20874 - ALGORITHMS FOR OPTIMIZATION AND INFERENCE
Department of Computing Sciences
Course taught in English
Go to class group/s: 29
Course Director:
LAURA SANITA'
LAURA SANITA'
Mission & Content Summary
MISSION
The course will teach the students the fundamentals of designing and analyzing algorithms for optimization and inference problems.
The students will be able to estimate the computational complexity and the resource requirements of the algorithms they encounter, and to use them as building blocks in their own work.
They will be familiarized with fundamental algorithmic theory and optimization techniques, and their interplay with inference and learning methods.
CONTENT SUMMARY
Basic Notions and Algorithmic Background
Algorithmic efficiency
Complexity classes and reductions
Graph and Combinatorial Optimization
Fundamental graph optimization problems
Matroids and Matroid intersection, Submodularity
Approximation algorithms for hard combinatorial optimization problems
Mathematical Optimization techniques
Linear Programming models and algorithms
Duality and Sensitivity analysis
Integer Programming models and algorithms
Non-linear Programming models and algorithms
Stochastic and Robust Optimization
Large-scale optimization
Inference and Learning
Submodular optimization and its applications in ML and AI
Mathematics of Neural Networks
Optimization algorithms for Deep Learning
Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...
- Understand the concept of algorithmic efficiency
- Recognize fundamental optimization problems and distinguish their computational complexity classification
- Be familiar with mathematical programming theory and algorithms
- Deal with stochastic, robust, and large-scale aspects of optimization problems
- Understand the mathematics behind popular inference algorithms
APPLYING KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...
- Design and analyze efficient algorithms
- Estimate the computational and resource requirements of algorithms
- Classify optimization problems according to their computational complexity
- Formulate optimization problems as Linear/Integer/Non-linear programming models
- Solve stochastic, robust, and large-scale optimization problems using the appropriate techniques
- Apply inference algorithms
Teaching methods
- Face-to-face lectures
DETAILS
The teaching method is face-to-face lectures. Several lectures will include exercises to be done in class.
Assessment methods
| Continuous assessment | Partial exams | General exam | |
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ATTENDING AND NOT ATTENDING STUDENTS
There will be a written exam and two homework assignments. The homework assignments are not mandatory.
The final grade will be calculated by taking for each student the best outcome out of the following two ones:
(a) Final written test contributes 70% of the final grade, and homework assignments contribute 30%.
(b) Final written test contributes 100% of the final grade.
The exam will test the students' ability to explain and reproduce the concepts learned in class, and connect these concepts to specific problem instances. There will be no difference between attending and non-attending students.
Teaching materials
ATTENDING AND NOT ATTENDING STUDENTS
- Lecture slides and notes provided by the instructor
- T.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein, Introduction to Algorithms, (The MIT press), 3rd/4th edition
- W. Cook, W. Cunningham, W. Pulleyblank and A. Schrijver. Combinatorial Optimization. Wiley-Interscience, 1997
- B. Guenin, J. Könemann, L. Tuncel, A Gentle Introduction to Optimization, Cambridge University Press, 2014
- Computer and Intractability. A Guide to NP-Completeness. M. R. Garey and D. S. Johnson. Publisher W. H. Freeman, 1979
- Information Theory, Inference, and Learning Algorithms, D. J. C. MacKay, Cambridge University Press, 2003
Last change 03/06/2023 23:39