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Principles of Statistical Modeling (PSM) Fall 2016 (340101)

Jacobs University Bremen, Fall 2016, Herbert Jaeger and Adalbert Wilhelm

Classes: Thursdays and Fridays 14:15 - 15:30, West Hall 8

Contents. This course gives an introduction to the basic concepts of statistical modeling. We bring together the two views of statistics and of machine learning. While both traditions have developed advanced statistical tools to "analyse data", the fundamental questions that are asked (and answered) differ. Stated briefly, statisticians try to answer specific, decision-relevant questions on the basis of data, whereas machine learners aim at modeling complex pieces of the world in as accurately and comprehensively as possible, given data. Both views are important in the current fast developments in "Big Data" or "Data Analytics". The course proceeds in four main parts: (i) the fundamental concepts of statistical modeling: probability spaces, observation spaces, random variables; (ii) a crash refresher on basic mathematical formulas and laws; (iii) introduction to statistical methods (using the R programming language); (iv) introduction to methods of machine learning (using Matlab or Python). The course will be jointly taught by a statistician (A. Wilhelm) and a machine learner (H. Jaeger), and will be highly enriched by examples, exercises and miniprojects.

Lecture notes

Grading scheme

The course grade will be computed from the following components: 1. four miniquizzes will be written (each at the end of one of our four theme blocks), of which the best three will be taken and counting each by 15% toward the course grade; 2. classroom presence 10%; 3. Homeworks 20%; 4. final exam 25%.

Schedule (to be filled in agreement with the unfolding of reality

 

Sep 1

Introduction. Beginning or Part 1 (Herbert Jaeger)
Sep 2 Examples of data generating environments
Sep 8 Formalizing DGEs, DRPs, DVS's by three simple-looking symbols. Products of sample spaces and RV's. Modeling stochastic processes with RVs.  Exercise sheet 1
Sep 9 Formalizing stochastic processes; stopping times. Transformations of RVs. A first glimpse on sigma-fields.
Sep 15 Second glimpse on sigma-fields: the Borel sigma-field.  Exercise sheet 2
Sep 16 The full picture: probability spaces. Notation: how to correctly write down probability statements. Conditional probability.
Sep 22 Miniquiz 1 (25 min at beginning of class, room: CNLH).  Samples and estimators.
Sep 23 Beginning of Part 2 & 3 (Adi Wilhelm): Distributions and random variables
Sep 29  More on distributions and their characteristics Exercise sheet 3  Sample solution Some slides
Sep 30 Functions of random variables
Oct 6 The statistical model Exercise sheet 4 (incomplete) sample solution
Oct 7 The statistical problem
Oct 13 Criteria for choosing a statistical procedure Exercise sheet 5  Sample solution
Oct 14 Statistical Learning
Oct 20 Linear Regression in a Nutshell
Oct 21 The Mathematics of Linear Models
Oct 27 Cross-Validation
Oct 28 Miniquiz 2 (25 min at beginning of class, room: Lecture Hall, Research II) Bootstrap  Miniquiz 3 Data set
Nov 3 Beginning of Part 4 (Herbert Jaeger) ML as learning complex, high-dimensional probability distributions. Distance surprises in high-dimensional metric spaces. Manifolds.
Nov 4 Realizing complex manifold mappings by neural networks (intuitive). Subdomains of ML: statistical learning theory; symbolic learning & data mining.
Nov 10 Introducing the digits dataset. Classification task. Optimality criterion: minimal misclassification rate.
Nov 11 Machine learning as a special branch of statistics: ML algorithms as "statistical procedures". Curse of dimensionality. Feature extraction.
Nov 15 Due date: Miniproject (replacing miniquiz 3)
Nov 17 PCA - definition and algorithm.
Nov 18 PCA - singular values and how they relate to reconstruction accuracy. A basic learning pipeline for classifier training. Programming exercise: classifying digit images
Nov 24 Refresher on bias-variance dilemma / overfitting, cross-validation, regularization
Nov 25 Feedforward neural networks: architecture, universal approximation properties
Dec 1 Miniquiz 4  (Venue: CNLH)  Why deep neural networks work so well in principle
Dec 2 Impressions from deep learning
Dec 16 pre-exam tutorial, 15:45, East hall 8
Dec 19 Final exam   16:00 - 18:00 Conference Hall (IRC)