Channel Avatar

Melvin Leok @UC3x0QbvHPMEf_O0Usp4eoCQ@youtube.com

4.1K subscribers - no pronouns :c

Melvin Leok is a professor of mathematics at the University


00:26
Lie group collision variational integrator - bouncing cube/dice simulation - Example 5
01:05:10
PIMS Marsden Memorial Lecture by Melvin Leok at UNBC in March 2023
20:53
EM algorithm applied to Gaussian mixtures
34:43
Minimizing divergence between a model manifold and a data manifold
17:51
Boltzmann machine with hidden units
10:55
Gaussian mixture model as a system with hidden variables
28:12
Statistical models with hidden variables
23:16
Asymptotic Theory of Hypothesis Testing
24:01
Higher-order Asymptotic Theory of Estimation
30:41
First-order Asymptotic Theory of Estimation
35:10
Estimation in a Curved Exponential Family
14:38
Estimation in the Exponential Family
25:51
Estimation in the context of statistical inference
38:58
Canonical divergence in dually flat manifolds
16:22
Dually Flat Manifolds
20:42
Metric and Cubic Tensor Derived from Divergence or Convex Functions
26:20
Dual affine connections
16:39
Levi-Civita (Riemannian) connection
25:31
Holonomy (Round-the-world transport)
08:18
Flat manifolds
15:12
Parallel transport of a vector
13:26
Geodesics
23:08
Covariant derivatives using affine connections
26:55
Tensors
26:27
Affine connections
20:00
Riemannian metric
31:11
Manifolds and Tangent Spaces
05:41
Tangent vectors under changes of coordinates
23:01
Repeated observations and maximum likelihood estimators
13:24
Mutual information
20:02
Maximum entropy principle and e-projection
15:17
Bregman divergence and exponential family
09:59
Kernel exponential family of probability distributions
13:47
Infinite-dimensional manifold of probability distributions: KL-divergence
50:09
Infinite-dimensional manifold of probability distributions
18:11
Flat structure: e-flat and m-flat
17:30
Mixture family of probability distributions
13:23
Example of Exponential Family: Discrete Distributions
10:59
Example of Exponential Family: Gaussian Distributions
31:32
Exponential family of probability distributions
12:34
Divergence between submanifolds
29:38
Projection Theorem relating dual orthogonal projection and divergence minimizing projection
20:19
Generalized Pythagorean Theorem
27:49
Parallel Transport of Vectors
31:40
Tangent space, basis vectors, and Riemannian metric
18:03
Affine and dual affine coordinate systems
29:53
Legendre transform of convex functions and Bregman divergence
16:25
Convex functions and Bregman divergence: Examples of Bregman divergence
08:17
Convex functions and Bregman divergence: Bregman divergence
18:11
Convex functions and Bregman divergence: Convex functions
13:11
Examples of divergence
18:29
Divergence between two points
17:16
Manifolds of probability distributions: Discrete distributions
08:45
Manifolds of probability distributions: Gaussian distributions
26:45
Information geometry and mechanics
37:46
An overview of information geometry
28:52
Computational Geometric Mechanics
14:51
Solving tridiagonal systems
17:27
Tridiagonal system for cubic spline interpolation
11:19
Cubic spline interpolation