## CS 4301: Numerical Methods for Machine Learning and Data Science

Fall 2020### Course Info

An introduction to computational methods in linear algebra and numerical optimization methods with the aim of preparing students for higher level electives in data science, artificial intelligence, and machine learning. Learning outcomes:

- Ability to apply gradient descent to find local optima of differentiable functions
- Practical and theoretical understanding convex functions and convex sets
- Ability to solve constrained optimization problems via the method of Lagrange multipliers
- Ability to understand the precision issues that arise when applying iterative numerical methods to solve optimization problems
- Ability to formulate basic results in linear algebra as convex optimization problems (regression, projections, eigenvalues)
- Understand the differences, both practical and theoretical, between different matrix decomposition techniques

**Where:**Online**When:**MW, 10:00am-11:15am**Instructor:**Nicholas Ruozzi**Office Hours:**M 11:30-12:30, W 12:30pm-1:30pm, and by appointment online.**TA:**Shahab Shams**Office Hours:**R 10:30am - 12:30pm**Grading:**problem sets (70%), midterm (15%), final (15%)**Required Prerequisites:**CS3345, Data Structures and Algorithms**Recommended Prerequisites:**MATH 2413 (Differential Calculus) or MATH 2417 (Calculus I) and MATH 2418 (Linear Algebra). Comfort with programming, basic probability, and algorithms is also assumed.### Schedule & Lecture Slides

Week | Dates | Topic | Readings |

1 | Aug. 17 & 19 | Introduction Gradients and Multivariable Calculus | |

2 | Aug. 24 & 26 | Convex Sets and Convex Functions Gradient Descent |
Boyd 2.1-2.3 Boyd 9.1-9.3 (can skip example subsections) |

3 | Aug. 31 & Sept. 2 | Subgradient Methods Convex Optimization |
Boyd 9.1-9.3 Boyd 4.1-4.3 |

4 | Sept. 9 | Projected Gradient | |

5 | Sept. 14 & 16 | Duality and Lagrange Multipliers |
Boyd 5 |

6 | Sept. 21 & 23 | Constraint Qualification and KKT |
Boyd 5 |

7 | Sept. 28 & 30 | Second Order Methods |
Boyd 3.3, 9.5, 10.1-10.2 |

8 | Oct. 5 & 7 | ML Applications | |

9 | Oct. 12 & 14 | Linear Algebra Review Positive Semidefinite Matrices | Boyd A.5 |

10 | Oct. 19 & 21 | Eigenvectors, Eigenvalues, and Semidefinite Programming | Boyd A.5 |

11 | Oct. 26 & 28 | Singular Value Decomposition | |

12 | Nov. 2 & 4 | Midterm Discussion & More SVD | |

13 | Nov. 9 & 11 | Matrix Factorizations | CUR Decompositions |

14 | Nov. 16 & 18 | Submodular Functions Alternating Projections | |

15 | Nov. 23 & 25 | Proximal Gradient Review |

### Problem Sets

All problem sets will be available on eLearning and are to be turned in there. See the homework guidelines below for homework policies.

### Textbooks & References

There is no required textbook, but the following books may serve as useful references for different parts of the course.

*Convex Optimization*by Stephen Boyd and Lieven Vandenberghe (online) .*Convex Optimization Theory*by Dimitri P. Bertsekas

### Exams

All exams will be take home, open book, open notes.

**Midterm:**10/14, Take Home**Final:**TBD, during exam period### Homework Guidelines*

I expect you to try solving each problem set on your own. However, if you get stuck on a problem, I encourage you to collaborate with other students in the class, subject to the following rules:

- You may discuss a problem with any student in this class, and work together on solving it. This can involve brainstorming and verbally discussing the problem, going together through possible solutions, but should not involve one student telling another a complete solution.
- Once you solve the homework, you must write up your solutions on your own, without looking at other people's write-ups or giving your write-up to others.
- In your solution for each problem, you must write down the names of any person with whom you discussed it. This will not affect your grade.
- Do not consult solution manuals or other people's solutions from similar courses - ask the course staff, we are here to help!

**Late homework**will**NOT**be accepted except in extreme circumstances or those permitted by university policy (e.g., a religious holiday). All such exceptions**MUST**be cleared in advance of the due date.### UT Dallas Course Policies and Procedures

For a complete list of UTD policies and procedures, see here.

**adpated from*

*David Sontag*