2024/2025

Probability Theory

Type: Mago-Lego

Delivered by: Big Data and Information Retrieval School

When: 3 module

Open to: students of one campus

Language: English

ECTS credits: 3

Course Syllabus

Abstract

Exploration of Data Science requires a certain background in probability and statistics. This course introduces you to the necessary sections of probability theory, guiding you from the very basics all the way up to the level required for jump starting your ascent in Data Science.The core concept of the course is random variable — i.e. variable whose values are determined by random experiment. Random variables are used as a model for data generation processes we want to study. Properties of the data are deeply linked to the corresponding properties of random variables, such as expected value, variance and correlations. Dependencies between random variables are crucial factors that allow us to predict unknown quantities based on known values, which forms the basis of supervised machine learning. We begin with the notion of independent events and conditional probability, then introduce two main classes of random variables: discrete and continuous and study their properties. We'll discuss law of large numbers and central limit theorems that are crucial for statistics. Finally, we'll build our own classification algorithm based on probabilistic models. While introducing you to the theory, we'll pay special attention to practical aspects for working with probabilities, including probabilistic simulations with Python. This course requires basic knowledge in Discrete mathematics (combinatorics), Calculus (derivatives, integrals, a bit of limits) and basic Python programming skills.