Syllabus

LEARNING OUTCOMES

The goal of the course is to get introduced to key statistical network concepts and their mathematical foundations, the theory of random graphs. The course is targeted for students in mathematics, operations research, and computer science, with interest in probability, graphs, and networks. You will become familiar with basic statistical models used to model unknown network structures. You will gain insight into the type of structural network properties that can be learned from a single graph sample. You will learn to investigate how well an observed graph fits a given statistical model by comparing observed and theoretical graphlet densities. You learn to apply probabilistic inequalities for recognizing almost surely occurring events in large random systems.

Credits: 5

Schedule: 05.09.2022 - 13.10.2022

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Lasse Leskelä

Contact information for the course (applies in this implementation):

The course starts with the first lecture on Mon 5 Sep 2022, and there will be five weeks of lectures and exercises during Sep–Oct.  On the sixth week there will be a project workshop for presenting project assignments.

• Lectures: Mon 12–14 and Thu 12–14 at Room M3, Otakaari 1
  
• Exercise classes: Thu 14–16 at Room Y307, Otakaari 1

Lecturer: Prof Lasse Leskelä
Teaching assistant: MSc Kalle Alaluusua

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content

• valid for whole curriculum period:

  The first part of the course focuses on random graph models and their mathematical analysis. The second part focuses on the learning and identifiability of graph parameters and structural properties from observed network data.

Assessment Methods and Criteria

• valid for whole curriculum period:

  Homeworks and project work

• applies in this implementation

  There is no exam. Instead, the grade of the course is determined by written homework solutions and a project assignment. The course grade is primarily determined by the homework solutions, so that solving (40+10*k) percent of the homework problems with detailed solutions is sufficient to obtain a grade k. The project assignment is graded as fail/good/excellent. The project work must completed to pass the course. An excellent project work increases a course grade 0 < k < 5 up by one.
  

Workload

• valid for whole curriculum period:

  Contact hours 30-40h, independent work ca 100h

DETAILS

Study Material

• applies in this implementation

  The primary course material consists of lecture notes which will be partly updated during the course:
  

  • Lasse Leskelä: Random Graphs and Network Statistics
  
  Recommended auxiliary reading includes the following books:
  
  • Remco van der Hofstad. Random Graphs and Complex Networks I.  Cambridge University Press 2017.
  • Remco van der Hofstad. Random Graphs and Complex Networks II.
  • Roman Vershnynin. High-Dimensional Probability. Cambridge University Press 2018.
  
  

Substitutes for Courses

• valid for whole curriculum period:

  Substitutes for Courses

Prerequisites

• valid for whole curriculum period:

  Prerequisites

FURTHER INFORMATION

Further Information

• valid for whole curriculum period:

  Teaching Language : English

  Teaching Period : 2022-2023 Autumn I
  2023-2024 Autumn I

  Enrollment :

  Registration takes place in Sisu (sisu.aalto.fi).

Description