Uploaded July 2025 | Updated September 2026, 2 weeks ago
The covariance and correlation between two random variables is an important concept in probability and statistics that generalizes to data science and machine learning, especially for higher dimensional systems.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:50 Defining Covariance
03:48 Visual Intuitions of Covariance
08:05 Reformulation of Covariance
11:14 Covariance of Independents is 0
12:08 Covariance 0 is Not Independence
14:13 Additional Properties
16:06 Defining Correlation
17:51 Correlation Over Linear Transforms
18:53 Outro
The covariance and correlation between two random variables is an important concept in probability and statistics that generalizes to data science and machine learning, especially for higher dimensional systems.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:50 Defining Covariance
03:48 Visual Intuitions of Covariance
08:05 Reformulation of Covariance
11:14 Covariance of Independents is 0
12:08 Covariance 0 is Not Independence
14:13 Additional Properties
16:06 Defining Correlation
17:51 Correlation Over Linear Transforms
18:53 Outro
![AI/ML+Physics Part 5: Employing an Optimization Algorithm [Physics Informed Machine Learning]](https://i.ytimg.com/vi/T4iJ10TAIMg/mqdefault.jpg "AI/ML+Physics Part 5: Employing an Optimization Algorithm [Physics Informed Machine Learning]
This video discusses the fifth stage of the machine learning process: (5) selecting and implementing an optimization algorithm to train the model. There are opportunities to incorporate physics into this stage of the process, such as using constrained optimization to force a model onto a susbpace or submanifold characterized by a symmetry or other physical constraint.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:45 Case Study: KKT Constrained Least Squares
06:18 Case Study: Physics Informed DMD
14:00 Loss vs Optimization of Subspace Constraints
17:50 Subspace Constraints and Symmetry
19:28 Case Study: Symbolic Regression and Evolutionary Optimization
22:25 Parsimony and Sparse Optimization Algorithms
25:03 Case Study: SINDy and SR3
28:38 Parsimony and Sparsity Hyperparameters
30:55 Outro")
