🤖 AI & Machine Learning
Bayesian Networks and Decision Graphs
Master probabilistic graphical models from foundations to advanced decision analysis. This course builds progressively f...
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Sections
1. Foundations of Probability and Graphical Models18 views
Core probability concepts and the rationale for representing distributions with graphs.
15 topics (16 versions)
1.1Probability axioms
2
6
1.2Random variables and distributions
1
1.3Joint and marginal distributions
1
1.4Conditional probability and Bayes' rule
1
1.5Independence and conditional independence
1
1.6Chain rule of probability
1
1.7Factorization of joint distributions
1
1.8Graphical models overview
1.9Directed acyclic graphs (DAGs)
1
1.10I-maps and perfect maps
1
1.11d-separation intuition
1
1.12Markov blankets
1.13Plate notation
1
1.14Notation and conventions
1
1.15Common probability pitfalls
1
2. Bayesian Networks: Concepts and Construction10 views
Definition, semantics, and basic components of Bayesian networks with practical modeling steps.
15 topics (15 versions)
2.1Definition of Bayesian networks
3
2.2Structure and parameters
2.3Conditional probability tables (CPTs)
2
2.4Canonical CPDs: Noisy-OR
2.5Canonical CPDs: Noisy-AND
1
2.6Discrete vs continuous nodes
2.7Factor graphs vs Bayesian networks
1
2.8Moralization and triangulation basics
2.9BN semantics and assumptions
2.10Faithfulness and causal sufficiency
2.11Query types and evidence
1
2.12BN construction workflow
1
2.13Data and sample size needs
2.14Priors and smoothing choices
2.15Scalability considerations
1
3. Conditional Independence and d-Separation12 views
How graph structure encodes independence and how to reason about information flow.
15 topics (15 versions)
3.1Paths, colliders, and non-colliders
4
3.2Blocking and active trails
3.3Explaining away
3.4Local, pairwise, and global Markov properties
3.5Markov blanket derivations
1
3.6Minimal I-maps
3.7Conditional independence lattices
1
3.8d-separation algorithms
1
3.9Separation in moralized graphs
3.10Context-specific independence
3.11CSI via decision trees
1
3.12CSI via algebraic constraints
2
3.13Faithfulness violations
1
3.14Testing conditional independence
1
3.15CI in finite samples
4. Exact Inference in Bayesian Networks15 views
Algorithms that compute exact probabilities and MAP/MPE solutions when feasible.
15 topics (15 versions)
4.1Variable elimination
3
4.2Elimination order heuristics
2
4.3Complexity and treewidth
1
4.4Belief propagation on trees
1
4.5Junction tree construction
1
4.6Triangulation strategies
1
4.7Building cliques and separators
4.8Clique potential initialization
4.9Message passing and calibration
1
4.10Computing marginals
4.11MAP and MPE queries
1
4.12Evidence incorporation
1
4.13Arithmetic circuits
1
4.14Knowledge compilation (d-DNNF)
1
4.15Caching and memoization
1
5. Approximate Inference Techniques13 views
Sampling, variational, and message passing methods for large or loopy networks.
15 topics (15 versions)
5.1Rejection sampling
2
5.2Likelihood weighting
1
5.3Importance sampling
5.4Gibbs sampling
5.5Metropolis-Hastings
1
5.6Rao-Blackwellization
1
5.7Loopy belief propagation
1
5.8Mean-field variational inference
1
5.9Expectation propagation
5.10Variational objectives
1
5.11Particle filtering
1
5.12Annealed importance sampling
1
5.13Convergence diagnostics
1
5.14Mixing and autocorrelation
5.15Bias-variance trade-offs
2
6. Parameter Learning for Bayesian Networks10 views
Estimating CPDs from data using frequentist and Bayesian approaches with missingness.
15 topics (15 versions)
6.1Maximum likelihood for complete data
2
6.2Dirichlet-multinomial conjugacy
2
6.3Bayesian parameter estimation
6.4MAP estimation and smoothing
6.5Credible intervals for CPTs
1
6.6EM algorithm fundamentals
6.7Soft and hard EM
1
6.8Missing data mechanisms
6.9Parameter tying and sharing
1
6.10Regularization strategies
1
6.11Hierarchical priors
6.12Continuous CPDs with Gaussians
1
6.13Learning Noisy-OR parameters
1
6.14Uncertainty quantification
6.15Model averaging over parameters
7. Structure Learning and Causal Discovery7 views
Learning the network graph from data via scores, constraints, and hybrids.
15 topics (15 versions)
7.1Search spaces and DAG equivalence
3
7.2CPDAGs and Markov equivalence
7.3Score functions: BIC and AIC
1
7.4Bayesian scores: BDeu and BGe
7.5Hill-climbing and tabu search
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7.6Order-based search
7.7Constraint-based methods (PC)
7.8Hybrid methods (MMHC)
7.9Local score caching
7.10Statistical CI tests
7.11Dealing with latent variables
1
7.12Controlling false discoveries
7.13Sample complexity considerations
7.14Parallel and distributed search
1
7.15Human-in-the-loop refinement
8. Continuous and Hybrid Bayesian Networks12 views
Modeling with linear Gaussian, mixture, and mixed discrete-continuous variables.
