Current focus
I’m currently working with Dr. Bernhard Bodmann in order to build operator theoretic tools to learn CTMC dynamics on graphs from censored data where only X(0) and X(T) are observed.
My goals are twofold:
Create a rigorous framework with identifiability stability and uncertainty bounds for the generator in continuous and discrete time under structural constraints.
Design efficient algorithms that inherit these guarantees and scale to real data.
The models respect graph geometry using incidence Dirac and Laplacian structure with regularization to encode adjacency and smoothness. Hidden paths are reconstructed with Doob bridges inside an EM routine.
This work draws on time frequency analysis functional analysis, operator algebras, harmonic analysis, probability thoery, Bayesian statistics, dynamical systems, optimization, ordinary differential equations and numerical analysis, with applications to mobility networks molecular switching, mathematical biology and population dynamics.
Theory: I prove existence, identifification, stability, and uncertainty guarantees for estimating Q from sparse observations.
Algorithms: I translate those guarantees into efficient estimators that aim to outperform black-box methods.
Geometry-aware models: The estimators respect graph geometry leveraging Dirac structure and column-sum constraints. So, learned flows follow the network rather than fight it.
Censored-path inference: To reconstruct the unobserved path segments, I use Doob bridges inside an EM routine: alternate exact conditional expectations with updates to a structured, regularized likelihood for Q.
Maximum likelihood estimation of markov processes with censored data: The Ehrenfest model and beyond.
Inferring hidden trajectories in endpoint-only markov jump processes: regularized likelihood with applications to the NYC yellow taxi graph and predator–prey model
(Planned arXiv posting February 2026)
I’m excited to collaborate on problems in:
Dynamical systems and operator algebras
Quantum information theory
Inverse problems on networks, spectral methods, and learning stochastic dynamics
Compressed sensing and time–frequency analysis, especially where structure can be exploited for sample- and compute-efficiency