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2023/2024

Operational research

Code: 100125 ECTS Credits: 6
Degree Type Year Semester
2500149 Mathematics OT 4 1

Errata

Due to an error in the data transfer, the following information is corrected:

The responsible of the subject is the teacher Juan Ramon Gonzalez Ruiz (juanramon.gonzalez@uab.cat).

Activities

Title

Hours

ECTS

Learning Outcomes

Type: Directed

 

 

 

Lab sessions

50

2

1, 3, 2, 6, 4, 18, 7, 8, 9, 11, 5, 16, 13, 14, 17

Type: Supervised

 

 

 

Theory sessions

50

2

1, 12, 2, 6, 4, 18, 7, 8, 5, 16

Type: Autonomous

 

 

 

Weekly tasks + self-evaluation

50

2

1, 12, 3, 2, 6, 4, 18, 7, 8, 9, 11, 5, 16, 15, 13, 14, 19, 10, 17

Assessment

The evaluation of the course will be carried out with one exam (final) some weekly tasks and self-evaluation questions. The final grade will be calculated with the formula:

NF = 0.5 * NE + 0.4 * NT + 0.1*NS

where NT is the average grade of weekly tasks, NS the average grade of self-evaluated questions and NE the grade of the examen that should be greater than 5. 

At the end of the semester there will be a recovery examen for those students whose NE is less than 5 and/or NF lower than 5. In this case, the final grade will be calculated with the formula:

NF = 0.7 * NR + 0.3 * NT

where NR is the grade of the recovery exam.

Single evaluation (optional):

A comprehensive exam (4 hours) will be conducted to assess the knowledge and skills acquired throughout the course. This exam will be designed to evaluate the student's ability to apply the statistical analyses learned and their understanding of theoretical concepts.

The exam will consist of two main parts: statistical analysis and theoretical questions. In the statistical analysis section, relevant data will be provided, requiring the student to apply the statistical techniques and tools learned during the course. The following steps are expected from the student:

  1. Problem identification: The student should understand the nature of the data and the analysis objectives.
  2. Selection and application of techniques: The student will use the acquired knowledge to select and apply appropriate statistical techniques to analyze the data. This may include determining measures of central tendency, dispersion, correlation, regression, hypothesis testing, among others.
  3. Interpretation of results: Once the analyses are performed, the student should interpret the results accurately, explaining their significance in the context of the given problem.

The second part of the exam will consist of theoretical questions that require written responses. These questions will be related to fundamental statistical concepts, their applicability in different situations, and their importance in decision-making. The student should demonstrate a clear understanding of the concepts and the ability to explain them coherently.

The evaluation of this exam will consider several criteria:

  1. Accuracy and correctness in analyses: The student's ability to perform statistical analyses accurately and correctly will be evaluated, including selecting appropriate techniques and using the correct procedures.
  2. Interpretation of results: The student's capacity to interpret and explain the results obtained from the statistical analyses will be assessed.
  3. Completeness of theoretical responses: The student's ability to provide clear and comprehensive answers to the theoretical questions, demonstrating mastery of the concepts and their application, will be considered.
  4. Organization and clarity of presentation: The overall organization of the exam, clarity of written responses, and quality of statistical result presentation will be taken into account.

NOTE: Student’s assessment may experience some modifications depending on the restrictions to face-to-face activities enforced by health authorities.

Assessment Activities

Title

Weighting

Hours

ECTS

Learning Outcomes

Final exam

50%

0

0

12, 2, 4, 18, 7, 8, 16, 13, 10

Self-evaluation

10%

0

0

1, 3, 6, 7, 8, 16, 13, 17

Tasks + self-learning

40%

0

0

1, 12, 3, 2, 6, 4, 18, 7, 8, 9, 11, 5, 16, 15, 13, 14, 19, 10, 17

Contact

Name:
Antoni Sintes Blanc
Email:
antoni.sintes@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

This course assumes that the student has obtained the knowledge taught in different courses on the following topics:

- Calculus in several variables.

- Probability

- Linear models.

- R programming.


Objectives and Contextualisation

This course aims to familiarize the student with different methods of machine learning by applying the point of view used when large amounts of data are available.


Competences

  • Actively demonstrate high concern for quality when defending or presenting the conclusions of one's work.
  • Effectively use bibliographies and electronic resources to obtain information.
  • Recognise the presence of Mathematics in other disciplines.
  • 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 develop the necessary learning skills to undertake further training with a high degree of autonomy.
  • Students must have and understand knowledge of an area of study built on the basis of general secondary education, and while it relies on some advanced textbooks it also includes some aspects coming from the forefront of its field of study.
  • Use computer applications for statistical analysis, numeric and symbolic calculus, graphic display, optimisation or other purposes to experiment with Mathematics and solve problems.
  • When faced with real situations of a medium level of complexity, request and analyse relevant data and information, propose and validate models using the adequate mathematical tools in order to draw final conclusions

