SF1935 Probability Theory and Statistics with Application to Machine Learning 7.5 credits
The overall purpose of the course is that the student should be well acquainted with basic concepts, theory, models and solution methods in probability theory and statistical inference. The course provides a foundational understanding of machine learning, building on probability theory and statistics.
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Application
For course offering
Spring 2025 Start 17 Mar 2025 programme students
Application code
60998
Content and learning outcomes
Course contents
Basic concepts such as probability, conditional probability and independent events. Discrete and continuous stochastic variables, especially one-dimensional stochastic variables. Location, spread and dependency measures for stochastic variables and data sets. Common distributions and their model situations, including the normal distribution, the binomial distribution and the Poisson distribution. The Central limit value theorem and the Law of large numbers.
Descriptive statistics. Point estimates and general estimation methods such as the Maximum likelihood method and the Minimum square method. General confidence intervals but special confidence intervals for expected value and variance in normal distribution. Confidence interval for participations and difference in expected values and participations. Hypothesis testing. Chi2 test of distribution, homogeneity test and independence test. Linear regression.
Machine learning paradigms, appoaches and applications. Supervised / unsupervised learning, generalization, model selection, validation and evaluation, probabilistic methods, dimensionality reduction and representations.
Intended learning outcomes
To pass the course, the student should be able to:
- solve problems that require knowledge about standard concepts and methods in probability theory
- solve problems that require knowledge about standard concepts and methods in statistical theory
- carry out a project work in a group with oral or written presentation and apply machine learning methods for data analysis problems
Literature and preparations
Specific prerequisites
Completed course SF1625 Calculus in One Variable
Recommended prerequisites
Equipment
Literature
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
Examination
- PRO1 - Project work, 1.5 credits, grading scale: P, F
- TEN1 - Written exam, 6.0 credits, grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.