Bayesian computational statistics
My research focuses on bridging the gap between practical optimization and sampling techniques and their mathematical foundations. While connecting theory and practice remains a challenge, I explore Markov chain theory and the Stochastic Approximation framework as tools for advancing this understanding.
Time series analysis
Time series are pervasive in medicine, presenting a fascinating challenge in modeling. Understanding their varying patterns across different time scales and inferring the underlying latent phenomena are key issues I aim to address.
Riemannian geometry
Riemannian geometry provides a flexible framework for analyzing complex data while preserving geometric concepts like geodesics and curvature. Discovering efficient ways to learn these structures is, in my view, a key future direction for machine learning research.
Biomedical applications
All of these research topics have applications in biomedical research. I have worked with data from patients with Alzheimer's disease, those in Intensive Care Units, individuals in recovery monitored through gait analysis, prostate cancer screening and psychological experiments related to anxiety.