STATISTICAL INFERENCE AND LEARNING

This course belongs to the educational activities of the Master in Computer Science that allow the student to acquire advanced instruments for data analysis and machine learning. The objective of the course is to develop statistical skills for the analysis of high dimensional data and solve forecasting and classification problems occurring in a wide variety fields, including technology, science, medicine, economics and business.

Regular and active participation in the teaching activities offered by the course and in independent research activities will enable students to:
1. (knowledge and understanding)
- acquire knowledge and understanding regarding advanced statistical learning methods for synthesis, prediction and classification using data also in presence of complex structures and high-dimensionality
2. (applying knowledge and understanding)
- apply autonomously advanced statistical methods for synthetize information, make predictions and classifications using high-dimensional data
- apply autonomously statistical software for the analysis of high-dimensional data
3. (making judgements)
- make autonomous judgements about the validity and feasability of different statistical techniques and understand the effects of these on the outcomes of the analyses

Basic knowledge of probability at the level of a Bachelor in Computer Science is assumed. List of assumed topics: events, axioms of probability, conditional probability and independence, random variables, expected value, variance, covariance and correlation, principal discrete random variables (binomial and Poisson), principal continuous random variables (uniform, normal and exponential), central limit theorem, law of large numbers. For example, the above topics are covered in Baron (2014), chapters 2-3-4.

Baron M (2014). Probability and Statistics for Computer Scientistis. Second Edition. CRC Press.

The course is divided into two parts. The first part focuses on statistical inference based on the likelihood function. The topics of the first part are propaedeutic for the second part about statistical learning. Table of contents that will be presented and discussed through the course:
1. Statistical inference
-- the likelihood function
-- maximum likelihood estimation
-- confidence intervals and hypothesis testing
2. Statistical learning
-- linear regression
-- classification
-- resampling methods
-- linear model selection and regularization
-- nonlinear models
Applications with R language (www.r-project.org) are an integral part of the two parts of the course.

- James G, Witten D, Hastie T, Tibshirani R (2015). An Introduction to Statistical Learning. 6th version. Springer. Webpage http://www-bcf.usc.edu/~gareth/ISL/ Chapters 1-7
- Additional reading and materials distributed during the course through Moodle

The achievement of the course objectives is assessed through a written exam. The exam consists of four exercises designed to measure
1. the theoretical knowledge of the course topics,
2. the ability to apply the knowledge for solving real data problems.
The maximal score for each exercise is 8 points. The final score is the sum of the scores of the four exercises. A total score exceeding 30 corresponds to 30 with honors.

Conventional theoretical lectures complemented by exercise classes, discussion of case studies and computer labs. Teaching material prepared by the lecturer will be distributed during the course through the Moodle platform. The statistical software used in the course is R (www.r-project.org).

English

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