Reasoning Under Uncertainty Questions and Answers

Q: What does the Viterbi algorithm compute?

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.

Q: Why is the most likely sequence not the sequence of most likely states?

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.

Q: What problem does resampling address in a particle filter?

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.

Q: What is a certainty factor in an early expert system?

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.

Q: Why did certainty factors give way to probability?

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.

Q: What is the Dempster Shafer theory of evidence?

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.

Q: What distinction does Dempster Shafer theory try to capture?

Knowing nothing about a coin is treated differently from knowing it is fair, whereas both give a probability of one half. Whether that difference should be represented in the formalism or in a distribution over parameters is the substance of the disagreement with the Bayesian position. Interpretation, reliability and continuity are separate issues. An objection resting on what a formalism cannot distinguish is answerable either by extending it or by showing the distinction unnecessary, and both replies have been made.

Q: What is fuzzy logic concerned with?

Fuzzy logic addresses vagueness, where a man of a certain height is partly tall, rather than uncertainty about a definite fact. That is a different phenomenon from probability, and confusing the two produces a great deal of fruitless argument. Belief, second order probability and defeasibility are separate notions. Distinguishing vagueness in the predicate from uncertainty about the world is the first step in deciding which formalism a problem requires.

Q: Why is fuzzy membership not the same as probability?

Whether a definite man of definite height counts as tall is a question about the word, not about the world, and no amount of evidence resolves it. A probability that he is tall would presuppose a sharp boundary and uncertainty about which side he falls. Arithmetic, normalisation and application area are consequences or incidental. Identifying which kind of imperfection in knowledge a problem exhibits is what selects the right formalism rather than the fashionable one.

61.

What does the Viterbi algorithm compute?

A.The most likely state at each individual time step
B.The probability of the observation sequence occurring
C.The parameters of the model from an observation sequence
D.The single most likely sequence of hidden states

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.

Discuss in Forum

62.

Why is the most likely sequence not the sequence of most likely states?

A.Transitions between individually likely states may be impossible
B.The two are always the same in a correctly specified model
C.The most likely states are computed from different evidence
D.The sequence probability is not defined for individual states

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.

Discuss in Forum

63.

What is a particle filter?

A.An exact inference algorithm for continuous state models
B.A sampling method representing the belief by weighted samples
C.A filter removing outliers from a stream of observations
D.A method for tracking particles in a physical simulation

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.

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64.

What problem does resampling address in a particle filter?

A.The number of particles grows with each observation
B.The weights become negative after enough updates
C.Most particles acquire negligible weight over time
D.The particles drift away from the true state gradually

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.

Discuss in Forum

65.

What is a certainty factor in an early expert system?

A.The probability that the rule's conclusion is true
B.The proportion of cases in which the rule was applied
C.A measure of how reliable the rule's author considered it
D.A number attached to a rule expressing confidence in it

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.

Discuss in Forum

66.

Why did certainty factors give way to probability?

A.Their combination rules had no principled justification
B.They were too slow to compute in a large knowledge base
C.They could not represent complete certainty in a conclusion
D.Probability required fewer numbers to be supplied by experts

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.

Discuss in Forum

67.

What is the Dempster Shafer theory of evidence?

A.An extension of probability to continuous variables
B.A formalism assigning belief to sets rather than single outcomes
C.A method for combining probabilities from independent sources
D.A theory of how evidence should be gathered and evaluated

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.

Discuss in Forum

68.

What distinction does Dempster Shafer theory try to capture?

A.Between evidence from reliable and unreliable sources
B.Between discrete and continuous uncertainty in a model
C.Between lack of belief and belief in the negation
D.Between subjective and objective interpretations of probability

Answer: C

Knowing nothing about a coin is treated differently from knowing it is fair, whereas both give a probability of one half. Whether that difference should be represented in the formalism or in a distribution over parameters is the substance of the disagreement with the Bayesian position. Interpretation, reliability and continuity are separate issues. An objection resting on what a formalism cannot distinguish is answerable either by extending it or by showing the distinction unnecessary, and both replies have been made.

Discuss in Forum

69.

What is fuzzy logic concerned with?

A.Degrees of belief in propositions that are true or false
B.Probabilities that are themselves uncertain quantities
C.Reasoning with rules whose conclusions may be retracted
D.Degrees of membership in vaguely defined categories

Answer: D

Fuzzy logic addresses vagueness, where a man of a certain height is partly tall, rather than uncertainty about a definite fact. That is a different phenomenon from probability, and confusing the two produces a great deal of fruitless argument. Belief, second order probability and defeasibility are separate notions. Distinguishing vagueness in the predicate from uncertainty about the world is the first step in deciding which formalism a problem requires.

Discuss in Forum

70.

Why is fuzzy membership not the same as probability?

A.It concerns vagueness of the predicate rather than uncertainty of the fact
B.It uses different arithmetic to combine the numbers involved
C.Fuzzy values need not sum to one across the alternatives
D.Fuzzy logic applies only to control systems rather than reasoning

Answer: A

Whether a definite man of definite height counts as tall is a question about the word, not about the world, and no amount of evidence resolves it. A probability that he is tall would presuppose a sharp boundary and uncertainty about which side he falls. Arithmetic, normalisation and application area are consequences or incidental. Identifying which kind of imperfection in knowledge a problem exhibits is what selects the right formalism rather than the fashionable one.

Discuss in Forum

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