Matrix Methods in Data Analysis, Signal Processing and Machine Learning (P2)
Channel: Code Geek
Date: 2022-02-20

Matrix Methods in Data Analysis, Signal Processing and Machine Learning. This course reviews linear algebra with applications to probability and statistics and optimization–and above all a full explanation of deep learning.
Linear Algebra - Full College Course
☞ https://morioh.com/p/0fd44b66d9d1
Linear Algebra Tutorial for Beginners - Full Course 
☞ https://morioh.com/p/beb142e8b2c3
Top 12 Machine Learning Algorithms You Should Know to Become a Data Scientist
☞ https://morioh.com/p/1013a5f310dd

Matrix Methods in Data Analysis, Signal Processing and Machine Learning (P1): https://morioh.com/p/a9cddec7f55d 

Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization–and above all a full explanation of deep learning.

1. Four Ways to Solve Least Squares Problems
In this lecture, Professor Strang details the four ways to solve least-squares problems. Solving least-squares problems comes in to play in the many applications that rely on data fitting.

2. Survey of Difficulties with Ax = b
The subject of this lecture is the matrix equation Ax=b. Solving for x presents a number of challenges that must be addressed when doing computations with large matrices.

3. Minimizing ‖x‖ Subject to Ax = b
In this lecture, Professor Strang revisits the ways to solve least squares problems. In particular, he focuses on the Gram-Schmidt process that finds orthogonal vectors.

4. Computing Eigenvalues and Singular Values
Numerical linear algebra is the subject of this lecture and, in particular, how to compute eigenvalues and singular values. This includes discussion of the Hessenberg matrix, a square matrix that is almost (except for one extra diagonal) triangular.

5. Randomized Matrix Multiplication
This lecture focuses on randomized linear algebra, specifically on randomized matrix multiplication. This process is useful when working with very large matrices. Professor Strang introduces and describes the basic steps of randomized computations.


6. Low Rank Changes in A and Its Inverse
In this lecture, Professor Strang introduces the concept of low rank matrices. He demonstrates how using the Sherman-Morrison-Woodbury formula is useful to efficiently compute how small changes in a matrix affect its inverse.

7. Matrices A(t) Depending on t, Derivative = dA/dt
This lecture is about changes in eigenvalues and changes in singular values. When matrices move, their inverses, their eigenvalues, and their singular values change. Professor Strang explores the resulting formulas.

8. Derivatives of Inverse and Singular Values
In this lecture, Professor Strang reviews how to find the derivatives of inverse and singular values. Later in the lecture, he discusses LASSO optimization, the nuclear norm, matrix completion, and compressed sensing.

9. Rapidly Decreasing Singular Values
Professor Alex Townsend gives this guest lecture answering the question 'Why are there so many low rank matrices that appear in computational math?'  Working effectively with low rank matrices is critical in image compression applications.

10. Counting Parameters in SVD, LU, QR, Saddle Points
In this lecture, Professor Strang reviews counting the free parameters in a variety of key matrices. He then moves on to finding saddle points from constraints and Lagrange multipliers.

11. Saddle Points Continued, Maxmin Principle
Professor Strang continues his discussion of saddle points, which are critical for deep learning applications. Later in the lecture, he reviews the Maxmin Principle, a decision rule used in probability and statistics to optimize outcomes.


#DataAnalysis #MachineLearning #Morioh

License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
------------------------------------------------------------------------------------ 
Social Network for Developers: http://bit.ly/2R1Lw31
Developer's Store: http://bit.ly/2L27JNR 
Fanpage: http://bit.ly/2LyM4fJ
Twitter: http://bit.ly/2J7vCS0