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CompSci37: AI > Lec 2 | Uncertainty > Flashcards

Lec 2 | Uncertainty Flashcards

1
Q

This can be represented as a number of events and the likelihood, or probability, of each of them happening.

A

Uncertainty

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2
Q

Every possible situation can be thought of as a world, represented by which lowercase Greek letter?

A

omega ω

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3
Q

How do we represent the probability of a certain world?

A

we write P(ω)

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4
Q

Axioms in Probability

every value representing probability must range between 0 and 1

A

0 < P(ω) < 1

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5
Q

Axioms in Probability

________ is an impossible event, like rolling a standard die and getting a 7.

A

Zero or 0

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6
Q

Axioms in Probability

________ is an event that is certain to happen, like rolling a standard die and getting a value less than 10.

A

One or 1

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7
Q

Axioms in Probability

The probabilities of every possible event, when summed together, are equal to ?

A

1

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8
Q

the degree of belief in a proposition in the absence of any other evidence

A

Unconditional Probability

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9
Q

The degree of belief in a proposition given some evidence that has already been revealed.

A

Conditional Probability

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10
Q

AI can use partial information to make educated guesses about the future. To use this information, which affects the probability that the event occurs in the future, we rely on?

A

Conditional Probability

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11
Q

How do we express conditional probability?

A

P(a | b)

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12
Q

What does P(a | b) mean?

A

“the probability of event a occurring given that we know event b to have occurred” or “the probability of a given b.”

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13
Q

What formula do we use to compute the conditional probability of a given b?

A 
         P(a∧b)
P(a|b)=-------------
          P(b)
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14
Q

It is a variable in probability theory with a domain of possible values that it can take on

A

Random Variable

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15
Q

It is the knowledge that the occurrence of one event does not affect the probability of the other event.

A

Independence

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16
Q

How do we define independence?

A

Independece can be defined mathematically: events a and b are independent if and only if the probability of a and b is equal to the probability of a times the probability of b: P(a ∧ b) = P(a)P(b)

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17
Q

It is commonly used in probability theory to compute conditional probability

A

Baye’s Rule

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18
Q

Bayes’ rule says that the probability of b given a is equal to the probability of a given b, times the probability of b, divided by the probability of a.

A 
              P (b) P(a | b)
P(b | a) = ------------------
                  P(a)
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19
Q

It is the likelihood of multiple events all occurring

A

Joint Probability

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20
Q

Probability Rules

This stems from the fact that the sum of the probabilities of all the possible worlds is 1, and the complementary literals a and ¬a include all the possible worlds.

A

Negation: P(¬a) = 1 - P(a).

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21
Q

Probability Rules

This can interpreted in the following way: the worlds in which a or b are true are equal to all the worlds where a is true, plus the worlds where b is true. However, in this case, some worlds are counted twice (the worlds where both a and b are true)). To get rid of this overlap, we subtract once the worlds where both a and b are true (since they were counted twice).

A

Inclusion-Exclusion: P(a ∨ b) = P(a) + P(b) - P(a ∧ b).

22
Q

Probability Rules

The idea here is that b and ¬b are disjoint probabilities. That is, the probability of b and ¬b occurring at the same time is 0. We also know b and ¬b sum up to 1. Thus, when a happens, b can either happen or not. When we take the probability of both a and b happening in addition to the probability of a and ¬b, we end up with simply the probability of a.

A

Marginalization: P(a) = P(a, b) + P(a, ¬b).

23
Q

Probability Rules

How is Marginalization expressed for random variables?

A 
P(X = xsubi) = ∑subjP(X = xsubi, Y = ysubj)

yati unsaon ni

24
Q

Probability Rules

This is a similar idea to marginalization. The probability of event a occurring is equal to the probability of a given b times the probability of b, plus the probability of a given ¬b time the probability of ¬b.

A

Conditioning: P(a) = P(a | b)P(b) + P(a | ¬b)P(¬b).

25
Q

It is a data structure that represents the dependencies among random variables.

A

Bayesian network

26
Q

What are the Bayesian networks properties?

A
  • They are directed graphs.
  • Each node on the graph represent a random variable.
  • An arrow from X to Y represents that X is a parent of Y. That is, the probability distribution of Y depends on the value of X.
  • Each node X has probability distribution P(X | Parents(X)).
27
Q

What are the properties of Inference?

