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STATISTICAL LEARNING

Syllabus

EN IT

Learning Objectives

LEARNING OUTCOMES:
The course provides an introduction to Statistical Learning and Data Mining.
The advances in information technology have made available very rich information data sets, often generated automatically as a by-product of the main institutional activity of a firm or business unit. Most organizations today produce an electronic record of essentially every transaction in which they are involved. Firms collect terabytes data over operating periods (transactions data, e.g. credit cards). Most often these data are collected as secondary data, with no specific sampling design or research question on top.

The course offers an insight into the main statistical methodologies for the visualisation and the analysis of business and market data, providing the information requirements for specific tasks such as credit scoring, prediction and classification, market segmentation and product positioning. Emphasis will be given to empirical applications using modern software tools (Rstudio).

The course has the following intended learning outcomes:
- to provide a thorough knowledge of data mining methods and statistical learning techniques;
- to provide the expertise to manage complexity in information and to be able to distil the stylized facts that are relevant for interpretation;
- to be able to predict business outcomes;
- to be able to select a predictive method among those available;
- to be able to communicate the statistical findings to a non expert audience;
- to be able to perform sophisticated statistical analyses with the appropriate software.
- to critically appraise the potential and the limitation of the available methodologies.

KNOWLEDGE AND UNDERSTANDING:
The course covers the modern statistical methodologies for the visualisation and the analysis of business and market data, that are relevant for making decisions in a complex and rapidly changing business environment.
The fundamental theme is supervised statistical learning, which deals with the prediction of quantitative and qualitative outcomes using a potentially large set of inputs. The two problems, regression and classification, constitute the core of the course.
Emphasis is given to the problem of variable and model selection and on the generalizability of a prediction method outside the training sample, via the optimization of the trade-off between model complexity and the in-sample goodness of fit.


APPLYING KNOWLEDGE AND UNDERSTANDING:

The methodologies exposed during the course are applied to real life datasets and case studies, dealing with the prediction of sales, credit scoring and pricing goods.

Two hours per week are dedicated to tutorials where statistical analyses are conducted in the Laboratory and implemented in the software R-studio.

Students are expected to perform their statistical analyses in a group assignment.

MAKING JUDGEMENTS:

The prediction of an outcome is an informed decision based on the knowledge of covariates and antecedents. An important supervised learning problem is classification. We discuss Bayes classification rule and how to select the prediction rule that is optimal for a particular target variable. The student is expected to be able to draw conclusions on the basis of the statistical evidence and to validate those conclusions on validation or test samples drawn from the same target population.

COMMUNICATION SKILLS:

Particular attention is dedicated to the ability to communicate the statistical evidence in a systematic and synthetic way, using graphs and summaries, to a non-specialist target audience.

The software used in the tutorials is oriented towards graphical displays and visualization of data. The student is asked to report on the statistical analysis carried out for a particular purpose in the individual assignments.

LEARNING SKILLS:

Students develop their learning skills by comparing the teaching material provided by the instructor and exposed in the lectures with the readings suggested with weekly periodicity. The software tutorials and the analysis of cases studies in the assignments will help build their applied skills and their autonomous progress towards the intended learning outcomes.

Prerequisites

Basic knowledge of mathematics and statistics at the level of the Preliminary Courses in Maths and Statistics organized by EEBL.

Program

1. Introduction to data mining. Tools for data analysis, visualisation and description.
(Lectures 1-3)

2. The linear regression model. Estimation and prediction. (Lectures 4-6)

3.Model selection and evaluation: bias-variance trade-off, model complexity and goodness of fit. Cross-validation. Selection using information criteria. (Lectures 6-9)

4. Regularization and shrinkage methods: rigde regression, lasso, forward stagewise regression. Principal components regression. (Lectures 10-11).

5. Linear methods for classication: Bayes Classication Rule.
Discriminant analysis. Canonical variates. Logistic regression. (Lectures 12-14)

6. Semiparametric regression: Regression splines and smoothing splines. (Lecture 15)

7. Kernel smoothing methods: Local polynomial regression.
Density estimation. Nearest neighbor classication. (Lecture 16)

8. Additive Models, tree-based methods. GAM, Regression and classication trees. Boosting. (Lectures 17-18)

Books

The textbook for the course is the following:

G James, D Witten, T Hastie, and R Tibshirani and J Friedman. An Introduction to Statistical Learning with Applications in R. Springer, Springer Series in Statistics, 2009.
Dowloadable at http://www-bcf.usc.edu/~gareth/ISL/


The course material will be made available on the course website: slides, suggested readings, datasets, supplementary materials (script of Matlab, R and SAS).

Additional useful reference:
-
• T Hastie, R Tibshirani and J Friedman. The Elements of StatisticalLearning: Data Mining, Inference, and Prediction, Second Edition. Springer, Springer Series in Statistics, 2009. Website: http://www-stat.stanford.edu/ElemStatLearn/

* G. Bekes and G. Kezdi. Data Analysis for Business, Economics, and Policy

Bibliography

G James, D Witten, T Hastie, and R Tibshirani and J Friedman. An Introduction to Statistical Learning with Applications in R. Springer, Springer Series in Statistics, 2009.
Dowloadable at http://www-bcf.usc.edu/~gareth/ISL/

•- Hastie, R Tibshirani and J Friedman. The Elements of StatisticalLearning: Data Mining, Inference, and Prediction, Second Edition. Springer, Springer Series in Statistics, 2009. Website: http://www-stat.stanford.edu/ElemStatLearn/

G. Bekes and G. Kezdi. Data Analysis for Business, Economics, and Policy

Teaching methods

• Lectures
• Classes
• Exercises
• Tutorials (Matlab, R)

Exam Rules

The assessment of the students has two main components

30% Individual and Group Assignments
70% Final Exam

The assignments contribute to 30% of the final assessment and aim at evaluating the capabilities of processing and analysing statistical modelling, as well as the ability to communicate the relevant findings. Students face a case study and a real life dataset; they are expected to produce a technical report which summarizes their statistical findings and provides the necessary insight into the solution of the case study.

The final exam is a 2 hours written test that evaluates the learning of the program topics. Students face open questions with subquestions that test the understanding of the techniques presented throughout the course and the ability to critically assess their scope. The questions deal with the specification, estimation and validation of models for the prediction of quantitative (regression) and qualitative variables (classification). The students will have to prove their proficiency in understanding the basic assumptions that are made, how the data are used to learn about the model parameters, and finally how we diagnose the external and predictive validity of the methods and models. The assessment criteria are based on the students' critical appraisal of the scope and applicability of the methods, on their deep understanding of the trade-offs between goodness of fit and complexity, bias and variance, and on the rigour with which the properties are presented in the written exam paper. Main questions and items are scored according to difficulty. The score is disclosed to the students directly on the exam paper.


The final grade will be expressed in thirtieths with the following breakdown:
- Fail: significant deficiencies and/or inaccuracies in the knowledge and understanding of the topics; limited analytical and synthesis skills, frequent generalizations.
- 18-20: barely sufficient knowledge and understanding of the topics with possible imperfections; sufficient analytical, synthesis, and judgment autonomy skills.
- 21-23: routine knowledge and understanding of the topics; correct analytical and synthesis skills with consistent logical reasoning.
- 24-26: good knowledge and understanding of the topics; good analytical and synthesis skills with rigorously expressed arguments.
- 27-29: excellent and comprehensive knowledge and understanding of the topics; notable analytical and synthesis skills, and excellent judgment autonomy.
- 30-30L: outstanding level of knowledge and understanding of the topics; notable analytical, synthesis, and judgment autonomy skills. Arguments are expressed in an original manner.