Daniel J. Lawson

Ed Davis, Ian Gallagher, Daniel John Lawson et al.

In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While the field of static network embedding is wide and established, the field of dynamic network embedding is comparatively in its infancy. We propose that a wide class of established static network embedding methods can be used to produce interpretable and powerful dynamic network embeddings when they are applied to the dilated unfolded adjacency matrix. We provide a theoretical guarantee that, regardless of embedding dimension, these unfolded methods will produce stable embeddings, meaning that nodes with identical latent behaviour will be exchangeable, regardless of their position in time or space. We additionally define a hypothesis testing framework which can be used to evaluate the quality of a dynamic network embedding by testing for planted structure in simulated networks. Using this, we demonstrate that, even in trivial cases, unstable methods are often either conservative or encode incorrect structure. In contrast, we demonstrate that our suite of stable unfolded methods are not only more interpretable but also more powerful in comparison to their unstable counterparts.

Daniel J. Lawson, Vinesh Solanki, Igor Yanovich et al.

Integrating datasets from different disciplines is hard because the data are often qualitatively different in meaning, scale, and reliability. When two datasets describe the same entities, many scientific questions can be phrased around whether the (dis)similarities between entities are conserved across such different data. Our method, CLARITY, quantifies consistency across datasets, identifies where inconsistencies arise, and aids in their interpretation. We illustrate this using three diverse comparisons: gene methylation vs expression, evolution of language sounds vs word use, and country-level economic metrics vs cultural beliefs. The non-parametric approach is robust to noise and differences in scaling, and makes only weak assumptions about how the data were generated. It operates by decomposing similarities into two components: a `structural' component analogous to a clustering, and an underlying `relationship' between those structures. This allows a `structural comparison' between two similarity matrices using their predictability from `structure'. Significance is assessed with the help of re-sampling appropriate for each dataset. The software, CLARITY, is available as an R package from https://github.com/danjlawson/CLARITY.

Samuel Stockman, Daniel Lawson, Maximilian Werner

For decades, classical point process models, such as the epidemic-type aftershock sequence (ETAS) model, have been widely used for forecasting the event times and locations of earthquakes. Recent advances have led to Neural Point Processes (NPPs), which promise greater flexibility and improvements over such classical models. However, the currently-used benchmark for NPPs does not represent an up-to-date challenge in the seismological community, since it contains data leakage and omits the largest earthquake sequence from the region. Additionally, initial earthquake forecasting benchmarks fail to compare NPPs with state-of-the-art forecasting models commonly used in seismology. To address these gaps, we introduce EarthquakeNPP: a collection of benchmark datasets to facilitate testing of NPPs on earthquake data, accompanied by an implementation of the state-of-the-art forecasting model: ETAS. The datasets cover a range of small to large target regions within California, dating from 1971 to 2021, and include different methodologies for dataset generation. Benchmarking experiments, using both log-likelihood and generative evaluation metrics widely recognised in seismology, show that none of the five NPPs tested outperform ETAS. These findings suggest that current NPP implementations are not yet suitable for practical earthquake forecasting. Nonetheless, EarthquakeNPP provides a platform to foster future collaboration between the seismology and machine learning communities.