Identifying Data 2021/22
Subject (*) Statistical Modeling of High Dimensional Data Code 614G02013
Study programme
Grao en Ciencia e Enxeñaría de Datos
Descriptors Cycle Period Year Type Credits
Graduate 1st four-month period
 Second Obligatory 6
Language
Spanish
Galician
English
Teaching method Face-to-face
Prerequisites
Department Matemáticas
Coordinador
Cao Abad, Ricardo
 E-mail
ricardo.cao@udc.es
Lecturers
Cao Abad, Ricardo
López Cheda, Ana
 E-mail
ricardo.cao@udc.es
ana.lopez.cheda@udc.es
Web http://http://dm.udc.es/staff/ricardo_cao/
General description Esta materia proporciona un primeiro contacto do alumnado coa modelización estatística de grandes conxuntos de datos: técnicas de análise multivariante, ferramentas estatísticas e programas informáticos avanzados para a análise de datos de alta dimensión, identificación das vantaxes e limitacións dos diferentes métodos, e procedementos de crítica, diagnose e interpretación dos resultados en termos do problema proposto.
Contingency plan 1. Modificacións nos contidos:
Non se realizarán cambios.

2. Metodoloxías:
• Metodoloxías docentes que se manteñen:
Probas resposta breve: realizarase unha proba de resposta breve, aproximadamente na metade do cuadrimestre, mediante a plataforma Moodle.udc.es. No día do exame oficial, en xaneiro de 2022, realizarase a segunda proba de resposta breve, tamén a través da plataforma Moodle.udc.es. Cada unha destas probas computa un 20% na avaliación.
Traballo tutelado: traballo práctico, en parellas, que computa na avaliación (20%). A presentación oral (que computa o 10%) realizarase a través de TEAMS.
Probas sobre prácticas con R: realizarase unha proba, aproximadamente na metade do cuadrimestre, e entregarase mediante a plataforma Moodle.udc.es. No día do exame oficial, en xaneiro de 2022, realizarase o segundo exercicio avaliable en R, e tamén se fará a entrega a través da plataforma Moodle.udc.es. Cada unha destas probas computa un 20% na avaliación.

• Metodoloxías docentes que se modifican:
As sesións maxistrais: non computan na avaliación. Impartiranse usando TEAMS na franxa horaria que ten asignada a materia no calendario de aulas da facultade. Ademais, estas sesións por TEAMS poderanse complementar con vídeos explicativos.
As prácticas TIC: non computan na avaliación. Na modalidade presencial consistían en análises de datos usando software estatístico (R). Substitúense por vídeos onde se explica con detalle o desenvolvemento da práctica. Eses vídeos poderían ser realizados e gravados en TEAMS na mesma hora da clase, ou subidos á plataforma con anterioridade. Ademais, realizaranse titorías grupais semanais por TEAMS (ou mais segundo o demande o alumnado) para seguimento e apoio dos alumnos.

3. Mecanismos de atención personalizada ao alumnado:
Ferramenta: Correo Electrónico, Vídeo conferencia e Moodle.

Temporalización:
Correo Electrónico: Diariamente. De uso para facer consultas, solicitar encontros virtuais para resolver dúbidas e facer o seguimento dos traballos tutelados.
Vídeo conferencia (Teams): Dúas sesións semanais, para o avance dos contidos, na franxa horaria que ten asignada a materia no calendario de aulas da facultade. Tamén se realizarán titorías individuais e grupais fixadas previamente mediante correo electrónico.
Moodle: Diariamente, segundo a necesidade do alumnado. Presentaranse “foros temáticos” asociados aos módulos da materia, para formular as consultas necesarias.

4. Modificacións na avaliación:
Manterase o peso da cualificación en cada unha das probas. A diferencia está en que a presentación do traballo tutelado se realizará a través de TEAMS, e as probas (parciais e/ou finais) de conceptos realizaranse por Moodle e as de prácticas en R entregaranse por esa mesma plataforma.

Observacións de avaliación: Ao longo do curso realízanse dous parciais, un para a parte dos Bloques 0-2 e outro da parte dos Bloques 3-4, que permiten liberar a parte correspondente da materia.

5. Modificacións da bibliografía ou webgrafía:
Non se realizarán cambios. Xa dispoñen de todos os materiais de traballo da maneira dixitalizada en Moodle.

