe chronic disability, but also to secondary adaptive changes upstream to the injury in the brain which are most likely induced due to the lack of afferent information. These neuroplastic changes are a potential target for innovative therapies such as neuroprostheses, e.g., by stimulation in order to evoke sens...

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information, typically in the form of summary representations of topological features. However, such topological signatures often c...

We consider the task of constructing (metric) shape space(s) from a topological perspective. In particular, we present a generic construction scheme and demonstrate how to apply this scheme when shape is interpreted as the differences that remain after factoring out translation, scaling and rotation. This is achieved by leveraging a recently propos...