PREDICTIVE ANALYTICS

This course belongs to the interdisciplinary educational activities of the Data Science curriculum of the Bachelor in Informatics. The course is designed to give a panoramic view of several statistical tools available for predictive modelling, at an intermediate level.
The course covers the main concepts in linear models and generalized linear models and possibly further extension of these modelling frameworks including time series analysis. The focus is placed on providing the main insights on the statistical/mathematical foundations of the models and on showing the effective implementation of the methods through the use of statistical software. This is achieved by a mixture of theory and reproducible code. Real data examples and case studies are also introduced.

1. Knowledge and understanding
- Know and understand the mathematical concepts underlying linear models, including generalized models, and their estimation
- Understand the relationship between linear models and basic probabilistic and inferential concepts
- Know and understand the different types of statistical analyses with predictive purpose for which linear models, including generalized models, can be used

2. Ability to apply knowledge and understanding

- Ability to apply techniques for analyzing, designing and solving statistical problems.
- Ability to apply data processing techniques to real data using appropriate statistical software.
- Ability to use the results of statistical model estimation in the context of prediction and classification

3. Communication Skills.

- Being able to use technical language and notation to communicate the details of a predictive statistical model.
- Being able to translate statistical and mathematical concepts related to linear models into common language and vice versa.

Students are assumed to have reached the learning objectives of the courses
Calculus 1 and 2
Linear Algebra
Probability and Statistics
Data Analysis
although it is not formally required to have passed the examination.

1. Introduction
1.1 Course overview
1.2 What is predictive modeling?
1.3 General notation and background

2. Linear models I: simple and multiple linear model
2.1 Model formulation and least squares
2.2 Assumptions of the model
2.3 Inference for model parameters
2.4 Prediction
2.5 ANOVA
2.6 Model fit

3. Linear models II: model selection, extensions, and diagnostics
3.1 Model selection
3.2 Use of qualitative predictors
3.3 Nonlinear relationships
3.4 Model diagnostics
3.5 Potential critical issues in regression models

4. Generalized linear models
4.1 Model formulation and estimation
4.2 Inference for model parameters
4.3 Prediction
4.4 Deviance
4.5 Model selection
4.6 Model diagnostics

If time allows:
5. Time-series forecasting
5.1: elements of time series
5.2: auto-regressive models
5.3: forecasting by means exponential smoothing

The program might be slightly modified during the semester. Students are encouraged to actively request for the course to also cover specific statistical questions of interest.

Julian J. Faraway, 2014. Linear Models with R Second Edition, Chapman and Hall/CRC
Julian J. Faraway, 2016. Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, Second Edition Chapman and Hall/CRC
Peter H. Westfall, Andrea L. Arias, Understanding Regression Analysis - A Conditional Distribution Approach, Chapman and Hall/CRC
James, Gareth, Daniela Witten, Trevor Hastie, and Robert Tibshirani. 2013. An Introduction to Statistical Learning. Springer

The exam lasts 90 minutes, takes place in the IT lab and is composed of two parts: a written part, worth 18 points, and an R-based part, worth 16 points. Both parts will be made of exercises which aim to evaluate
1. the theoretical knowledge of the course topics,
2. the ability to apply them for solving real data problems.
3. the ability to use R and interpret its output to solve real data problems.
4. the ability to use the R software to present the results of a statistical data analysis.

Typically the grading will follow the following criteria:
A. grades between 18 and 22 will be assigned when there is evidence of
- comprehension of basic theoretical concepts underlying statistical predictive analysis;
- limited ability to interpret and present a statistical predictive analysis;
- limited ability to adapt the predictive analysis to the problem address in a specific real case;
B. grades between 23 and 26 will be assigned when there is evidence of
- comprehension of theoretical concepts underlying statistical predictive analysis beyond the basic ones;
- moderate ability to interpret and present a statistical predictive analysis;
- moderate ability to adapt the predictive analysis to the problem address in a specific real case;
C. grades between 27 and 30 will be assigned when there is evidence of
- good or very good comprehension of theoretical concepts underlying statistical predictive analysis;
- good or very good ability to interpret and present a statistical predictive analysis;
- good or very good ability to adapt the predictive analysis to the problem address in a specific real case;
D. the honors grade (lode) is assigned when a student shows particular ability in completing all assigned task with exceptional care and skill level

written

The course is based on in-person class-based lessons which consist on a mixture of theory (methods description) and practice (implementation and practical usage of methods). The implementation of the methods is done with the statistical language R. Students are encouraged to bring their own laptops and to have a first hand experience with the code during some parts of the lessons.

Italian