Test 2

Question 1

!P is true if

Answer 1

P is false in the current model (negation)

Question 2

P and Q is true IF

Answer 2

Both P & Q are true in the model (conjunction)

Question 3

P or Q is true IF

Answer 3

P or Q is true in the model (disjunction)

Question 4

P -> Q is true UNLESS

Answer 4

P is true and Q is false in M (implication)

Question 5

P <-> Q is true IF

Answer 5

P & Q are both false or both true (bi conditional)

Question 6

Sentences have a truth value with respect to a model. This means that:

Answer 6

The model is the list of the values of the variables slotted into the given sentence. I.e. a sentence might have 3 variables, and for a particular model, those values might be, say, “true, true, false”

Question 7

A ^ B is logically equivalent too

Answer 7

B ^ A

Question 8

A v B is logically equivalent to

Answer 8

B v A

Question 9

((A ^ B) ^ C) is logically equivalent to

Answer 9

(A ^ (B ^ C))

Question 10

((A v B) v C) is logically equivalent to

Answer 10

(A v (B v C))

Question 11

!(!A) is logically equivalent to

Answer 11

A

Question 12

A -> B is logically equivalent to

Answer 12

!B -> !A and also !A v B

Question 13

A <-> B is logically equivalent to

Answer 13

((A -> B) ^ (B->A))

Question 14

!(A ^ B) is logically equivalent to

Answer 14

!A v !B

Question 15

!(A v B) is logically equivalent to:

Answer 15

!A ^ !B

Question 16

((A ^ (B v C)) is logically equivalent too:

Answer 16

((A ^ B) v (A ^ C))

Question 17

(A v (B ^ C)) is logically equivalent to:

Answer 17

((A v B) ^ (A v C))

Question 18

A sentence is satisfiable if:

Answer 18

It is true in some models.

Question 19

A sentence is valid if:

Answer 19

It is true in all models.

Question 20

A sentence is unsatisfiable if:

Answer 20

It is true in no models.

Question 21

Horn Clause:

Answer 21

A clause where at most one literal is positive.

E.I: (!P v !Q v V) and (!P v !W) are Horn Clauses.

Question 22

Definite Clause:

Answer 22

A clause where exactly 1 literal is positive.

EX: (!P v !Q v H v !D) is a definite clause

Question 23

How do you rewrite a Horn Clause to an implication?

Ex: (!C v !B v A)

Answer 23

First separate ! Terms
(!C v !B) v A

Negate ! Terms
(C ^ B) v A

Switch to implicate
(C ^ B) -> A

Question 24

What is Bayes Theorum?

Answer 24

P(b | a) = P(a | b) P(b) / P(a)

Question 25

What can P(a | b, c), and P(c | b) get us

Answer 25

P(a | b) = P(a | b, c) P(c | b)

Question 26

P(a ^ b) = ?

Answer 26

P(a | b) (P(b)

Question 27

P(x,y) = ? When both are independant

Answer 27

P(x) P(y)

Question 28

P(x, y) = ? When x & y are related to each other

Answer 28

P(x) P(y | x)

Question 29

If you want the probability of P(!d), but dont have it, what could you use to solve it

Answer 29

If you had them, you could: P(!d | f)P(f) + P(!d | !f)P(!f) to get P(!d)

Aka: The probability of it being !day given that aliens are friendly + probaility of it being !day given aliens are !friendly

Question 30

What does random forest do and why does it work?

Answer 30

Random Forest is when you take a random sample of your data, and build an ongoing series of decision trees. This gives us a larger model. The more decision trees you have with different criteria, the better the random forest will perform due to it increasing prediction accuracy.

It reduces overfitting, variance, and bias.

Question 31

What is Underfitting & what are its causes?

Answer 31

Underfitting usually occurs when your model doesnt have enough time or enough data. This results in it being unable to recognize general patterns and making bad predicitions.

Might also be due to having a bad model.

Question 32

What is overfitting and how does it occur?

Answer 32

Overfitting tends to occur when your model is too accurate, or rather, too tuned to the training data.

It’ll occur when your model has learned patterns which are only seen in the training data.

New predicitions will be much less accurate because they dont have the patterns only seen in the training data.

If there is a large variance between Validation data and Training data (Where you have high training data accuracy and low validation accuracy), you likely have overfitting.

To resolve it

Question 33

Suppose you train a classifier and test it on a validation set. It gets 30% classification accuracy on the training set and 30% accuracy on the validation set.

What is your model suffering from?
How can you resonably improve it?

Answer 33

It is likely suffering from Underfitting. To improve the model, you could likely add new features, as well as collect more training data.

Question 34

What does very low error on the training data, but high error on the test data represent?

Answer 34

Overfitting (high variance)

Question 35

What does High error on training data and higher error on the the test data suggest?

Answer 35

Underfitting

Question 36

If you have high bias, low variance, and low complexity, your model is

Answer 36

Underfitting.

Question 37

If you have low bias, high variance, and high complexity, you have…

Answer 37

Overfitting

Question 38

What are some ways to reduce overfitting

Answer 38

-Get more training data
-Add better features (to better capture the structure)
-Remove some features (to reduce noise)

Question 39

P( a | b) = ?

Answer 39

P(a | b) = P(a ^ b) / P(b)

Question 40

P(a ^ b) = ?

Answer 40

P(a ^ b) = P(a | b) P(b)

Question 41

What is modus ponens?

Answer 41

A <-> B, A / B

B <-> A, B / A