Teorija verjetnosti: (pogojna) verjetnost in neodvisnost, diskretne in zvezne slučajne spremenljivke, matematično upanje in kovarianca, multivariatne skupne, marginalne in pogojne porazdelitve, nekoreliranost in neodvisnost, variančno-kovariančna matrika, slučajni vektorji.
Uvod v statistiko: nekatere posebne porazdelitve (binomska, Poissonova, multivariatna, normalna, eksponentna), vzorčenje in statistike (vrstilne statistike, intervali zaupanja, testiranje hipotez, Pearsonov hi-kvadrat, metode Monte Carlo, »Kljukčeva« metoda, metoda največjega verjetja), limitni izreki (zakoni velikih števil, centralni limitni izrek).
Bayesova statistika: subjektivne verjetnosti, Bayesove procedure (apriorne in aposteriorne porazdelitve, točkasto in intervalsko ocenjevanje, testiranje, Gibbsov vzorčevalnik).
Uporaba matematično statističnih metod v strojnem učenju: Bayesov pristop h konkretnim porazdelitvam (Gaussova, eksponentna družina porazdelitev, neparametrične metode), teorija odločanja (drevesa odločanja, največja koristnost in najmanjše obžalovanje), teorija informacij, metoda podpornih vektorjev (primerjava z diskriminantno analizo), vzpodbujeno učenje, nevronske mreže, globoko učenje.
Izvedba učnega načrta se bo prilagajala slušateljem glede na njihovo predznanje, izbrani program in individualno usmeritev študija. Temu je prilagojena tudi seminarska naloga.
Probability theory: (conditional) probability and independence, discrete and continuous random variables, mathematical expectation and covariance, multivariate joint, marginal and conditional probabilities, non-correlated and independent random variables, variance covariance matrix, random vectors.
Introduction to statistics: some special distributions (binomial, Poisson, multivariate normal, exponential) sampling and statistics (order statistics, confidence intervals, testing of hypotheses, Pearson’s chi-squared test, Monte Carlo methods, Bootstrap method, maximum likelihood method), limit theorems (laws of large numbers, the central limit theorem).
Bayesian statistics: subjective probabilities, Bayesian procedures (prior and posterior distributions, point estimation and interval estimation, testing, Gibbs sampler).
Applications of mathematical and statistical methods to machine learning: Bayesian approach to some important distributions (Gaussian and exponential family of distributions, non parametric methods), decision theory (decision trees, maximizing utility and minimizing regret), support vector machines (comparison to discriminant analysis), reinforcement learning, neuron networks including deep learning.
Realization of the syllabus will be adjusted to the students enrolled with respect to their previous knowledge and the program of study. Their seminar work will also be adjusted accordingly.