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2023　Fundamentals of Data Science

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Academic unit or major
Undergraduate major in Systems and Control Engineering
Instructor(s)
Tanaka Masayuki 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(SL-101(S011))  Fri3-4(SL-101(S011))  
Group
-
Course number
SCE.I205
Credits
2
Academic year
2023
Offered quarter
4Q
Syllabus updated
2023/3/20
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

The real-world signal can be considered as a random signal. The random signal processing is a technique to estimate parameters from the random signal. For that purpose, typical probability distributions will introduced. Then, statistical estimators will be discussed. The course will demonstrate how to use the statistical estimators for real-world problems.


This course will provide a comprehensive overview of the probability distributions and the statistical estimators. The derivations of Gaussian and Poisson distributions will be presented. Law of large numbers and central limit theorem will be proven. Maximum likelihood and maximum a priori will be introduced. The course will conclude by discussing how to apply those estimators to the real-world problem.

Student learning outcomes

By the end of this course, students will be able to:
1. Explain and derive Gaussian and Poisson distributions
2. Prove and use the law of large numbers and the central limit theorem
3. Explain and apply the maximum likelihood and the maximum a posteriori estimators

Course taught by instructors with work experience

✔ Applicable How instructors' work experience benefits the course
A faculty who has a private company experience give a lecture.

Keywords

Gaussian distribution, Poisson distribution, the law of large numbers, the central limit theorem, the maximum likelihood estimator, and a posteriori estimator

Competencies that will be developed

✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Assignment is checked and reviewed. Then, main points are discussed in detailed. Student are asked to provide the solution of quick expiries during class.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Introduction of the course Understand importance
Class 2 Various types of distributions Understand various types of distributions
Class 3 Moment generating function Understand moment generating function
Class 4 The law of large numbers Understand the law of large numbers
Class 5 The central limit theorem Understand moment the central limit theorem
Class 6 Least square Understand Least square
Class 7 Maximum likelihood Understand Maximum likelihood
Class 8 Conditional probability, posterior distribution, and Bayes’ theorem Understand conditional probability, posterior distribution, and Bayes’ theorem
Class 9 Maximum a posteriori estimator Understand maximum a posteriori estimator
Class 10 Stochastic process, filter Understand stochastic process, filter
Class 11 Optimization of quadratic form Understand optimization of quadratic form
Class 12 Optimization of function Understand optimization of function

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

Slides

Reference books, course materials, etc.

Books in Japanese

Assessment criteria and methods

Assignments, excersises, final exams.

Related courses

  • SCE.I201 ： Introduction to Measurement Engineering

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Basics of statistics

Other

Students who already have the credits for Random Signal Processing can not take this class.

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