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September 21, 2023

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Description

18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning (Spring 2018, MIT OCW).

Instructor: Prof. Gilbert Strang. 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. (from ocw.mit.edu)

https://www.youtube.com/watch?v=Cx5Z-OslNWE&ab_channel=MITOpenCourseWare

Course Curriculum

  • Lecture 01 – The Column Space of A Contains All Vectors Ax Unlimited
  • Lecture 02 – Multiplying and Factoring Matrices Unlimited
  • Lecture 03 – Orthogonal Columns in Q Give QTQ = I Unlimited
  • Lecture 04 – Eigenvalues and Eigenvectors Unlimited
  • Lecture 05 – Positive Definite and Semidefinite Matrices Unlimited
  • Lecture 06 – Singular Value Decomposition (SVD) Unlimited
  • Lecture 07 – Eckart-Young: The Closest Rank k Matrix to A Unlimited
  • Lecture 08 – Norms of Vectors and Matrices Unlimited
  • Lecture 09 – Four Ways to Solve Least Squares Problems Unlimited
  • Lecture 10 – Survey of Difficulties with Ax = b Unlimited
  • Lecture 11 – Minimizing ∥X∥ Subject to Ax = b Unlimited
  • Lecture 12 – Computing Eigenvalues and Singular Values Unlimited
  • Lecture 13 – Randomized Matrix Multiplication Unlimited
  • Lecture 14 – Low Rank Changes in A and its Inverse Unlimited
  • Lecture 15 – Matrices A(t) Depending on t, Derivative = dA/dt Unlimited
  • Lecture 16 – Derivatives of Inverse and Singular Values Unlimited
  • Lecture 17 – Rapidly Decreasing Singular Values Unlimited
  • Lecture 18 – Counting Parameters in SVD, LU, QR, Saddle Points Unlimited
  • Lecture 19 – Saddle Points (cont.), Maxmin Principle Unlimited
  • Lecture 20 – Definitions and Inequalities Unlimited
  • Lecture 21 – Minimizing a Function Step by Step Unlimited
  • Lecture 22 – Gradient Descent: Downhill to a Minimum Unlimited
  • Lecture 23 – Accelerating Gradient Descent (Use Momentum) Unlimited
  • Lecture 24 – Linear Programming and Two-Person Games Unlimited
  • Lecture 25 – Stochastic Gradient Descent Unlimited
  • Lecture 26 – Structure of Neural Nets for Deep Learning Unlimited
  • Lecture 27 – Backpropagation: Find Partial Derivatives Unlimited
  • Lecture 30 – Completing a Rank-One Matrix, Circulants Unlimited
  • Lecture 31 – Eigenvectors of Circulant Matrices: Fourier Matrix Unlimited
  • Lecture 32 – ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule Unlimited
  • Lecture 33 – Neural Nets and the Learning Function Unlimited
  • Lecture 34 – Distance Matrices, Procrustes Problem Unlimited
  • Lecture 35 – Finding Clusters in Graphs Unlimited
  • Lecture 36 – Alan Edelman and Julia Language Unlimited

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