Melvin Leok
Melvin Leok is a professor of mathematics at the University of California, San Diego, where his research is supported by grants from NSF, AFOSR, and DoD, including the NSF CAREER Award, and the DoD Newton Award for Transformative Ideas. He is a NAS Kavli Frontiers of Science Fellow, a Simons Fellow in Mathematics, and received the SciCADE New Talent Prize, SIAM Student Paper Prize, and Leslie Fox Prize in Numerical Analysis. He gave plenary talks at Foundations of Computational Mathematics, NUMDIFF, and the IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control.
He is affiliated with the Center for Control Systems and Dynamics, the Contextual Robotics Institute, the Halicioglu Data Science Institute, and the NSF AI Institute, TILOS.
Available as a consultant for modeling, simulating, controlling, quantifying uncertainty, machine learning, and optimization for large scale interconnected systems that evolve on nonlinear configuration spaces.
Geometric Mechanics Formulations for Field Theories
PIMS Marsden Memorial Lecture by Melvin Leok at UNBC in March 2023
EM algorithm applied to Gaussian mixtures
Minimizing divergence between a model manifold and a data manifold
Boltzmann machine with hidden units
Gaussian mixture model as a system with hidden variables
Statistical models with hidden variables
Asymptotic Theory of Hypothesis Testing
Higher-order Asymptotic Theory of Estimation
Асимптотическая теория оценивания первого порядка
Estimation in a Curved Exponential Family
Estimation in the Exponential Family
Estimation in the context of statistical inference
Canonical divergence in dually flat manifolds
Dually Flat Manifolds
Metric and Cubic Tensor Derived from Divergence or Convex Functions
Dual affine connections
Levi-Civita (Riemannian) connection
Голономия (кругосветный транспорт)
Flat manifolds
Parallel transport of a vector
Geodesics
Covariant derivatives using affine connections
Тензоры
Affine connections
Riemannian metric
Manifolds and Tangent Spaces
Tangent vectors under changes of coordinates
Repeated observations and maximum likelihood estimators