A

Query X, Evidence Variable E, Hidden Variable Y, The goal

28
Q

Inference

The variable for which we want to compute the probability distribution.

A

Query X

29
Q

Inference

one or more variables that have been observed for event e

A

Evidence Variables E

30
Q

Inference

variables that aren’t the query and also haven’t been observed.

A

Hidden variables Y

31
Q

Inference

What is the goal?

A

calculate P(X | e)

32
Q

It is a process of finding the probability distribution of variable X given observed evidence e and some hidden variables Y.

A

Inference by Enumeration

33
Q

It is one technique of approximate inference

A

Sampling

34
Q

What are the steps of Likelihood Weighting?

A
  • Start by fixing the values for evidence variables.
  • Sample the non-evidence variables using conditional probabilities in the Bayesian network.
  • Weight each sample by its likelihood: the probability of all the evidence occurring.
35
Q

It is an assumption that the current state depends on only a finite fixed number of previous states.

A

Markov Assumption

36
Q

What do you need to construct a Markov Chain?

A

Transition Model

37
Q

It is a type of a Markov model for a system with hidden states that generate some observed event.

A

Hidden Markov Model

38
Q

Sometimes, the AI has some measurement of the world but no access to the precise state of the world. In these cases, the state of the world is called the ________________ and whatever data the AI has access to are the ____________________.

A

Hidden state and observations

39
Q

Give an example of a hidden state and its observation.

A
  • For a robot exploring uncharted territory, the hidden state is its position, and the observation is the data recorded by the robot’s sensors.
  • In speech recognition, the hidden state is the words that were spoken, and the observation is the audio waveforms.
  • When measuring user engagement on websites, the hidden state is how engaged the user is, and the observation is the website or app analytics.
  • Our AI wants to infer the weather (the hidden state), but it only has access to an indoor camera that records how many people brought umbrellas(observation?) with them.
40
Q

What is another term for sensor model?

A

emission model

41
Q

The assumption that the evidence variable depends only on the corresponding state.

A

Sensor Markov Assumption

42
Q

What are the multiple tasks that can be achieved based on hidden Markov models?

A

Filtering, Prediction, Smoothing, Most Likely Explaination

43
Q

Hidden Markov Model Tasks:

given observations from start until now, calculate the probability distribution for the current state.

A

Filtering

44
Q

Hidden Markov Model Tasks:

given observations from start until now, calculate the probability distribution for a future state.

A

Prediction

45
Q

Hidden Markov Model Tasks:

given observations from start until now, calculate the probability distribution for a past state.

A

Smoothing

46
Q

Hidden Markov Model Tasks:

given observations from start until now, calculate most likely sequence of events.

A

Most likely explanation:

47
Q

Can a hidden Markov model be represented using a Markov chain?

A

Yes.

48
Q

From CS50 quiz

Consider a standard 52-card deck of cards with 13 card values (Ace, King, Queen, Jack, and 2-10) in each of the four suits (clubs, diamonds, hearts, spades). If a card is drawn at random, what is the probability that it is a spade or a two?
* About 0.019
* About 0.077
* About 0.17
* About 0.25
* About 0.308
* About 0.327
* About 0.5
* None of the above

Note that “or” in this question refers to inclusive, not exclusive, or.

A

About 0.308

49
Q

From CS50 quiz

Imagine flipping two fair coins, where each coin has a Heads side and a Tails side, with Heads coming up 50% of the time and Tails coming up 50% of the time. What is probability that after flipping those two coins, one of them lands heads and the other lands tails?

A

0.5 = 1/2

50
Q

From CS50 quiz

Two factories — Factory A and Factory B — design batteries to be used in mobile phones. Factory A produces 60% of all batteries, and Factory B produces the other 40%. 2% of Factory A’s batteries have defects, and 4% of Factory B’s batteries have defects. What is the probability that a battery is both made by Factory A and defective?
* 0.008
* 0.012
* 0.02
* 0.024
* 0.028
* 0.06
* 0.12
* 0.2
* 0.429
* 0.6
* None of the above

A

0.012

CompSci37: AI (7 decks)

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