Insights By Scott Ernst

Project Autodidact

Project Details: https://insightsbyse.com/projectautodidact/

Scott Ernst Bio: https://insightsbyse.com/aboutscotternst/

Project Contact: InsightsBySE@protonmail.com

Progress Report Scope (S01-M03-D05-AllParts) (End of Stage 1)

Stage 1 of 4: Review of Mathematics, Probability, and Statistics

Module 3 of 3: Linear Algebra, Calculus, and Applications

Day 5 of 5: Multivariable Calculus and Optimization

Parts 1 through 8: See below (NOTE: Only 8 parts for these topics)

Summary Of Goals Achieved

1. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of partial derivatives of multivariable functions
2. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for computing partial derivatives of multivariable functions
3. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of gradient vectors of multivariable functions
4. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of directional derivatives of multivariable functions
5. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for computing gradient vectors and directional derivatives of multivariable functions
6. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for iterative optimization of gradient descent of multivariable functions
7. Reviewed similarities and differences in the applicability of the Jacobian matrix, Hessian matrix, Taylor series (aka Taylor expansion), and Maclaurin series
8. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of the Jacobian matrix for multivariable functions
9. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of the Hessian matrix for multivariable functions
10. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of the Taylor series (aka Taylor expansion) for multivariable functions
11. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of the Maclaurin series for multivariable functions
12. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for computing Hessian matrices and Jacobian matrices of multivariable functions
13. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for computing the Taylor series (aka Taylor expansion) and Maclaurin series of multivariable functions
14. Reviewed similarities and differences among the objective function, Lagrange multiplier, constraint function, and Lagrangian function for multivariable functions
15. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for the method of Lagrange multipliers for multivariable functions
16. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of the cost function (aka loss function) optimization for multivariable functions
17. Reviewed similarities and differences between model parameters (aka weights and biases) and hyperparameters
18. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of parameter tuning for multivariable functions (as distinguished from hyperparameter tuning)
19. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of hyperparameter tuning for multivariable functions (as distinguished from parameter tuning)
20. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for cost function optimization for multivariable functions
21. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for parameter tuning for multivariable functions (as distinguished from hyperparameter tuning)
22. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for hyperparameter tuning for multivariable functions (as distinguished from parameter tuning)
23. Reviewed similarities and differences among feature analysis, feature importance, sensitivity analysis, and local interpretability (SHAP)
24. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for feature analysis for multivariable functions
25. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for feature importance for multivariable functions
26. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for sensitivity analysis for multivariable functions
27. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for local interpretability (SHAP) for multivariable functions
28. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for identifying and analyzing multidimensional trends for multivariable functions
29. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for visualizing multivariable functions and gradients, such as contour plots and gradient fields

Part 1 of 8

Goal 1 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of partial derivatives of multivariable functions

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for computing partial derivatives of multivariable functions

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Part 2 of 8

Goal 1 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of gradient vectors of multivariable functions

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of directional derivatives of multivariable functions

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for computing gradient vectors and directional derivatives of multivariable functions

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for iterative optimization of gradient descent of multivariable functions

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Part 3 of 8

Goal 1 Statement: Review similarities and differences in the applicability of the Jacobian matrix, Hessian matrix, Taylor series (aka Taylor expansion), and Maclaurin series

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of the Jacobian matrix for multivariable functions

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of the Hessian matrix for multivariable functions

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of the Taylor series (aka Taylor expansion) for multivariable functions

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of the Maclaurin series for multivariable functions

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Goal 6 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for computing Hessian matrices and Jacobian matrices of multivariable functions

Goal 6 Plan: Read source materials

Goal 6 Work Product: None

Goal 6 Result: Completed

Goal 7 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for computing the Taylor series (aka Taylor expansion) and Maclaurin series of multivariable functions

Goal 7 Plan: Read source materials

Goal 7 Work Product: None

Goal 7 Result: Completed

Part 4 of 8

Goal 1 Statement: Review similarities and differences among the objective function, Lagrange multiplier, constraint function, and Lagrangian function for multivariable functions

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for the method of Lagrange multipliers for multivariable functions

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Part 5 of 8

Goal 1 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of the cost function (aka loss function) optimization for multivariable functions

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review similarities and differences between model parameters (aka weights and biases) and hyperparameters

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of parameter tuning for multivariable functions (as distinguished from hyperparameter tuning)

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of hyperparameter tuning for multivariable functions (as distinguished from parameter tuning)

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for cost function optimization for multivariable functions

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Goal 6 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for parameter tuning for multivariable functions (as distinguished from hyperparameter tuning)

Goal 6 Plan: Read source materials

Goal 6 Work Product: None

Goal 6 Result: Completed

Goal 7 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for hyperparameter tuning for multivariable functions (as distinguished from parameter tuning)

Goal 7 Plan: Read source materials

Goal 7 Work Product: None

Goal 7 Result: Completed

Part 6 of 8

Goal 1 Statement: Review similarities and differences among feature analysis, feature importance, sensitivity analysis, and local interpretability (SHAP)

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for feature analysis for multivariable functions

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for feature importance for multivariable functions

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for sensitivity analysis for multivariable functions

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for local interpretability (SHAP) for multivariable functions

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Part 7 of 8

Goal 1 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for identifying and analyzing multidimensional trends for multivariable functions

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Part 8 of 8

Goal 1 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for visualizing multivariable functions and gradients, such as contour plots and gradient fields

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

End of Stage 1