Melvin Leok

Convex functions and Bregman divergence: Convex functions

Estimation in the context of statistical inference

Exponential maps on matrix Lie groups

Convex functions and Bregman divergence: Bregman divergence

Cubic spline interpolation

Minimizing divergence between a model manifold and a data manifold

Divergence between submanifolds

Lie group collision variational integrator - bouncing cube/dice simulation - Example 5

Proof of Taylor's theorem with integral remainder

Parallel transport of a vector

Error Analysis - Local vs. Global Error

First-order Asymptotic Theory of Estimation

Geometric Tracking Control of a Quadrotor UAV on SE(3)

Covariant derivatives using affine connections

Dually Flat Manifolds

Statistical models with hidden variables

Higher-order Asymptotic Theory of Estimation

Tensors

Geodesics

Flat manifolds

Estimation in a Curved Exponential Family

Boltzmann machine with hidden units

Asymptotic Theory of Hypothesis Testing

Estimation in the Exponential Family

Canonical divergence in dually flat manifolds

Convergence of line-search methods on manifolds

Gradient-related sequences, Armijo points, and accelerated line search

PIMS Marsden Memorial Lecture by Melvin Leok at UNBC in March 2023

Levi-Civita (Riemannian) connection

Metric and Cubic Tensor Derived from Divergence or Convex Functions

Holonomy (Round-the-world transport)

EM algorithm applied to Gaussian mixtures

Gaussian elimination

Riemannian metric, distance, and gradients

Lagrange polynomial interpolation

Convex functions and Bregman divergence: Convex functions

Gaussian mixture model as a system with hidden variables

Legendre transform of convex functions and Bregman divergence

Homology groups