Reasoning Under Uncertainty Questions and Answers

Answer: A

The model has a state evolving by a Markov chain and an observation generated from each state, so the state must be inferred from the observation sequence. Speech recognition and gene sequence analysis are classic applications. Unknown structure, unobserved transitions and assumed properties are different notions. A model combining a temporal process with partial observation, and admitting efficient exact inference, is unusually well suited to a wide class of problems.

Answer: B

Filtering maintains a belief over the present state, updating it as each observation arrives, and is what a tracking system does continuously. Smoothing looks backwards, prediction looks forwards, and the most likely sequence is the different problem the Viterbi algorithm solves. Naming the four temporal inference tasks separately matters because each has its own algorithm and its own cost.

Answer: C

Smoothing uses observations from after the time of interest as well as before, so its estimate of a past state is better than the filtered estimate was at the time. It is used in offline analysis where the whole sequence is available. Filtering, averaging and the most likely sequence are different tasks. Distinguishing what can be computed online from what requires the whole record is a practical distinction that determines which algorithm an application may use.

Answer: D

Viterbi finds the sequence maximising the joint probability, which is not the same as taking the most likely state at each step independently, since the latter may produce a sequence with zero probability of occurring. The forward algorithm gives the sequence probability and the Baum Welch algorithm estimates parameters. That a sequence of individually best choices need not be the best sequence is a general point about joint optimisation worth recognising.

Answer: A

Each step's most likely state may be reachable only through a transition of very low or zero probability from its predecessor, so the assembled sequence may be impossible. Viterbi optimises the whole sequence jointly and avoids that. The two coincide only in special cases. Optimising a whole structure rather than its parts independently is a distinction that recurs throughout structured prediction and it is worth having a concrete example of.

Answer: B

Representing the belief state by a population of weighted samples, propagating them through the transition model and reweighting by the observation, handles continuous and non-linear models that exact methods cannot. Resampling concentrates the population where the probability is. Outlier removal, physical simulation and exactness are different notions. Approximating a distribution by a sample, when no closed form exists, is a technique whose generality is its main attraction. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: C

Without resampling almost all the weight concentrates on a single particle and the effective sample size collapses, a failure called degeneracy. Drawing a new population in proportion to the weights restores diversity where the probability actually is. Drift, growth and negative weights are different or impossible. A failure mode in which a population representation quietly reduces to a single member is worth watching for in any sampling scheme.

Answer: D

Certainty factors attached ad hoc numbers to rules and combined them by formulas chosen for convenience rather than derived from any axioms. They worked adequately in small systems and behaved oddly as systems grew, which is what drove the field towards probability. They are not probabilities, and frequency and authorship are different notions. A scheme adopted because it seemed reasonable, and abandoned when its behaviour could not be justified, is instructive about why foundations matter.

Answer: A

The combination formulas implicitly assumed independences that the rule base did not satisfy, so conclusions could be badly wrong in ways nobody could predict or diagnose. Probability makes those assumptions explicit and derives its rules from axioms about consistent belief. Speed, expressiveness and elicitation burden are not the reason. Replacing a scheme that works by luck with one that works by construction is worth doing even when the second demands more of the modeller.

Answer: B

The theory distinguishes belief committed to a proposition from belief merely not committed against it, so ignorance is represented separately from disbelief. Its combination rule behaves surprisingly when sources conflict strongly. Probability combination, evidence gathering and continuity are different notions. A formalism motivated by a genuine distinction that probability handles differently is worth knowing about, even where probability has prevailed.