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Home / Syllabus / B.E. (Computer Engineering) / Third Year CE / Semester 5 / Probabilistic Graphical Models

B.E. (Computer Engineering) Probabilistic Graphical Models Syllabus - Mumbai University 2026

The University has moved this degree onto NEP 2020 one year at a time. The first and second years are NEP 2020 syllabi; the third and fourth years are still examined on the REV-2019 'C' Scheme, which is what the University sets for them this year.

Probabilistic-Graphical-Models.pdf
Semester 5 · Third Year CE

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Syllabus for Probabilistic Graphical Models

Semester 5 · Third Year CE

Module 1: Introduction to Probabilistic Graphical Modeling

  • 1.1 Introduction to Probability Theory: Probability Theory, Basic Concepts in Probability, Random Variables and Joint Distribution, Independence and Conditional Independence, Continuous Spaces, Expectation and Variances
  • 1.2 Introduction to Graphs: Nodes and Edges, Subgraphs, Paths and Trails, Cycles and Loops
  • 1.3 Introduction to Probabilistic Graph Models: Bayesian Network, Markov Model, Hidden Markov Model
  • 1.4 Applications of PGM

Module 2: Bayesian Network Model and Inference

  • 2.1 Directed Graph Model: Bayesian Network-Exploiting Independence Properties, Naive Bayes Model, Bayesian Network Model, Reasoning Patterns, Basic Independencies in Bayesian Networks, Bayesian Network Semantics, Graphs and Distributions. Modelling: Picking variables, Picking Structure, Picking Probabilities, D separation
  • 2.2 Local Probabilistic Models: Tabular CPDs, Deterministic CPDs, Context Specific CPDs, Generalized Linear Models.
  • 2.3 Exact inference variable elimination: Analysis of Complexity, Variable Elimination, Conditioning, Inference with Structured CPDs.

Module 3: Markov Network Model and Inference

  • 3.1 Undirected Graph Model : Markov Model-Markov Network, Parameterization of Markov Network, Gibb's distribution, Reduced Markov Network, Markov Network Independencies, From Distributions to Graphs, Fine Grained Parameterization, Over Parameterization
  • 3.2 Exact inference variable elimination: Graph Theoretic Analysis for Variable Elimination, Conditioning

Module 4: Hidden Markov Model and Inference

  • 4.1 Template Based Graph Model : HMM- Temporal Models, Template Variables and Template Factors, Directed Probabilistic Models, Undirected Representation, Structural Uncertainty.

Module 5: Learning and Taking Actions and Decisions

  • 5.1 Learning Graphical Models: Goals of Learning, Density Estimation, Specific Prediction Tasks, Knowledge Discovery. Learning as Optimization: Empirical Risk, over fitting, Generalization, Evaluating Generalization Performance, Selecting a Learning Procedure, Goodness of fit, Learning Tasks. Parameter Estimation: Maximum Likelihood Estimation, MLE for Bayesian Networks
  • 5.2 Causality: Conditioning and Intervention, Correlation and Causation, Causal Models, Structural Causal Identifiability, Mechanisms and Response Variables, Learning Causal Models. Utilities and Decisions: Maximizing Expected Utility, Utility Curves, Utility Elicitation. Structured Decision Problems: Decision Tree

Module 6: Applications

  • 6.1 Application of Bayesian Networks: Classification, Forecasting, Decision Making
  • 6.2 Application of Markov Models: Cost Effectiveness Analysis, Relational Markov Model and its Applications, Application in Portfolio Optimization
  • 6.3 Application of HMM: Speech Recognition, Part of Speech Tagging, Bioinformatics.

Useful Links

  • 1 Daphne Koller and Nir Friedman, "Probabilistic Graphical Models: Principles and Techniques”, Cambridge, MA: The MIT Press, 2009 (ISBN 978-0-262-0139 2).
  • 2 David Barber, "Bayesian Reasoning and Machine Learning", Cambridge University Press, 1st edition, 2011.
  • 1 Finn Jensen and Thomas Nielsen, "Bayesian Networks and Decision Graphs (Information Science and Statistics )", 2nd Edition, Springer, 2007.
  • 2 Kevin P. Murphy, "Machine Learning: A Probabilistic Perspective" , MIT Press, 2012.
  • 3 Martin Wainwright and Michael Jordan, M., "Graphical Models, Exponential Families, and Variational Inference", 2008.
  • 1 https://www.coursera.org/specializations/probabilistic-graphical-models
  • 2 https://www.mooc-list.com/tags/probabilistic-graphical-models
  • 3 https://scholarship.claremont.edu/cgi/viewcontent.cgi?referer=https://www.google.c om/&httpsredir=1&article=2690&context=cmc_theses
  • 4 https://www.upgrad.com/blog/bayesian-networks/
  • 5 https://www.utas.edu.au/__data/assets/pdf_file/0009/588474/TR_14_BNs_a_resour ce_guide.pdf
  • 6 https://math.libretexts.org/Bookshelves/Applied_Mathematics/Book%3A_Applied_ Finite_Mathematics_(Sekhon_and_Bloom)/10%3A_Markov_Chains/10.02%3A_A pplications_of_Markov_Chains/10.2.01%3A_Applications_of_Markov_Chains_(E xercises)
  • 7 https://link.springer.com/chapter/10.1007/978-3-319-43742-2_24
  • 8 https://homes.cs.washington.edu/~pedrod/papers/kdd02a.pdf
  • 9 https://core.ac.uk/download/pdf/191938826.pdf
  • 10 https://cs.brown.edu/research/pubs/theses/ugrad/2005/dbooksta.pdf
  • 11 https://web.ece.ucsb.edu/Faculty/Rabiner/ece259/Reprints/tutorial%20on%20hmm %20and%20applications.pdf
  • 12 https://mi.eng.cam.ac.uk/~mjfg/mjfg_NOW.pdf
  • 13 http://bioinfo.au.tsinghua.edu.cn/member/jgu/pgm/materials/Chapter3 LocalProbabilisticModels.pdf Suggested List of Experiments: Sr. No Experiment
  • 1 Experiment on Probability Theory
  • 2 Experiment on Graph Theory
  • 3 Experiment on Bayesian Network Modelling
  • 4 Experiment on Markov Chain Modeling
  • 5 Experiment on HMM
  • 6 Experiment on Maximum Likelihood Estimation
  • 7 Decision Making using Decision Trees
  • 8 Learning with Optimization ** Suggestion: Laboratory work based on above syllabus can be incorporated along with mini project in CSM501: Mini-Project.

Reproduced from the University of Mumbai syllabus for B.E. (Computer Engineering) under REV-2019 'C' Scheme, in force from the academic year 2021-22. Wording is as printed in that syllabus. Module numbering is as printed there too.

The complete syllabus

This subject is cut from the University circular for its year. Open a document here if you want the whole thing rather than a single subject.

PDF 7.9 (R-A) B.E. (Computer Engineering) Sem I & II (Revised, NEP 2020) NEP 2020 syllabus Read full PDF Read
PDF 6.24 (N) B.E. (Computer Engineering) Sem III & IV (NEP 2020) NEP 2020 syllabus Read full PDF Read
PDF 6.15 B.E. (Computer Engineering) Third Year, Sem V & VI (REV-2019 'C' Scheme) REV-2019 'C' Scheme syllabus Read full PDF Read
PDF 6.41 (R) B.E. (Computer Engineering) Fourth Year, Sem VII & VIII (REV-2019 'C' Scheme) REV-2019 'C' Scheme syllabus Read full PDF Read
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