This course is a continuation of the course "Statistics and Data Analysis for Computer and Systems Sciences". It provides advanced and expanded knowledge in probability theory, modelling, and statistical inference theory, which forms the foundation for modern machine learning and AI. Theoretical derivations are connected with practical applications in programming languages for data analysis and machine learning. Regression and classification models are a significant part of the course. Prediction-based methods such as cross-validation are used for model selection. The course offers an introduction to the mathematical methods that are essential tools for the course and ends with an introduction to time series analysis.

The following topics are covered:

• Mathematical methods: derivatives, integrals, optimization, numerical optimization, vectors, and matrices.
• Probability theory: discrete and continuous stochastic variables, density and probability functions, distribution functions, multivariate distributions, multivariate normal distribution, marginal distributions, conditional distributions, independence, expected value, variance, and covariance, functions of stochastic variables, sampling distributions, law of large numbers, central limit theorem.
• Modelling and prediction: linear and non-linear regression, dummy variables and interactions, model selection, cross-validation, overfitting, regularization, classification, logistic regression, multinomial logistic regression, Poisson regression.
• Inference: point estimations, bias-variance trade-off, maximum likelihood (ML), likelihood theory, numerical optimization for ML estimations, bootstrap.
• Time series: trend and seasonality, autocorrelation, autoregressive models.