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Probabilistic Models For Data Science

Public syllabus for 2025-2026

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Academic overview

Programme
BD
Period
Year 1, Semester 1
Credits
6
Weeks
14

Curriculum placement

Appears in study plans

BD (2025 - 2027) Year 1, Semester 1 Mandatory subject

Teaching team

Course coordinator
(none)
Seminar coordinators
(none)

Learning time distribution

Total
Curriculum Lecture Practice Total Weekly Lecture Practice
42 28 14 3 2 1
Exam hours
8
Individual Study Bibliography study Field study Homework Tutoring Others
108 20 32 40 8 0
Overall
150

Learning outcomes

Knowledge

  • (C1) Cunoașterea, înţelegerea şi utilizarea în context practic a unor concepte de modelare probabilistă (distribuţii de probabilitate, modele markoviene), statistică (analiză descriptivă, tehnici de inferenţă, teste statistice, regresie) şi tehnici de optimizare liniară şi neliniară;
  • (C2) Cunoaşterea metodelor statistice specifice diferitelor tipuri de prelucrări şi înţelegerea modului în care pot fi utilizaţi algoritmii de învăţare automată;
  • (C3) Înţelegerea modului în care volumele mari de date pot fi prelucrate în manieră distribuită şi a principiilor care stau la baza calculului de înaltă performanţă;
  • (C4) Înţelegerea modului în care funcţioneză platformele specifice prelucrării volumelor mari de date;
  • (C5) Înţelegerea modului în care se stabileşte complexitatea computaţională a unui algoritm şi a cerinţelor specifice scalabilităţii;

Skills

  • (A1) Utilizarea conceptelor din informatică, matematică şi statistică în definirea modelelor şi proiectarea strategiilor de analiză a datelor şi interpretare a rezultatelor;
  • (A2) Identificarea tehnicilor statistice şi de învăţare automată precum şi a instrumentelor informatice adecvate prelucrării datelor şi construirii unor modele de decizie;
  • (A3) Proiectarea, implementarea şi testarea unor module software adecvate procesării şi analizei unor volume mari de date;
  • (A4) Utilizarea principiilor procesării paralel distribuite în proiectarea aplicaţiilor scalabile;
  • (A5) Utilizarea cunoştinţelor privind construirea modelelor induse din date pentru a dezvolta sisteme de asistare a decizie specifice diferitelor domenii aplicative.

Responsibility

  • (R1) Responsabilitate de acțiune în conformitate cu interesul utilizatorilor;
  • (R2) Respectarea confidențialității angajatorului și a clienților, dar și protejarea proprietății intelectuale a acestora;
  • (R3) Reprezentarea corectă a nivelului de competență și acceptarea de sarcini în limitele acestuia;
  • (R4) Responsabilitatea de a respecta cele mai înalte standarde profesionale în prelucrarea datelor;
  • (R5) Păstrarea autonomiei, integrității și independenței în opiniile profesionale;
  • (R6) Promovarea integrității și reputației profesiei, în concordanță cu interesul public;
  • (R7) Perfecționarea continuă relativ la practicarea profesiei;
  • (R8) Comportament etic, cinstit și colegial în practicarea profesiei.

Online platform

(none)

Course content

Content Methods Obs
1. Linear algebra tools Lecturing, conversation, demonstration. / Google Classroom Resources: [5], [8]
2. Multivariate calculus concepts. Lecturing, conversation, demonstration Resources: [1], [5]
3. Basic probability theory Lecturing, conversation, demonstration Resources: [3], [5]
4. Random variables Lecturing, conversation, demonstration Resources: [3], [5], [6]
5. Multivariate random variables Lecturing, conversation, demonstration Resources: [3], [5], [7]
6. Mixture models Lecturing, conversation, demonstration Resources: [3], [6]
7. Random processes Lecturing, conversation, demonstration Resources: [3], [6]
8. Convergence of random processes Lecturing, conversation, demonstration Resources: [3], [6]
9. Information theory. Lecturing, conversation, demonstration Resources: [1], [5]
10. Statistical distance Lecturing, conversation, demonstration Resources: [3], [5]
11. Discrete-time Markov chains. Lecturing, conversation, demonstration Resources:[3], [4], [6]
12. Continous-time Markov chains Lecturing, conversation, demonstration Resources: [3], [4], [6]
13. Monte Carlo Markov Lecturing, conversation, demonstration Resources: [1],[3], [5], [6]
14. Hidden Markov Lecturing, conversation, demonstration Resources: [1],[3], [5], [6]

