Daphne Koller

Local Structure

Context-Specific CPDs

ProbabilisticGraphicalModels

Representation

Daphne Koller

A

S

L

(0.8,0.2)

(0.9,0.1) (0.4,0.6)

(0.1,0.9)

s1

a0 a1

s0

l1l0Letter SAT

Job

Apply

Tree CPD

Which context-specific independencies are implied by the structure of this CPD? (Mark all that apply.)

A

S

L

(0.8,0.2)

(0.9,0.1) (0.4,0.6)

(0.1,0.9)

s1

a0 a1

s0

l1l0

Daphne Koller

Letter1 Letter2

Job

Choice

Tree CPD

Cc1 c2

L2

(0.8,0.2) (0.1,0.9)

l1l0L1

(0.9,0.1) (0.3,0.7)

l1l0

Which non-context-specific independency is implied by the structure of this CPD? C

c1 c2

L

(0.8,0.2) (0.1,0.9)

l1l0L

(0.9,0.1) (0.3,0.7)

l1l0

Letter1 Letter2

Job

Choice

Daphne Koller

Cc1 c2

L

(0.8,0.2) (0.1,0.9)

l1l0L

(0.9,0.1) (0.3,0.7)

l1l0

Letter1 Letter2

Job

Choice

Daphne Koller

Multiplexer CPDZ1 ZkZ2 . . .

YA

Daphne Koller

Microsoft Troubleshooters

# of parameters: 145 to 55

Daphne Koller

END END END

Suppose q is at a local minimum of a function. What will one iteration of gradient descent do?

Leave q unchanged.

Change q in a random direction.

Move q towards the global minimum of J(q).

Decrease q.

Consider the weight update:

Which of these is a correct vectorized implementation?

Fig. A corresponds to a=0.01, Fig. B to a=0.1, Fig. C to a=1.

Fig. A corresponds to a=0.1, Fig. B to a=0.01, Fig. C to a=1.

Fig. A corresponds to a=1, Fig. B to a=0.01, Fig. C to a=0.1.

Fig. A corresponds to a=1, Fig. B to a=0.1, Fig. C to a=0.01.