| 1. Introduction to Probabilistic Graphical Modelling |
Introduction to Probability Theory: |
Probability Theory |
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Basic Concepts in Probability |
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Random Variables and Joint Distribution |
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Independence and Conditional Independence |
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Continuous Spaces |
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Expectation and Variances Theory of Predicate Calculus |
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Mathematical Induction |
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Introduction to Graphs: |
Nodes and Edges |
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Subgraphs |
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Paths and Trails |
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Cycles and Loop |
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Introduction to Probabilistic Graph Models: |
Bayesian Network |
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Markov Model |
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Hidden Markov Model |
| 2. Bayesian Network Model and Inference |
Directed Graph Models: |
Bayesian Network Exploiting Independence Properties |
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Naive Bayes Model |
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Bayesian Network Model |
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Reasoning Patterns |
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Basic Independencies in Bayesian Networks |
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Bayesian Network Semantics |
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Graphs and Distributions |
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Modelling: |
Picking variables |
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Picking Structure |
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Picking Probabilities |
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D-separation |
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Local Probabilistic Models: |
Tabular CPDs |
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Deterministic CPDs |
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Context Specific CPDs |
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Generalized Linear Models |
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Exact inference variable elimination: |
Analysis of Complexity |
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Variable Elimination |
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Conditioning |
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Inference with Structured CPDs |
| 3. Markov Network Model and Inference |
Undirected Graph Models: |
Markov Model-Markov Network |
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Parameterization of Markov Network |
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Gibb's distribution |
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Reduced Markov Network |
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Markov Network Independences |
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From Distributions to Graphs |
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Fine Grained Parameterization |
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Over Parameterization |
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Exact inference variable elimination: |
Graph Theoretic Analysis for Variable Elimination |
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Conditioning |
| 4. Hidden Markov Model and Inference |
Template Based Graph Model : |
HMM- Temporal Models |
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Template Variables and Template Factors |
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Directed Probabilistic Models |
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Undirected Representation |
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Structural Uncertainty |
| 5. Learning and Taking Actions and Decisions |
Learning Graphical Models: |
Goals of Learning |
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Density Estimation |
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Specific Prediction Tasks |
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Knowledge Discovery |
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Learning as Optimization: |
Empirical Risk |
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Over fitting |
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Generalization |
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Evaluating Generalization Performance |
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Selecting a Learning Procedure |
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Goodness of fit |
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Learning Tasks |
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Parameter Estimation: |
Maximum Likelihood Estimation |
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MLE for Bayesian Networks |
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Causality: |
Conditioning and Intervention |
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Correlation and Causation |
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Causal Models |
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Structural Causal Identifiability |
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Mechanisms and Response Variables |
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Learning Causal Models |
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Utilities and Decisions: |
Maximizing Expected Utility |
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Utility Curves |
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Utility Elicitation |
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Structured Decision Problems: |
Decision Tree |
| 6. Applications |
Application of Bayesian Networks: |
Classification |
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Forecasting |
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Decision Making |
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Application of Markov Models: |
Cost Effectiveness Analysis |
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Relational Markov Model and its Applications |
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Application in Portfolio Optimization |
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Application of HMM: |
Speech Recognition |
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Part of Speech Tagging |
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Bioinformatics |
