Data Science: Lectures & Exercises
This page brings together graduate-level lectures and exercises in measure theory, probability, statistics, machine learning, and deep learning. Resources are provided in PDF and video formats.
Measure & Probability
Measure & Probability: Lectures on the foundations of probability theory, covering measure theory, the Lebesgue integral, random variables (discrete and continuous), transforms (generating functions, characteristic functions, Laplace transform), and the convergence of random variables. Includes exercises with detailed solutions.
Statistics Theory
Statistics Theory: Lectures on univariate and multivariate statistics, covering statistical estimation, confidence intervals, hypothesis testing, linear fitting and regression, logistic regression, Principal Component Analysis (PCA), and Factor Analysis.
Machine & Deep Learning
Machine & Deep Learning: Lectures on machine learning frameworks, Vapnik-Chervonenkis (VC) theory, empirical processes theory, learnability characterization, neural networks, and approximation theory. Includes a tutorial on Python software for machine learning and deep learning with PyTorch.
About This Domain
These resources cover the mathematical foundations of data science, from measure-theoretic probability to modern machine learning. Topics include random variables, convergence theorems, parametric and non-parametric estimation, regression models, dimensionality reduction, statistical learning theory, and the theoretical underpinnings of neural networks.
The material is intended for graduate students, doctoral researchers, and practitioners seeking a rigorous treatment of probability, multivariate statistics, supervised and unsupervised learning, and deep learning architectures. Each lecture combines theoretical results with practical applications and exercises with detailed solutions.
A dedicated Python tutorial guides readers through setting up a complete machine learning environment with PyTorch, building neural networks, and handling data for real-world projects.
Last Updated on 23 mai 2026 by Mohamed Kadhem KARRAY