Unsupervised Learning
Code: 104869 ECTS Credits: 6| Degree | Type | Year | Semester |
|---|---|---|---|
| 2503852 Applied Statistics | OB | 2 | 2 |
Contact
- Name:
- Maria Merce Farre Cervello
- Email:
- merce.farre@uab.cat
Teaching groups languages
You can check it through this link. To consult the language you will need to enter the CODE of the subject. Please note that this information is provisional until 30 November 2023.
Prerequisites
A previous course in linear algebra is essential, as well as courses in probability, multidimensional dustributions and statistical inference. It is also assumed that you know how to use the R language with agility.
Objectives and Contextualisation
The need to process a large amount of data with many variables of a diverse nature, while reducing information that is not relevant and discovering patterns of association between variables and/or cases, have led to the development of a large number of procedures that are us they place in the multivariate scenario. Unsupervised Learning deals with the methods that are closest to describing, exploring and modeling vector data. The subject is designed as the student's first contact with the world of so-called "statistical learning", so that he understands the power and applicability, and at the same time the limitations, of the methods, some of the which are based on rather intuitive heuristic ideas. Most of the methods worked on in the course are unsupervised, that is to say, there is no set of cases with known answers that allow the method to be evaluated. The approach of the subject is eminently applied in terms of working with data using the potential of the free software R, accompanied by the appropriate rigor and generality in the definition of theoretical models and the corresponding methods of analysis and validation of the results.
Competences
- Analyse data using statistical methods and techniques, working with data of different types.
- Critically and rigorously assess one's own work as well as that of others.
- Make efficient use of the literature and digital resources to obtain information.
- Select and apply the most suitable procedures for statistical modelling and analysis of complex data.
- Select the sources and techniques for acquiring and managing data for statistical processing purposes.
- Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
- Students must be capable of collecting and interpreting relevant data (usually within their area of study) in order to make statements that reflect social, scientific or ethical relevant issues.
- Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
- Students must develop the necessary learning skills to undertake further training with a high degree of autonomy.
- Summarise and discover behaviour patterns in data exploration.
- Use quality criteria to critically assess the work done.
- Work cooperatively in a multidisciplinary context, respecting the roles of the different members of the team.
Learning Outcomes
- Analyse data using an automatic learning methodology.
- Characterise homogeneous groups of individuals through multivariate analysis.
- Critically assess the work done on the basis of quality criteria.
- Describe the advantages and disadvantages of algorithmic methods compared to the conventional methods of statistical inference.
- Identify the statistical assumptions associated with each advanced procedure.
- Identify, use and interpret the criteria for evaluating compliance with the requisites for applying each advanced procedure.
- Make effective use of references and electronic resources to obtain information.
- Obtain and manage complex databases for subsequent analysis.
- Reappraise one's own ideas and those of others through rigorous, critical reflection.
- Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
- Students must be capable of collecting and interpreting relevant data (usually within their area of study) in order to make statements that reflect social, scientific or ethical relevant issues.
- Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
- Students must develop the necessary learning skills to undertake further training with a high degree of autonomy.
- Use summary graphs of multivariate or more complex data.
- Work cooperatively in a multidisciplinary context, accepting and respecting the roles of the different team members.
Content
Statistical learning and dimension reduction
- Supervised and unsupervised learning. Multivariate methods. Examples.
- Random vectors. Expectation vector and covariance-correlation matrices. Properties.
- Multivariate data. Sample expectation and covariance-correlation matrices. Maximum likelihood estimation in the Gaussian case.
- Spectral decomposition (SD) and singular value decomposition (SVD).
- Maximizing quadratic forms under constrains: The fundamental theorem.
Factorial methods I: Principal components analysis (PCA)
- Introduction to PCA. Definition of components. The fundamental result.
- Criteria for deciding on the number of components: The principal components.
- Variables and individuals plots. Standardizations.
- Row and column analysis of the eigenvectors matrix and other related matrices.
- A geometric point of view of the principal components.
Factorial methods II: Factorial analysis (FA)
- The factorial model. Communalities and specificities.
- The covariance matrix decomposition theorem.
- Discussing the existence and uniqueness of the factorial model. Rotations.
- Parameters estimation methods. Factorial scores estimation or prediction.
- Interpreting the results. Comparing PCA and FA.
Factorial methods III: Multidimensional scaling (MDS) and correspondence analysis (CA)
- Objectives and methods.
- Classic and metric multidimensional scaling.
- Non-metric multidimensional scaling.
- Distances, proximities and dissimilarities.
- Categorical data: Chi-square distance and others.
- Correspondence analysis (CA) as a MDS method.
- Profiles and inertias. Decomposing inertia.
- Graphical representation and interpretation of results in CA.
Cluster analysis (CLA)
- Comparing different approaches. Examples.
- Analyzing and validating the clusters.
- Hierarchical clustering: Link functions.
