Linear algebra (eigenvalue problem, singular value decomposition,
and generalized inverse matrix), optimization technique (gradient method, conjugate gradient method, and quasi-Newton method), and statistics (estimation and test) are lectured.
The objective of this course is to provide fundamental optimization technique
and statistics to handle various quantities with respect to international development.
In order to understand those knowledges, basic mathematics for them is also provided.
2. Eigenvalue decomposition and singular value decomposition
3. Generalized inverses of matrix
4. Maximum gradient method and Conjugate gradient method
5. Newton method and Quasi-Newton method
6. Lagrange窶冱 method and Karush–Kuhn–Tucker condition
7. Dual problem
8. Penalty method
9. Probability (Definition of Random variable)
10. Estimator (Maximum likelihood estimator and Bayesian estimator)
11. Cramer-Rao lower bound
12 Principle component analysis
15. Statistical learning theory
Copy of slide is prepared