Reasoning Under Uncertainty Questions and Answers

Answer: C

Ordering symptoms before diseases produces a correct but densely connected network whose tables are far larger and far harder to elicit. The distribution represented is identical. Construction and inference remain possible but expensive. That correctness and compactness are separate properties, and that only the second depends on the ordering, is worth demonstrating once on a small example.

Answer: D

Each node carries a distribution over its own values for every combination of parent values, and those tables together with the structure determine the full joint. The table is local: it never mentions non-parents. A joint listing, an independence catalogue and raw frequency counts are all different objects. Seeing that the network is nothing but structure plus these local tables is what makes its storage saving concrete rather than a slogan.

Answer: A

Three Boolean parents give 8 parent combinations, and each row needs one number because the complement is determined, so 8 free parameters rather than 16. Counting rows first and then halving each row is the reliable procedure, and it generalises directly to non-Boolean variables. Getting this arithmetic automatic is what lets you judge at a glance whether a proposed structure is elicitable from an expert or hopeless.

Answer: B

Noisy-or gives each parent its own inhibition probability and multiplies them, so the effect is absent only when every present cause is independently inhibited. That reduces a table exponential in the parents to one number per parent. Additive combination, output noise and exclusivity are different models. The saving is why noisy-or appears in almost every large diagnostic network built by hand.

Answer: C

Conditioned on its parents, its children and its children's other parents, a node is independent of everything else in the network. The co-parents belong because observing a child creates a dependence between its parents. Ancestors, neighbours and connectivity subsets are different sets. Gibbs sampling resamples a node from exactly this set, so the definition is a working tool and not a curiosity.

Answer: D

A common effect couples its causes once it is observed, so knowing a co-parent's value then changes belief about the node. This is explaining away seen from the blanket's side. Path membership, normalisation and sampling order are different reasons and none of them produces the co-parents. Deriving the blanket from the explaining-away pattern is more durable than memorising the three-part list.

Answer: A

The criterion reads conditional independence off the graph alone, without touching the numbers, by checking whether every path between the sets is blocked. Decomposition, tractability and edge reversal are separate questions. Because the answer depends only on structure, it holds for every parameterisation of that structure, which is what makes graphical reasoning worth doing before any table is filled in.

Answer: B

A collider blocks by default and is unblocked by observing it or any of its descendants, which is the reverse of the rule for chains and forks. That asymmetry is explaining away in graphical form. Observing a parent, or counting descendants, does not enter the rule. Keeping the collider case straight is the whole difficulty of d-separation, and it repays being checked on a three-node example every time.

Answer: C

Enumeration expands the query into a sum of products of table entries and evaluates it term by term, correct but exponential in the number of hidden variables because subexpressions are recomputed. Structure search, sampling and search over query values are different algorithms. Its cost is what motivates variable elimination, so it is worth tracing once on a four-node network to see the repetition appear.

Answer: D

A factor is a function from assignments of some variables to non-negative numbers, starting as the conditional tables and growing or shrinking as variables are joined and summed out. It need not be a distribution and need not sum to one. Final multipliers, eliminated variables and normalising constants are different things. Thinking of the algorithm as arithmetic on tables keeps the bookkeeping straight.