Course Details - RWTHx: Statistical and Probabilistic Foundations of AI

Course Description

"Statistical and Probabilistic Foundations of AI" is an intermediate-level course designed to provide students with a comprehensive understanding of the mathematical and statistical principles that underpin machine learning, data science, and artificial intelligence. This course offers a perfect blend of theory and practical application, equipping learners with the essential skills to analyze data, construct statistical models, and apply probabilistic methods in the field of AI.

What Students Will Learn

Describing and summarizing data using various statistical techniques
Creating and interpreting statistical visualizations
Developing and analyzing stochastic models for random processes
Applying probabilistic tools and methods to extract meaningful information
Understanding and implementing basic inferential statistical methods
Constructing point estimators, confidence intervals, and hypothesis tests
Building and evaluating regression models
Utilizing R programming for efficient data analysis and visualization

Prerequisites

Introductory knowledge of calculus and linear algebra
R installation on your computer (RStudio IDE recommended)
Basic knowledge of R programming (desirable but not mandatory)

Course Content

Descriptive and exploratory data analysis
Data visualization techniques (box plots, histograms, kernel density estimates)
Principles of probability and stochastic models
Univariate and multivariate probability distributions
Expected values, variance, and covariance
Limit theorems and stochastic simulation
Inferential statistics (parametric and non-parametric approaches)
Point and interval estimation
Hypothesis testing
Regression analysis and model evaluation

Who This Course Is For

Computer science students interested in AI and machine learning
Data scientists looking to strengthen their statistical foundations
AI enthusiasts seeking to understand the mathematical principles behind AI algorithms
Professionals in fields such as finance, engineering, or research who want to apply AI techniques to their work

Real-World Applications

Developing more robust and efficient AI algorithms
Improving data-driven decision-making in various industries
Enhancing predictive modeling and forecasting capabilities
Conducting more accurate scientific research and analysis
Optimizing business processes through data analysis and machine learning
Creating more sophisticated AI-powered products and services

Syllabus

Week 1: Elementary Statistics

Introduction to basic statistical vocabulary
Data summarization methods
Data binning and histograms
Key characteristics (means, quantiles, empirical variance)

Week 2: Elementary Statistics (continued)

Box plots and linear transformations
Exploring relationships between variables
Regression models, focusing on (multiple) linear regression

Week 3: Fundamentals of Probability

Basic principles of probability
Sample spaces and probability calculation
Conditional probability and independence of random events

Week 4: Random Variables

Introduction to random variables and distributions
Univariate discrete probability distributions
Univariate probability distributions with Riemann density functions
Introduction to multivariate distributions

Week 5: Random Variables (continued)

Multivariate distributions, marginal and conditional distributions
Expectation of random variables and random vectors
Properties of expected values, variance, and covariance

Week 6: Random Variables (final)

Sums of random variables
Convolution and generation function techniques
Limit results for sequences of random variables
Strong law of large numbers and central limit theorem

Week 7: Inferential Statistics

Core concepts of inferential statistics
Constructing point estimators and confidence intervals
Non-parametric examples
Introduction to statistical tests
Selected statistical tests for Gaussian distributions