Course bibliography

1. Asmussen S., Glynn P.W., Stochastic Simulation: Algorithms and Analysis, Springer 2007 2. Everitt B S, Hothron T., A Handbook of Statistical Analyses Using R, Chapman &Hall /CRC 2010 3. Lange K. , Applied Probability, Second Edition, Springer Science - Business Media, 2010 4. Murphy, K. P., Machine learning : a probabilistic perspective, Massachusetts Institute of Technology, 2012 5. Robert P.C., Casella G., Introduction Monte Carlo Methods with R, Springer, 2010 6. Ross M. S., Introduction to Probability Models, Elsevier Inc. , 2007 7. Strang G., Introduction to linear algebra, fourth Edition, Wellesley - Cambridge Press, 2009

Seminar content

Content Methods Obs
1.Linear algebra and calculus Problem-based approach, dialogue, learning through collaboration For each laboratory, the students must read and be familiar with the materials presented in the corresponding lectures.
2. Random variables. Examples Problem-based approach,dialogue, learning through collaboration Idem
3. Multivariate random variables and mixture models Problem-based approach, dialogue, learning through collaboration Idem
4. Random processes and applications. Problem-based approach, dialogue, learning through collaboration Idem
5. Comparing distribution. Applications in classification Problem-based approach, dialogue, learning through collaboration Idem
6. Markov chain applications Problem-based approach, dialogue, learning through collaboration Idem
7. Monte Carlo Markov Chain. Hidden Markov Chain. Problem-based approach, dialogue, learning through collaboration Idem
Bibliography: Asmussen S., Glynn P.W., Stochastic Simulation: Algorithms and Analysis, Springer 2007 Everitt B S, Hothron T., A Handbook of Statistical Analyses Using R, Chapman &Hall /CRC 2010 Lange K. , Applied Probability, Second Edition, Springer Science - Business Media, 2010 Murphy, K. P., Machine learning : a probabilistic perspective, Massachusetts Institute of Technology, 2012 Robert P.C., Casella G., Introduction Monte Carlo Methods with R, Springer, 2010 Ross M. S., Introduction to Probability Models, Elsevier Inc. , 2007 Strang G., Introduction to linear algebra, fourth Edition, Wellesley - Cambridge Press, 2009

Seminar bibliography

The course is consistent with similar ones from representative universities and covers the most important aspects regarding probability tools. The concepts are presented using the open source software R.

Corroboration

(none)

AI tools guidance

(none)

Evaluation and delivery

Activity Criteria Methods Percentage
C
  • Knowledge of basic probability theory and random processes
  • Homework /topics during the semester with deadline.
  • 25.0%
C
  • Knowledge of specific methods and algorithms used to solve a given problem
  • Exam:presentation of a
  • Project
  • 25.0%
S
  • Usage of software tools for stochastic modeling.
  • Lab applications
  • 50.0%

Performance standards

Minimal standards (knowledge and skills for the grade 5) Knowledge of basic concepts in probability theory Ability to identify and apply the appropriate stochastic method in solving real-world problems The final grade is the weighted average of grades obtained for components 9.4 and 9.5. The exam is passed if the final grade is at least 5 (it is not necessary for each grade to be greater than 5). For every exam session, the grade is computed by the same rule. During the semester, students may attend tutoring hours, during which the teacher answers their questions and provides supplementary explanations regarding the lecture, lab applications and homework.

Additional info

(none)