arXiv subjects

Joshua Corneck

Publications and source records attributed to Joshua Corneck.

4 recordsLinked to original sources

arXiv2026

Synthesizing Epileptic Seizures: Gaussian Processes for EEG Generation

Reliable seizure detection from electroencephalography (EEG) time series is a high-priority clinical goal, yet the acquisition cost and scarcity of labeled EEG data limit the performance of machine learning methods. This challenge is exacerbated by the long-range, high-dimensional, and non-stationary nature of epileptic EEG recordings, which makes realistic data generation particularly difficult. In this work, we revisit Gaussian processes as a principled and interpretable foundation for modeling EEG dynamics, and propose a novel hierarchical framework, \textit{GP-EEG}, for generating synthetic epileptic EEG recordings. At its core, our approach decomposes EEG signals into temporal segments modeled via Gaussian process regression, and integrates a domain-adaptation variational autoencoder. We validate the proposed method on two real-world, open-source epileptic EEG datasets. The synthetic EEG recordings generated by our model match real-world epileptic EEG both quantitatively and qualitatively, and can be used to augment training sets.

stat.ME↗

arXiv2026

Spectral embedding of inhomogeneous Poisson processes on multiplex networks

In many real-world networks, data on the edges evolve in continuous time, naturally motivating representations based on point processes. Heterogeneity in edge types further gives rise to multiplex network point processes. In this work, we propose a model for multiplex network data observed in continuous-time. We establish two-to-infinity norm consistency and asymptotic normality for spectral-embedding-based estimation of the model parameters as both network size and time resolution increase. Drawing inspiration from random dot product graph models, each edge intensity is expressed as the inner product of two low-dimensional latent positions: one dynamic and layer-agnostic, the other static and layer-dependent. These latent positions constitute the primary objects of inference, which is conducted via spectral embedding methods. Our theoretical results are established under a histogram estimator of the network intensities and provide justification for applying a doubly unfolded adjacency spectral embedding method for estimation. Simulations and real-data analyses demonstrate the effectiveness of the proposed model and inference procedure.

stat.ME↗

arXiv2025

Simultaneous global and local clustering in multiplex networks with covariate information

Understanding both global and layer-specific group structures is useful for uncovering complex patterns in networks with multiple interaction types. In this work, we introduce a new model, the hierarchical multiplex stochastic blockmodel (HMPSBM), that simultaneously detects communities within individual layers of a multiplex network while inferring a global node clustering across the layers. A stochastic blockmodel is assumed in each layer, with probabilities of layer-level group memberships determined by a node's global group assignment. Our model uses a Bayesian framework, employing a probit stick-breaking process to construct node-specific mixing proportions over a set of shared Griffiths-Engen-McCloseky (GEM) distributions. These proportions determine layer-level community assignment, allowing for an unknown and varying number of groups across layers, while incorporating nodal covariate information to inform the global clustering. We propose a scalable variational inference procedure with parallelisable updates for application to large networks. Extensive simulation studies demonstrate our model's ability to accurately recover both global and layer-level clusters in complicated settings, and applications to real data showcase the model's effectiveness in uncovering interesting latent network structure.

stat.ME↗

arXiv2024

Online Bayesian changepoint detection for network Poisson processes with community structure

Network point processes often exhibit latent structure that govern the behaviour of the sub-processes. It is not always reasonable to assume that this latent structure is static, and detecting when and how this driving structure changes is often of interest. In this paper, we introduce a novel online methodology for detecting changes within the latent structure of a network point process. We focus on block-homogeneous Poisson processes, where latent node memberships determine the rates of the edge processes. We propose a scalable variational procedure which can be applied on large networks in an online fashion via a Bayesian forgetting factor applied to sequential variational approximations to the posterior distribution. The proposed framework is tested on simulated and real-world data, and it rapidly and accurately detects changes to the latent edge process rates, and to the latent node group memberships, both in an online manner. In particular, in an application on the Santander Cycles bike-sharing network in central London, we detect changes within the network related to holiday periods and lockdown restrictions between 2019 and 2020.

stat.CO↗