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