Mathematical Foundations of Machine Learning(MATH 601)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MATH 601 | Mathematical Foundations of Machine Learning | 1 | 3 | 0 | 0 | 3 | 7 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | English |
| Course Type | Elective |
| Course Level | Doctoral Degree |
| Course Instructor(s) | Ayberk ZEYTİN azeytin@gsu.edu.tr (Email) |
| Assistant | |
| Objective | To teach students machine learning principles and equip them with focused tools to apply data analysis, manifestations, regression, clustering, and dimensionality reduction techniques. |
| Content | This course covers the principles of machine learning, focusing particularly on its mathematical foundations. Students will learn fundamental machine learning concepts such as data analysis, regression, classification, clustering, and dimensionality reduction techniques, and will use mathematical tools to apply them. |
| Course Learning Outcomes |
1. Understand and use basic linear algebraic concepts used in data science. 2. Understand and use basic mathematical analysis and optimization concepts used in data science. 3. Understand and use basic statistical concepts used in data science. |
| Teaching and Learning Methods | Face to face lectures, Problem Solving Sessions |
| References |
Learning Theory from First Principles, Francis Bach Deep Learning, Ian Goodfellow, Yoshua Bengio and Aaron Courville High-Dimensional Probability, Vershynin Convex Optimization, Boyd ve Vandenberghe Elements of Information Theory, Cover ve Thomas Understanding Machine Learning, Shalev-Shwartz ve Ben-David Pattern Recognition and Machine Learning, Christopher Bishop, Machine Learning: A Probabilistic Perspective, Kevin Murphy |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Linear Algebra Basics |
| 2 | Spectral Theory |
| 3 | Singular Value Decomposition |
| 4 | Positive Matrices and Perron--Frobenius |
| 5 | Calculus Refresher |
| 6 | Convex Sets and Functions |
| 7 | Convex Optimization |
| 8 | Nonconvex Optimization |
| 9 | Probability Theory Foundations |
| 10 | Concentration Inequalities |
| 11 | Advanced Probability for Machine Learning |
| 12 | Statistical Estimation |
| 13 | High-Dimensional Statistics |
| 14 | Information Theory Essentials |
Practice Topics
| Week | Weekly Contents |
|---|---|
| 1 | --- |
| 2 | --- |
| 3 | --- |
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Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 6 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 7 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 0 | 0 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 6 | 60 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Make-up | 0 | 0 |
| Toplam | 6 | 60 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 3 | 42 |
| Working Hours out of Class | 14 | 3 | 42 |
| Assignments | 6 | 5 | 30 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 1 | 36 | 36 |
| Quiz | 6 | 3 | 18 |
| Term Paper/ Project | 0 | 0 | 0 |
| Portfolio Study | 0 | 0 | 0 |
| Reports | 0 | 0 | 0 |
| Learning Diary | 0 | 0 | 0 |
| Thesis/ Project | 0 | 0 | 0 |
| Seminar | 0 | 0 | 0 |
| Other | 0 | 0 | 0 |
| Make-up | 0 | 0 | 0 |
| Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Bütünleme | 0 | 0 | 0 |
| Total Workload | 168 | ||
| Total Workload / 25 | 6.72 | ||
| Credits ECTS | 7 | ||