Applied R&D, Machine Learning & Mathematical Modeling

Architecting foundational mathematical frameworks, graph algorithms, and scalable statistical models for high-dimensional, noisy data systems.

NoteCore R&D Focus

I specialize in solving complex data problems where off-the-shelf statistical models fail. My work bridges Graph & Network Analytics, Statistical Physics & Phase Transitions, and High-Dimensional Statistical Modeling to extract clean, actionable insights from noisy, large-scale systems.

Core Technical Research Pillars

1. Graph AI, Network Science & Dynamic Clustering

Developing robust algorithms for community detection, constrained graph partitioning, and signal tracking in large-scale networks subject to measurement noise.

  • Constrained community detection in social networks. W. D. Viles and A. J. O’Malley. The New England Journal of Statistics in Data Science, 2(3):368–379, 2024.
    [DOI]
    • Technical Impact: Formulated constrained optimization algorithms for graph partitioning under topological and node-level operational boundaries.
  • Robust dynamic community detection with applications to human brain functional networks. L.-E. Martinet, M. A. Kramer, W. D. Viles, et al. Nature Communications, 11:2785, 2020.
    [DOI]
    • Technical Impact: Engineered noise-resilient clustering algorithms to track temporal state transitions and dynamic network evolution in high-dimensional time-series graphs.
  • On the propagation of low-rate measurement error to subgraph counts in large networks. P. Balachandran, E. D. Kolaczyk, and W. D. Viles. Journal of Machine Learning Research, 18(61): 1–33, 2017.
    [Paper]
    • Technical Impact: Quantified mathematical error bounds for graph motif analysis, establishing reliable network analytics in noisy, real-world data pipelines.

2. Phase Transitions, Statistical Physics & Network Dynamics

Designing mathematical models to infer critical phase transitions and percolation dynamics in noisy, evolving complex systems.

  • Percolation under noise: Detecting explosive percolation using the second-largest component. W. Viles, C. E. Ginestet, A. Tang, M. A. Kramer, and E. D. Kolaczyk. Physical Review E, 93(5): 052301, 2016.
    [DOI]
    • Technical Impact: Formulated statistical inference frameworks and hypothesis tests to detect explosive percolation phase transitions in noisy, dynamically evolving graph structures.

3. Complex Systems & High-Dimensional Biological Analytics

Modeling high-order interactions and multi-modal feature spaces in sparse, irregularly sampled observational data.

  • Identifying stationary microbial interaction networks based on irregularly spaced longitudinal 16S rRNA gene sequencing data. J. Zhou, J. Gui, W. D. Viles, et al. Frontiers in Microbiomes, 3, 2024.
    [DOI]
    • Technical Impact: Constructed longitudinal network inference frameworks tailored for asynchronous sampling intervals and non-stationary dynamic systems.
  • Information content of high-order associations of the human gut microbiota network. W. D. Viles, J. C. Madan, H. Li, M. R. Karagas, and A. G. Hoen. The Annals of Applied Statistics, 15(4):1788–1807, 2021.
    [JSTOR]
    • Technical Impact: Designed higher-order graphical model estimators capable of capturing non-pairwise, hyper-graph dependency structures in multivariate counts.

Funded R&D & Cross-Functional Research Leadership

Co-Investigator | Multi-omic Functional Integration using Networks

National Institutes of Health (NIH) / National Library of Medicine | 2017 – 2021

  • Project Scope: Led quantitative methodology development for integrating multi-omic biological data streams using graph-based computational pipelines.
  • Deliverables: Built scalable network inference algorithms to isolate key statistical associations in complex biological ecosystems, facilitating automated hypothesis generation for clinical domain experts.

Technical Capability Summary Matrix

Domain Pillar Core Methodologies Industry Value & Application
Graph & Network Analytics Community Detection, Motif Analysis, Dynamic Graphs, Error Bounds Social Network Analysis, Fraud/Entity Resolution, Brain-Computer Interfaces
Network Dynamics & Physics Phase Transitions, Percolation Modeling, Noisy Systems, Graph Phase Inferences Anomaly Detection, System Stability Modeling, Reliability Engineering
Complex Systems Hyper-graph Associations, Longitudinal Inference, High-Dimensional Data Bioinformatics, Health Tech, Sensor Stream Analytics, Time-Series Forecasting