Self-Attentive hawkes process

Capturing the occurrence dynamics is crucial to predicting which type of events will happen next and when. A common method to do this is through Hawkes processes. To enhance their capacity, recurrent neural networks (RNNs) have been incorporated due to RNNs successes in processing sequential data such as languages. Recent evidence suggests that self-Attention is more competent than RNNs in dealing with languages. However, we are unaware of the effectiveness of self-Attention in the context of Hawkes processes. This study aims to fill the gap by designing a self-Attentive Hawkes process (SAHP). SAHP employs self-Attention to summarise the influence of history events and compute the probability of the next event. One deficit of the conventional selfattention, when applied to event sequences, is that its positional encoding only considers the order of a sequence ignoring the time intervals between events. To overcome this deficit, we modify its encoding by translating time intervals into phase shifts of sinusoidal functions. Experiments on goodness-of-fit and prediction tasks show the improved capability of SAHP. Furthermore, SAHP is more interpretable than RNN-based counterparts because the learnt attention weights reveal contributions of one event type to the happening of another type. To the best of our knowledge, this is the first work that studies the effectiveness of self-Attention in Hawkes processes

Model-Based Therapeutic Correction of Hypothalamic-Pituitary-Adrenal Axis Dysfunction

The hypothalamic-pituitary-adrenal (HPA) axis is a major system maintaining body homeostasis by regulating the neuroendocrine and sympathetic nervous systems as well modulating immune function. Recent work has shown that the complex dynamics of this system accommodate several stable steady states, one of which corresponds to the hypocortisol state observed in patients with chronic fatigue syndrome (CFS). At present these dynamics are not formally considered in the development of treatment strategies. Here we use model-based predictive control (MPC) methodology to estimate robust treatment courses for displacing the HPA axis from an abnormal hypocortisol steady state back to a healthy cortisol level. This approach was applied to a recent model of HPA axis dynamics incorporating glucocorticoid receptor kinetics. A candidate treatment that displays robust properties in the face of significant biological variability and measurement uncertainty requires that cortisol be further suppressed for a short period until adrenocorticotropic hormone levels exceed 30% of baseline. Treatment may then be discontinued, and the HPA axis will naturally progress to a stable attractor defined by normal hormone levels. Suppression of biologically available cortisol may be achieved through the use of binding proteins such as CBG and certain metabolizing enzymes, thus offering possible avenues for deployment in a clinical setting. Treatment strategies can therefore be designed that maximally exploit system dynamics to provide a robust response to treatment and ensure a positive outcome over a wide range of conditions. Perhaps most importantly, a treatment course involving further reduction in cortisol, even transient, is quite counterintuitive and challenges the conventional strategy of supplementing cortisol levels, an approach based on steady-state reasoning