Study programme competencies
Code Study programme competences
A17 CE17 - Capacidade para a construción, validación e aplicación dun modelo estocástico dun sistema real a partir dos datos observados e a análise crítica dos resultados obtidos.
A20 CE20 - Coñecemento das ferramentas informáticas no campo da análise dos datos e modelización estatística, e capacidade para seleccionar as máis adecuadas para a resolución de problemas.
B2 CB2 - Que os estudantes saiban aplicar os seus coñecementos ao seu traballo ou vocación dunha forma profesional e posúan as competencias que adoitan demostrarse por medio da elaboración e defensa de argumentos e a resolución de problemas dentro da súa área de estudo
B3 CB3 - Que os estudantes teñan a capacidade de reunir e interpretar datos relevantes (normalmente dentro da súa área de estudo) para emitir xuízos que inclúan unha reflexión sobre temas relevantes de índole social, científica ou ética
B7 CG2 - Elaborar adecuadamente e con certa orixinalidade composicións escritas ou argumentos motivados, redactar plans, proxectos de traballo, artigos científicos e formular hipóteses razoables.
B8 CG3 - Ser capaz de manter e estender formulacións teóricas fundadas para permitir a introdución e explotación de tecnoloxías novas e avanzadas no campo.
B9 CG4 - Capacidade para abordar con éxito todas as etapas dun proxecto de datos: exploración previa dos datos, preprocesado, análise, visualización e comunicación de resultados.
B10 CG5 - Ser capaz de traballar en equipo, especialmente de carácter multidisciplinar, e ser hábiles na xestión do tempo, persoas e toma de decisións.
C1 CT1 - Utilizar as ferramentas básicas das tecnoloxías da información e as comunicacións (TIC) necesarias para o exercicio da súa profesión e para a aprendizaxe ao longo da súa vida.

Learning aims
Learning outcomes Study programme competences
Knowledge related to the main techniques of multivariate statistical analysis. A17
 B2
B8
B9
B10
 C1
Awareness of the main problems when working with high dimensional data. A17
A20
 B2
B3
B9
B10
 C1
Ability to select the main variables and models in real data problems. A17
A20
 B2
B3
B8
B9
 C1
Ability to apply the main techniques of multivariate analysis to real or simulated datasets. A17
A20
 B2
B3
B7
B8
B9
B10
 C1
Ability to interpret the results and awareness of the limitations of the different models related to multivariate statistical analysis. A17
A20
 B2
B3
B7
B8
B9
B10
 C1
Ability to work with advanced software related to statistical analysis. A20
 B2
B10
 C1

Contents
Topic Sub-topic
0. Multidimensional distributions
 0.1 Concept of multidimensional distribution
0.2. Variance-covariance matrix. Linear transformations.
0.3. Multidimensional normal: definition and properties.
1. Dimension reduction methods 1.1 Objectives of the Principal Component Analysis (PCA)
1.2 Transformations to get incorrelation
1.3 Obtaining the principal components
1.4 Principal components and scale changes
1.5 Interpretation of the principal components
1.6 Factor analysis
1.7 Multidimensional scaling
2. Unsupervised classification
 2.1 Objectives of unsupervised classification: hierarchical and non-hierarchical methods
2.2 Cluster analysis: approach and objectives
2.3 Hierarchical tree or dendogram
2.4 Similarities and discrepancies between observations
2.5 Criteria for group formation: simple, complete chaining, group average, centroid method, Ward method
2.6 Non-hierarchical distance-based methods: closest neighbors, k means, methods based on density estimation
3. Supervised classification

 3.1 Objectives of supervised classification: classification rules and error criteria
3.2 Discriminant factor analysis: approach, objectives and calculation of discriminant factors
3.3 Fisher's linear discriminant analysis and quadratic discriminant analysis
3.4 Maximum likelihood discriminant rule, Bayes rule, nonparametric discriminant rules
3.5 Relationship with regression models with binary response
3.6 Estimation of Probability of Incorrect Classification: Cross Validation and Bootstrap
4. Models for high-dimensional data
 4.1 Variable selection in regression: significance tests.
4.2 The problem of multiple contrasts: false discovery rate (FDR) and familywise error rate (FWER)
4.3 Sparse coefficient regression models: ridge regression, lasso and their variants
4.4 Selection of variables and models with sparse coefficients for classification

Planning
Methodologies / tests Competencies Ordinary class hours Student’s personal work hours Total hours
Oral presentation A1 B2 B3 B4 C4 30 36 66
ICT practicals A9 A12 A17 A18 A19 A20 A26 A33 A3 A4 A5 A6 A8 B7 B9 B10 C1 C2 C3 14 21 35
Multiple-choice questions A19 A24 A25 A1 B3 B8 2 6 8
Problem solving A17 A33 A2 B2 B5 B6 B7 B8 B10 14 21 35
 
Personalized attention 6 0 6
 
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies Description
Oral presentation Presentation using the computer.
ICT practicals Statistical data analysis using R.
Multiple-choice questions Multiple-choice test on concepts.
Problem solving Deciding statistical tools and strategies for problem solving. Model formulation for multivariate data. Algorithm formulation for high dimensional data analysis.

Personalized attention
Methodologies
ICT practicals
Problem solving
Description
Attendance and participation in lectures.
Written multiple choice test.
Multivariate data analysis project.
Practicals to be performed by the student.

