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Advanced Matrix Calculus and Optimization Techniques for Quadratic Functions

This presentation delves into advanced matrix calculus concepts focusing on Hessian matrices and their applications in optimization. We explore the quadratic function (x-y)² with specific parameters a=1, b=-1, c=1, and examine methods like Expected Maximization (EM) and Deepest Descent over 2000 iterations. Additionally, we analyze Jensen's Approximation applied to EM after 30 iterations. The session concludes with strategies for incorporating learning into our models, providing a comprehensive understanding of these mathematical tools in machine learning contexts.

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Advanced Matrix Calculus and Optimization Techniques for Quadratic Functions

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Presentation Transcript

  1. UCF Week 11 Lam Tran

  2. Hessian Matrix 1

  3. Hessian Matrix 2

  4. Hessian Matrix 3

  5. Matrix Calculus Quadratic Equation

  6. Matrix Calculus Example For (x-y)^2, a=1, b=-1, and c=1

  7. Expected Maximization (EM)

  8. Deepest Descent using convolution (2000 iterations) Jensen’s Approximation with Expected Maximization after 30th iterations (Matrix Calculus)

  9. Next Step • Adding learning to our model

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