Michael Gutmann Edited and expanded by Arno Onken Spring Semester 2018

First Steps in Exploratory Data

Contents 1 First Steps in Exploratory Data

Probabilistic Modelling and Reasoning Solutions for Tutorial 2 Spring 2018

Solution. The Markov blanket of a node in a undirected graphical model equals the set of its neighbours: MB(x4) = ne(x4) = ne4 = {x1, x5}. This implies, for example, that x4 ⊥ x2, x3 | x1, x5. (e) On which minimal set of variables A do we need to condition to have x1 ⊥ x5 | A? Solution. We first identify all trails from x1 to x5. There are three such trails: (x1, x2, x5), (x1, x3, x2, x5), and ...

Probabilistic Modelling and Reasoning Solutions for Tutorial 7 Spring 2018

Solution. Since the logarithm is strictly monotonically increasing, the maximiser of the log-likelihood equals the maximiser of the likelihood. It is easier to take derivatives for the log-likelihood function than for the likelihood function so that the maximum likelihood estimate is typically determined using the log-likelihood. Given the algebraic expression of `(θ), it is simpler to work wit...

Introduction to Probabilistic Modelling

We give a brief introduction to probability and probabilistic modelling. The document is a refresher, prior knowledge about the topic is assumed.