We illustrate the detrimental effect, such as overconfident decisions, that exponential behavior can have in methods like classical LDA and logistic regression. We then show how polynomiality can remedy the situation. This, among others, leads purposefully to random-level performance in the tails, away from the bulk of the training data. A directly related, simple, yet important technical novelty we subsequently present is softRmax: a reasoned alternative to the standard softmax function employed in contemporary (deep) neural networks. It is derived through linking the standard softmax to Gaussian class-conditional models, as employed in LDA, and replacing those by a polynomial alternative. We show that two aspects of softRmax, conservativeness and inherent gradient regularization, lead to robustness against adversarial attacks without gradient obfuscation.

Parkinson's disease (PD) diagnosis is based on clinical criteria, i.e., bradykinesia, rest tremor, rigidity, etc. Assessment of the severity of PD symptoms with clinical rating scales, however, is subject to inter-rater variability. In this paper, we propose a deep learning based automatic PD diagnosis method using videos to assist the diagnosis in clinical practices. We deploy a 3D Convolutional Neural Network (CNN) as the baseline approach for the PD severity classification and show the effectiveness. Due to the lack of data in clinical field, we explore the possibility of transfer learning from non-medical dataset and show that PD severity classification can benefit from it. To bridge the domain discrepancy between medical and non-medical datasets, we let the network focus more on the subtle temporal visual cues, i.e., the frequency of tremors, by designing a Temporal Self-Attention (TSA) mechanism. Seven tasks from the Movement Disorders Society - Unified PD rating scale (MDS-UPDRS) part III are investigated, which reveal the symptoms of bradykinesia and postural tremors. Furthermore, we propose a multi-domain learning method to predict the patient-level PD severity through task-assembling. We show the effectiveness of TSA and task-assembling method on our PD video dataset empirically. We achieve the best MCC of 0.55 on binary task-level and 0.39 on three-class patient-level classification.

In domain generalization, multiple labeled nonindependent and non-identically distributed source domains are available during training while neither the data nor the labels of target domains are. Currently, learning so-called domain invariant representations (DIRs) is the prevalent approach to domain generalization. In this work, we define DIRs employed by existing works in probabilistic terms and show that by learning DIRs, overly strict requirements are imposed concerning the invariance. Particularly, DIRs aim to perfectly align representations of different domains, i.e. their input distributions. This is, however, not necessary for good generalization to a target domain and may even dispose of valuable classification information. We propose to learn so-called hypothesis invariant representations (HIRs), which relax the invariance assumptions by merely aligning posteriors, instead of aligning representations. We report experimental results on public domain generalization datasets to show that learning HIRs is more effective than learning DIRs. In fact, our approach can even compete with approaches using prior knowledge about domains.