15 topics (15 versions)
8.1Linear Gaussian Bayesian networks
3
8.2Conditional linear Gaussian CPDs
1
8.3Mixed discrete-continuous nodes
1
8.4Gaussian mixture CPDs
8.5Nonparametric CPDs
8.6Copula-based dependencies
8.7Discretization strategies
1
8.8Deterministic and functional nodes
1
8.9Soft vs hard evidence
1
8.10Numerical stability issues
8.11Inference with CLGs
1
8.12Parameter estimation for CLGs
8.13Handling outliers and robustness
8.14Approximation in hybrid models
2
8.15Software support for hybrids
1
9. Dynamic Bayesian Networks16 views
Temporal extensions of BNs for sequences and time-varying processes.
15 topics (15 versions)
9.1First-order Markov assumption
4
9.2Time-slice and 2-TBN representation
9.3Stationary vs nonstationary parameters
1
9.4HMMs as DBNs
1
9.5Kalman filters as DBNs
2
9.6Switching linear dynamical systems
1
9.7Forward filtering
1
9.8Backward smoothing
9.9Particle filtering for DBNs
1
9.10EM for temporal models
1
9.11Online learning and inference
1
9.12Change-point detection
1
9.13Long-term prediction
9.14Temporal structure learning
1
9.15Applications in tracking and speech
1
10. Decision Theory Foundations8 views
Utilities, risk, and principles underlying rational choices under uncertainty.
15 topics (15 versions)
10.1Utility theory axioms
3
10.2Expected utility principle
10.3Risk attitudes and curvature
10.4Lotteries and preferences
1
10.5Dominance and admissibility
10.6Value functions and scaling
10.7Multi-attribute utility
1
10.8Trade-offs and weights
10.9Certainty equivalents
1
10.10Stochastic dominance
10.11Sensitivity to utility transformations
1
10.12Prospect theory overview
10.13Utility elicitation methods
10.14Consistency checks
10.15Decision quality metrics
1
11. Decision Graphs and Influence Diagrams14 views
Representation of decisions, information, and utilities within graphical models.
15 topics (15 versions)
11.1Chance, decision, and utility nodes
3
11.2Arc semantics and information flow
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11.3Decision timing and information sets
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11.4Policies and strategies
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11.5Influence diagram syntax
1
11.6Asymmetric decision problems
1
11.7Value of information concepts
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11.8Additive and multiplicative utilities
11.9Deterministic policy nodes
11.10Arc reversal operations
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11.11Node reduction operations
11.12Strong vs weak influence diagrams
1
11.13Strategy graphs and policies
1
11.14Example influence diagram modeling
1
11.15Extensions to dynamic IDs
1
12. Algorithms for Decision Evaluation8 views
Computational methods to compute optimal policies and VOI within IDs and BNs.
15 topics (15 versions)
12.1Maximum expected utility (MEU) queries
3
12.2Variable elimination with decisions
1
12.3Backward induction for IDs
12.4Strong junction tree evaluation
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12.5Decision circuit compilation
1
12.6Policy construction algorithms
1
12.7Value of perfect information
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12.8Value of partial information
12.9Dominance testing and pruning
12.10Robust decision analysis
12.11Sensitivity analysis for utilities
12.12Interval probabilities and utilities
12.13Computational complexity results
12.14Heuristics for large IDs
12.15Case studies of ID evaluation
13. Causality and Interventions with Bayesian Networks11 views
Using BNs for causal reasoning, identification, and counterfactual analysis.
15 topics (15 versions)
13.1Interventions and the do-operator
3
13.2Causal vs associational queries
1
13.3Back-door criterion
1
13.4Front-door criterion
1
13.5Adjustment sets
1
13.6Mediation analysis
13.7Counterfactual queries
13.8Identifiability conditions
13.9Transportability overview
13.10Selection bias and correction
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13.11Unobserved confounding
1
13.12Causal discovery assumptions
13.13Instrumental variables
1
13.14Causal effect estimation methods
13.15Graphical criteria in practice
1
14. Model Validation, Diagnostics, and Explainability13 views
Assessing predictive performance, stability, and transparency of models.
15 topics (15 versions)
14.1Train, validation, and test splits
3
14.2Predictive log-likelihood and perplexity
14.3Cross-validation strategies
14.4Posterior predictive checks
1
14.5Residual analysis for BNs
1
14.6Parameter identifiability checks
1
14.7Structure stability via bootstrapping
1
14.8Sensitivity to priors and hyperparameters
14.9Marginal and local sensitivity analysis
1
14.10Conflict and surprise measures
1
14.11Debugging inconsistent evidence
1
14.12Explaining inferences to stakeholders
1
14.13Fairness and bias assessment
1
14.14Uncertainty communication
1
14.15Model risk management
15. Tools, Implementation, and Applications16 views
Practical workflows, software ecosystems, deployment, and real-world use cases.
15 topics (15 versions)
15.1End-to-end modeling workflow
5
15.2Data preprocessing and encoding
1
15.3Feature discretization tools
15.4Efficient CPT storage
15.5Sparse and factorized representations
1
15.6Software libraries and frameworks
1
15.7Graph editors and visualization
2
15.8Probabilistic programming integration
1
15.9Acceleration and parallelism
1
15.10Reproducibility and versioning
15.11Deployment and serving
1
15.12Monitoring and model drift
15.13Domain applications: healthcare
1
15.14Domain applications: finance
1
15.15Capstone project guidelines
1