Methodological innovations for inference and learning

  • Integrating modern AI with stochastic modeling: Bayesian inference has been tremendously successful in a variety of applied problems across biological, social, and physical sciences. A key feature of Bayesian inference is a principled way of quantifying uncertainty in the inferential procedure. Recently modern AI methods such as deep neural networks have transformed predictive modeling, especially in the data-rich setting. We will integrate Bayesian (stochastic) modeling with modern AI (deep neural networks).
  • Inferential algorithms that scale: As more data is collected and as each observation contains more and richer measurements, classical inferential procedures fail to scale. The failure is especially problematic if there is a requirement to quantify uncertainty. The standard workhorse for Bayesian inference is Markov chain Monte Carlo (MCMC) and does not scale to massive data.

Mathematical foundations of inference and learning

  • The interface of geometry and topology with probability and statistics: There will be two themes driving this research. The first theme is importing ideas from modern geometry and topology to probabilistic modeling. The second theme is understanding the geometry and topology of random processes.
  • Inference and dynamics: There also will be two driving themes: Firstly, understanding the limits of inference and learning of dynamical systems. Secondly, developing inferential theory by considering inference as a dynamical system.

Machine learning and statistics for biomedical applications

  • Methods development: Often novel methodology is required to answer new questions or model new data types or modalities or to scale to modern genomic technologies. Methods have been developed across statistical genetics, quantitative genetics, cancer biology, molecular ecology, morphology, clinical decision making, and medical imaging.
  • Collaborative data analysis: Our group collaborates with clinicians and experimental biologists to address challenging and/or important problems.