Reasoning Under Uncertainty Questions and Answers

Answer: C

Each combination of values needs its own probability:

\[ 2^{20} - 1 \approx 10^{6} \]

so about a million numbers, which could neither be stored nor estimated from any realistic data set. Conditional independence reduces that to a few dozen. Working out the size of the unstructured representation is what makes the case for structure concrete rather than abstract.

Answer: D

The network encodes a joint distribution as a product of conditional distributions, one per node given its parents, with the graph asserting the conditional independences. It is often drawn causally because that gives the sparsest structure, but the mathematics requires only that the independences hold. Rules with certainties and pairwise correlations are different formalisms. Separating what the network asserts from why it is usually drawn that way avoids claiming more than the formalism supports.

Answer: A

The conditional probability table gives one distribution for every combination of the parents' values, and the product of all such tables is the joint. A node with no parents carries its marginal. Correlations and causal strengths are different quantities. That the local tables multiply to give the global distribution is the whole content of the factorisation, and it is what makes local elicitation sufficient.

Answer: B

Each parent combination requires its own distribution:

\[ 2^{3} = 8 \]

so 8 rows, each holding one free number for a binary child. The exponential in the number of parents is why sparse structure matters and why nodes with many parents are avoided or given a structured table such as a noisy or. Counting parameters before building a network is what reveals whether it can be populated at all.

Answer: C

A node with ten binary parents needs a thousand rows, which no expert could supply and no realistic data set could estimate. Structured representations such as the noisy or reduce that to a parameter per parent. Algorithms cope, cycles come from the graph structure rather than the parent count, and interpretation is unaffected. A representation whose size explodes with a particular structural feature drives the modeller away from that feature, which is often no bad thing.

Answer: D

The noisy or assumes each parent independently fails to cause the child with its own probability, so a table exponential in the parents is replaced by one number per parent. It is the probabilistic generalisation of a disjunction and fits many medical models well. Estimation noise, the deterministic disjunction and added randomness are different notions. Replacing a general table with a parameterised family, when the family fits, is what makes large networks elicitable.

Answer: A

Given its blanket, a node is conditionally independent of every other node in the network, which is why the blanket is exactly what a local sampling algorithm needs. Children's other parents are included because observing a child makes its parents dependent. Adjacency alone omits them, and the other options describe different sets. A set that screens a variable off from everything else is what makes local computation sound in a global model.

Answer: B

Two causes of the same effect are independent until the effect is observed, after which learning one explains the observation away and lowers the probability of the other. That explaining away is why they must be in the blanket. Path length, table computation and model revision are not the reason. A dependence created rather than removed by observation is counter-intuitive and is the single most distinctive feature of these networks. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: C

If the alarm sounds, an earthquake and a burglary are both plausible, but learning of an earthquake makes a burglary less likely although the two are independent a priori. It is the characteristic pattern of reasoning that Bayesian networks capture and rule based systems do not. The other options describe different operations. A qualitative pattern of inference that people perform naturally, and that follows from the mathematics rather than being programmed, is strong evidence the formalism is the right one. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: D

The criterion examines the paths between two sets of nodes and determines, from the graph alone, whether they are conditionally independent given a third set. It is what allows the structure to be interpreted without consulting the numbers. Decomposition, elimination order and evidence selection are different tasks. A purely graphical test for a probabilistic property is what makes the network a genuine representation rather than a mere diagram.