Learning Outcomes

  1. Achieve mastery and security in the handling of specific scientific programs for problem-solving with real data and in order to perform simulations.
  2. Actively demonstrate high concern for quality when defending or presenting the conclusions of one's work.
  3. Distinguish, of a problem, which thing is important of expensive to the building of the mathematical model and his resolution of what is not it.
  4. Dominate the basic concepts of the theory and be able to combine them and use them to resolve problems.
  5. Draw adequate conclusions from the result of the model.
  6. Effectively use bibliographies and electronic resources to obtain information.
  7. Evaluate the difficulty to do a calculation of analytical probabilities in complex situations and know distinguish when can realise these calculations and when has to resort to the simulation stochastic.
  8. Find models of scientific or topological reality in relation to a decision-making problem and express it using the mathematical language of optimisation problems with dynamic programming or stochastic queues.
  9. Know generate and manipulate models of simulation of the reality to establish and check hypothesis in the study of problems or realities more complex.
  10. 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.
  11. 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.
  12. Students must develop the necessary learning skills to undertake further training with a high degree of autonomy.
  13. Students must have and understand knowledge of an area of study built on the basis of general secondary education, and while it relies on some advanced textbooks it also includes some aspects coming from the forefront of its field of study.
  14. Understand the rudiments of logistics and other fields in which operative research is applied to the technological and industrial fields

Content

These are the contents of the subject* 

  • Introduction to Tidyverse
  • Introduction to machine learning
  • Linear and logistic regression
  • Tractament de Big Data amb R
  • La llibrería caret
  • Mètodes d'aprenentatge automàtic
    • KNN
    • LDA
    • SVM
  • Methods to deal with non-balanced outcomes
  • Decision trees
    • Classification trees
    • Regression trees
    • Bagged trees
    • Random Forest
  • Boosting
    • AdaBoost
    • GBM 
    • Estochastic GBM 
    • XGBoost
    • Others

 *Unless the requirements enforced by the health authorities demand a prioritization or reduction of these contents.


Methodology

The course has two hours of theory and two hours of practices each week.

- Theory: the different methods with their particular characteristics are defined and explained and concrete examples are shown.

- Practices: working with the methods explained in theory class using different data sets and the R programming language.

It is considered that, for each hour of theory and practice, the student must dedicate an additional hour for the preparation and/or finalization of the session. Self-evaluating questionaires will be filled-in to check whether the main concepts are adquired after each session.

NOTE: 

*The proposed teaching methodology may experience some modifications depending on the restrictions to face-to-face activities enforced by health authorities.

 

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      
Problem sessions 14 0.56 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
Theoretical Classes 26 1.04 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
Type: Supervised      
Computer Sessions 12 0.48 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
Type: Autonomous      
Personal work 90.5 3.62 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

Assessment

Continued assesment

There are two partial exams, EP1 and EP2, both with a second chance or recovery exam, EF1 and EF2. To pass the subject, it is necessary that the NC course grade (weighted average of the two partial exams) is greater than or 
equal to 4, with min(EP1,EP2)>=3.
										
																					
										
																						In addition, it is also necessary that the mark of the practice exam is greater than or equal to 3.5. Then the final grade NF is calculated by making NF = 0.2*P + 0.8*NC, where P is the practice grade.
										
																					
										
																						In the recovery exam, the NC course mark is recovered. The practical mark is not recovered but is taken into account to calculate the final mark. In case of having to make the recovery, the final grade is calculated as follows.
										
																					
										
																						We say R the recovery note, calculated with the following formula R = 0.5*[max(EP1,EF1)+max(EP2,EF2)]. Then the final NCD course grade is calculated as NCD = 0.3*NC + 0.7*R.
										
																					
										
																						Note that NCD depends on recovery and also on the NC course grade. In this case, the final mark will be NF = 0.2*P + 0.8*NCD if the condition min(max(EP1,EF1),max(EP2,EF2))>=3 is met. Otherwise, the final grade will be 
min(NF, 4.5).

Unique evaluation

A final exam, EFU, is carried out, which has a second opportunity or recovery exam, ERU, if necessary. The EFU final exam has 2 parts, EFU1 and EFU2, which take place in a single day, one in the morning and one in the afternoon. In the same way,the ERU recovery exam has 2 parts, ERU1 and ERU2, which take place in a single day, one in the morning and one in the afternoon.

The content of the first part (of the two exams, EFU and ERU) coincides with that of the EP1 exam of the continuous evaluation. The content of the second part (both exams, EFU and ERU) coincides with that of the EP2 exam of the continuous evaluation.

To pass the subject in this modality, it is necessary that the final grade NFU (weighted average of the two parts, EFU1 and EFU2) is greater than or equal to 5, being min(EFU1,EFU2)>=3.5. Otherwise, it is necessary to take the recovery exam, and then the final grade, NFUR, is calculated as follows:

NFUR = 0.3*NFU + 0.35*[max(EFU1,ERU1)+max(EFU2,ERU2)] if the condition min[max(EFU1,ERU1) , max(EFU2,ERU2)]>=3 is met, or min(NFUR, 4.5) if this condition is not met.

 

Note (valid for both evaluation options): In no case are the second chance (or recovery) options to raise grades that are >= 5.


Assessment Activities

Title Weighting Hours ECTS Learning Outcomes
Final Exam 50% 3 0.12 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
Midterm Exam 30% 2 0.08 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
Tasks 20% 2.5 0.1 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

Bibliography

Basic bibliography:

- An Introduction to Statistical Learning with Applications in R - Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani

- The bookdown of the topic: https://isglobal-brge.github.io/Aprendizaje_Automatico_1/

 

Complementary bibliography:

- The Elements of Statistical Learning: Data Mining, Inference, and Prediction - Trevor Hastie, Robert Tibshirani and Jerome Friedman

- Data Science from Scratch - Joel Grus

- Computer Age Statistical Inference: Algorithms, Evidence and Data Science - Trevor Hastie and Bradley Efron


Software

Theory and practical exercises will be done using R