- Centroid based methods: The k-means algorithm.
- Model based methods: Expectation and maximization (EM).
Multivariate inference basics
- The likelihood ratio test.
- Tests for mean vectors.
- Tests for covariance matrices. ANOVA and MANOVA.
Discriminant analysis (DA)
- Objectives and criteria of discriminant analysis.
- Discriminant analysis in Gaussian models.
- Fisher's linear discriminant analysis.
Methodology
The theoretical sessions, where the multivariate methods will be exposed in detail and discussed on the bases of appropriate examples. The classroom presentations will be posted on the virtual campus. The revision and expansion of contents using the course bibliography will be encouraged.
The computer lab sessions are designed to be implemented in statistical software R. The exercises statements and other auxiliary material will be made available to the students in the Virtual Campus. Extension exercises will be proposed to be solved autonomously.
The theoretical sessions, where the multivariate methods will be exposed in detail and discussed on the bases of appropriate examples. The classroom presentations will be posted on the virtual campus. The revision and expansion of contents using the course bibliography will be encouraged.
The computer lab sessions are designed to be implemented in statistical software R. The exercises statements and other auxiliary material will be made available to the students in the Virtual Campus. Extension exercises will be proposed to be solved autonomously.
The collaboration and participation of all students will be sought, without discrimination based on sex or any other cause.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Activities
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Computer lab sessions | 26 | 1.04 | 1, 4, 14, 5, 6, 8, 10, 11, 15, 7 |
| Theoretical classes | 26 | 1.04 | 1, 9, 3, 2, 4, 14, 5, 6, 8 |
| Type: Autonomous | |||
| Personal work | 42 | 1.68 | 9, 4, 5, 6, 13, 7 |
| Tasks solving and delivery | 44 | 1.76 | 1, 2, 4, 14, 8, 13, 12, 10, 11, 15, 7 |
Assessment
The course grade (NC) will be calculated on the basis of the delivered tasks and the marks in two partial exams (P1 and P2), including both theoretical and computational exercices:
NC = 0.4• P1 + 0.5 • P2 + 0.10 • Lli
where P1 and P2 correspond to the first and second partial grades, respectively, and Lli is based on the delivered tasks and will not be recoverable.
In order to succeed in this course, it is mandatory that NC>=5 and P1>3.5 and P2>3.5. Besides that, the students will have the option of taking an additional recovery exam (F) with the same format (theoretical and computational questions). The final qualification will be:
NF = Max (NC, 0.90 • F + 0.10• Lli)
Observation: Only students who have participated in 2/3 of the continuous assessment activities will have the recovery option. Honor grades will be granted at the first complete evaluation. Once given, they will no be withdrawn even if another student obtains a larger grade after consideration of the final exam.
Single assessment
The single assessment will be a synthesis test of the skills of the two partials, based on: (1) An exam with theory and practical questions (weight: 50%). (2) A practice test in front of the computer (weight: 40%). (3) The delivery of the scheduled tasks that are indicated, with the possibility of the professor asking the student to explain details of these deliveries (weight: 10%).
Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Partial exam 1 (theory & comput) | 0,35 | 4 | 0.16 | 1, 14, 5, 6, 13, 12 |
| Partial exam 2 (theor & comput) | 0,45 | 4 | 0.16 | 1, 2, 4, 5, 6, 8, 13, 12, 10, 7 |
| Tasks delivery | 0,2 | 4 | 0.16 | 9, 3, 8, 13, 12, 10, 11, 15, 7 |
Bibliography
Everitt, B., Hothorn, T. ; An introduction to Applied Multivariate Analysis with R. Springer, 2011.
Härdle, W., Simar, L.; Applied Multivariate Statistical Analysis. Springer,2007.
Peña, D.; Análisis de datos multivariantes. McGraw Hill, 2002.
Rencher, A., Christensen, W.; Methods of Multivariate Analysis. Wiley Series in Probability and Mathematical Statistics, 2012.
Wehrens, R. (2020). Chemometrics with R: Multivariate data analysis in the natural sciences and life sciences. Heidelberg: Springer. https://link-springer-com.are.uab.cat/book/10.1007/978-3-662-62027-4
Complementary references
Coghlan, A.; Little book of R for Multivariate Analysis.
https://little-book-of-r-for-multivariate-analysis.readthedocs.io/en/latest/
Cuadras, C.; Nuevos Métodos de Análisis Multivariante (web), 2014.
Greenacre, M.; La pràctica del análisis de correspondencias. Fundacion BBA, 2003.
James, G., Witten, D., Hastie, T., Tibshirani, R.; An Introduction to Statistical Learning. Springer, 2014.
Mardia, K.V, Kent, J.T., Bibby, J.M.; Multivariate Analysis. Academic Press, 2003.
Rencher, A.; Multivariate Statistical Inference and Applications. John Wiley &Sons, 1998.
Software
R and RStudio.