Assessment
Methodologies Competencies Description Qualification
Oral presentation A1 B2 B3 B4 C4 Oral presentation of the work (in pairs of students) mentioned in the "Problem solving" item. 10
ICT practicals A9 A12 A17 A18 A19 A20 A26 A33 A3 A4 A5 A6 A8 B7 B9 B10 C1 C2 C3 Computer labs using the open statistical software R. 40
Problem solving A17 A33 A2 B2 B5 B6 B7 B8 B10 Work (in pairs of students) related to the topics 0-3 of the course. 10
Multiple-choice questions A19 A24 A25 A1 B3 B8 Comprehension tests. 40
 
Assessment comments

The assessment will be carried out through two tests on R labs, a work in pairs of students, as well as two written concept tests. The first of the tests on R labs and the first of the concept tests will be held approximately in the middle of the semester, and they will be related to topics 0-2. The corresponding second tests of both R labs and concepts will be held in the official exam date, in January 2022. These second tests will include all the topics given in the course, but those students who pass each of the first tests will be allowed to avoid topics 0-2 so that they will be evaluated only in topics 3-4.

Both the qualification of the R labs tests and the qualification of the concept tests will be 40% of the total qualification each, while the remaining 20% will correspond to the pairs student work, that has to be presented orally, in the second half of the semester. The half of the score of this pairs work (10% of the total score) corresponds to its oral presentation.

In summary, the assessment scoring will be the following:

  • Work in pairs: 20% of the total score (10% solving the practical exercise in R and 10% oral presentation).
  • Concept tests: two concept tests will be carried out (each one of them corresponds to the 20% of the total score). The first of the exams, related to Topics 0-2, will take place in the middle of the quadrimester. The second exam, related to Topics 3-4, will be carried out the day of the official exam. Note that students will avoid Topics 0-2 in the second exam if they pass the first exam, unless they pass it but want to get a higher score. Moreover, if students do not take the first exam, they will be evaluated (the day of the official exam) with two parts: one related to Topics 0-2 and another related to Topics 3-4. The sum of these two parts is the 40% of the total score.
  • Tests on R labs: following the same idea as for the concept tests, there will be two tests on R labs (each one of them corresponds to the 20% of the total score), using statistical software, R. The first exam, related to the R labs of Topics 0-2, will take place in the middle of the quadrimester. The second exam, related to the R labs of Topics 3-4, will be carried out the day of the official exam. Note that students will avoid Topics 0-2 in the second test on R labs if they pass the first exam, unless they pass it but want to get a higher score. Moreover, if students do not take the first exam, they will be evaluated (the day of the official exam) with two parts: one related to Topics 0-2 and another related to Topics 3-4. The sum of these two parts is the 40% of the total score.

To pass the subject is necessary to obtain a score of at least 5 out of 10 overall.

On July opportunity, students could avoid those tests with scores of at least 4 out of 10 in January tests.

Only students that didn't take any test will be qualified as NON ATTENDANT in the first opportunity (January-February). In July (2nd opportunity) only students that didn't take the final exam will be qualified as NON ATTENDANT.

If a student wants to take a test in a specific official language (Spanish or Galician), he/she must inform the professor at least 1 week in advance.

Sources of information
Basic Anderson, T.W. (2003). An Introduction to Multivariate Statistical Analysis. Wiley
Koch, I. (2014). Analysis of Multivariate and High-Dimensional Data. Cambridge University Press
Jobson, J.D. (1994). Applied Multivariate Data Analysis. Springer-Verlag
Johnson, R. A., Wichern, D. W. (2007). Applied multivariate statistical analysis. Prentice Hall
Muirhead, R.J. (1982). Aspects of multivariate statistical theory. John Wiley & Sons
Jambu, M. (1991). Exploratory and Multivariate Data Analysis. Boston, Academic Press
Wainwright, M.J. (2019). High-Dimensional Statistics: A Non-Asymptotic Viewpoint. Cambridge University Press
Giraud, C. (2014). Introduction to High-Dimensional Statistics. Chapman & Hall/CRC
Chatfield, C., Collins, A. J. (1980). Introduction to multivariate analysis. Chapman & Hall
Mardia, K.V., Kent, J.T., Bibby, J.M. (1994). Multivariate Analysis. Academic Press. Academic Press
Goldstein, M., Dillon,W. R. (1984). Multivariate Analysis: Methods and Applications. Wiley
Rencher, A.C. (1998). Multivariate Statistical Inference and Applications. Wiley
Complementary

Recommendations
Subjects that it is recommended to have taken before
Introduction to Databases/614G02008
Linear Algebra/614G02001
Multivariable Calculus /614G02006
Discrete Mathematics/614G02002
Fundamentals of Programming II/614G02009
Fundamentals of Programming I/614G02004
Statistical Inference/614G02007
Probability and Basic Statistics/614G02003

Subjects that are recommended to be taken simultaneously
Regression Models/614G02012

Subjects that continue the syllabus
Simulation and Resampling Techniques/614G02036
Statistical Analysis of Complex Data/614G02031
Machine Learning III/614G02026
Information Retrieval/614G02027
Machine Learning I/614G02019
Machine Learning II/614G02021
Statistical Analysis of Dependent Data/614G02022

Other comments


(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation.