Bayesian Networks and Probabilistic Inference Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Bayesian Networks and Probabilistic Inference short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Summary: Inference and CPT Cheat Sheet

Core Formulas

Joint Distribution: $P (X_{1}, \dots, X_{n}) = \prod_{i = 1}^{n} P (X_{i} ∣ P a r e n t s (X_{i}))$
Inference by Enumeration: $P (X ∣ e) = α \sum_{y} P (X, e, y)$
Independent Parameters: $d^{k} \times (r - 1)$

Algorithm Comparison

Feature	Inference by Enumeration	Variable Elimination
Mechanism	Generate full joint, sum out hidden	Push sums inward, compute factors
Redundancy	High (recomputes sub-expressions)	Low (caches intermediate factors)
Complexity	$O (d^{n})$	$O (d^{w})$ , where $w$ is max factor size

Final Exam Checks

Did I use $P (Child ∣ Parent)$ from the table, not the reverse?
Did I sum over all possible states of the hidden variables?
Did I normalize the final vector so it sums to 1?

Summary: Factorization and Independence Cheat Sheet

Core Rules

Markov Condition: $X_{i} ⊥ NonDescendants (X_{i}) ∣ P a r e n t s (X_{i})$
Factorization Decoding: In $P (A ∣ B, C)$ , $B$ and $C$ are parents of $A$ .

Path Blocking Rules (d-separation basics)

Structure	Pattern	Marginally (Unobserved)	Conditioned on Middle Node
Chain	$A \to B \to C$	Dependent	Independent (Blocked)
Fork	$A \leftarrow B \to C$	Dependent	Independent (Blocked)
Collider	$A \to B \leftarrow C$	Independent (Blocked)	Dependent (Active)

Final Exam Checks

Did I correctly identify all parents from the factorization equation?
Did I check for colliders on the path? (Remember: conditioning on a collider creates dependence).
Are there multiple paths between the variables? (All must be blocked for independence to hold).

More short notes in this unit

Logic, First-Order Representation and Entailment Short Notes

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Bayesian Networks and Probabilistic Inference Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Bayesian Networks and Probabilistic Inference short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practi

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