Hudson Smith

Ahmer Raza, Hudson Smith

Multivariate Hawkes processes are a widely used class of self-exciting point processes, but maximum likelihood estimation naively scales as $O(N^2)$ in the number of events. The canonical linear exponential Hawkes process admits a faster $O(N)$ recurrence, but prior work evaluates this recurrence sequentially, without exploiting parallelization on modern GPUs. We show that the Hawkes process intensity can be expressed as a product of sparse transition matrices admitting a linear-time associative multiply, enabling computation via a parallel prefix scan. This yields a simple yet massively parallelizable algorithm for maximum likelihood estimation of linear exponential Hawkes processes. Our method reduces the computational complexity to approximately $O(N/P)$ with $P$ parallel processors, and naturally yields a batching scheme to maintain constant memory usage, avoiding GPU memory constraints. Importantly, it computes the exact likelihood without any additional assumptions or approximations, preserving the simplicity and interpretability of the model. We demonstrate orders-of-magnitude speedups on simulated and real datasets, scaling to thousands of nodes and tens of millions of events, substantially beyond scales reported in prior work. We provide an open-source PyTorch library implementing our optimizations.

Alexander Bakumenko, Janine Hoelscher, Hudson Smith

Early identification of intensive care patients at risk of in-hospital mortality enables timely intervention and efficient resource allocation. Despite high predictive performance, existing machine learning approaches lack transparency and robustness, limiting clinical adoption. We present a lightweight, transparent multimodal ensemble that fuses physiological time-series measurements with unstructured clinical notes from the first 48 hours of an ICU stay. A logistic regression model combines predictions from two modality-specific models: a bidirectional LSTM for vitals and a finetuned ClinicalModernBERT transformer for notes. This traceable architecture allows for multilevel interpretability: feature attributions within each modality and direct per-case modality attributions quantifying how vitals and notes influence each decision. On the MIMIC-III benchmark, our late-fusion ensemble improves discrimination over the best single model (AUPRC 0.565 vs. 0.526; AUROC 0.891 vs. 0.876) while maintaining well-calibrated predictions. The system remains robust through a calibrated fallback when a modality is missing. These results demonstrate competitive performance with reliable, auditable risk estimates and transparent, predictable operation, which together are crucial for clinical use.