Figure 1 is a diagram of a small convolutional neural network that converts a 16 16...

 

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Figure 1 is a diagram of a small convolutional neural network that converts a 16 16 image into 6 output values. The network has the following layers/operations from input to output: convolution with 4 filters, max pooling, ReLu, and finally a fully- connected layer. For this network we will not be using any bias/offset parameters. Please answer the following questions about this network. 16x16 4@12x12 Convolution 4 filters 5x5 Stride 1 4@6x6 max pooling 2x2 Stride 2 6x1 fully- connected Figure 1: A small CNN network. (a) How many weights in the convolutional layer do we need to learn? (b) How many ReLu operations are performed on the forward pass? (c) How many weights do we need to learn for the entire network? [2 marks] [2 marks] [2 marks] (d) True or false: A fully-connected neural network with the same size layers as the above network (16 x 16 4 x12 x 12 4 x6 x 6 6 x1) can represent any classifier that the above convolutional network can represent. [2 marks] (e) What is the disadvantage of a fully-connected neural network compared to a convolutional neural network with the same size layers? [2 marks] Question# 01: Consider the following Bayesian Belief Network conditional probability table (CPT), and compute answers the following questions: P(B-T) P(B-F) 0.001 0.999 A P(AC-T) P(AC-F) T 0.90 0.10 F 0.05 0.95 Burglary Ali Calls Alarm Earthquake Veli Calls P(E=T) P(E=F) 0.002 0.998 BE|P(AT) P(A=F) TT 0.95 0.05 TF 0.94 0.06 FT 0.29 0.71 FF 0.001 0.999 A| P(VC=T) P(VC=F) T 0.70 0.30 F 0.01 0.99 c) What is the probability that there is a burglary given that Veli calls? d) What is the probability that there is earthquake given that Ali calls? I Question# 01: Consider the following Bayesian Belief Network conditional probability table (CPT), and compute answers the following questions: P(B-T) P(B-F) 0.001 0.999 A P(AC-T) P(AC-F) T 0.90 0.10 F 0.05 0.95 Burglary Ali Calls Alarm Earthquake Veli Calls P(E=T) P(E=F) 0.002 0.998 BE|P(A=T) P(A=F) TT 0.95 0.05 TF 0.94 0.06 FT 0.29 0.71 FF 0.001 0.999 A| P(VC=T) P(VC=F) T 0.70 0.30 F 0.01 0.99 c) What is the probability that there is a burglary given that Veli calls? d) What is the probability that there is earthquake given that Ali calls? I Question 2 Answer the questions based on the given network diagram. PC1 172.17.10.21 VLAN 10 PC2 172.17.20.22 VLAN 20 F0/11 F0/18 F0/6 S2 PC3 172.17.30.23 VLAN 30 GO/1 GO/1 S1 GO/2 GO/2 FO/11 S3 FO/18 F0/6 Phone0 PC6 172.17.30.26 VLAN 30 5 Marks PC4 172.17.10.24 VLAN 10 PC5 172.17.20.25 VLAN 20 a. If the switches in the network are able to carry traffic of different subnets, comment on the network type. b. Can PC1 and PC4 communicate each other? Justify your answer. c. What is your observation about G0/1, G0/2 links of $1? d. Write the command for adding VLAN 20 to $2. e. What techniques may be used for PC5 and PC3 to communicate each other? do a1 0.1 0.9 P(A) ao. bo ao,b bo b 0.4 0.6 do 0.9 0.7 d 0.1 0.3 fo fi do 0.8 0.2 d 0.3 0.7 p(B) p(F|D) p(D|A, B) p(EC, D) Use pomegranate to write a program for this Bayesian network. Use this program to compute the following probabilities. Please keep four digits after the decimal point. (6 marks, 2 marks for the last question) a1, bo 0.6 0.4 a1, b 0.1 0.9 (d) p(E =e A = ao, B = bo) (e) p(A= ao, B=bo E = ) Co C1 0.3 0.7 p(C) (a) p(E = co) (b) p(A= ao, B=b,C=co, D = d, E = o, F = f) (c) p(A= ao\F= fo) eo 0.9 e1 0.1 co, do Condi 0.8 0.2 0.7 0.3 C1, do C, di 0.1 0.9 do a1 0.1 0.9 P(A) ao. bo ao,b bo b 0.4 0.6 do 0.9 0.7 d 0.1 0.3 a1, bo 0.6 0.4 a1, b 0.1 0.9 fo fi do 0.8 0.2 d 0.3 0.7 p(B) p(F|D) p(D|A, B) p(EC, D) Use pomegranate to write a program for this Bayesian network. Use this program to compute the following probabilities. Please keep four digits after the decimal point. (6 marks, 2 marks for the last question) (d) p(E=eA = ao, B = bo) (e) p(A= ao, B =bo E =e) Co C1 0.3 0.7 p(C) (a) p(E = co) (b) p(A = do, B =b,C=co, D = d, E=co, F = f) (c) p(A= ao|F = fo) eo 0.9 e1 0.1 co, do Condi 0.8 0.2 0.7 0.3 C1, do C, d 0.1 0.9 Q2 Consider the Bayesian network from Chapter 14 of the AIMA text shown below P(B) 001 P(E) 002 Burglary e. Alarm A P(J) JohnCalls t 90 05 Earthquake B E P(A) 1 f 95 1 f 94 f 29 001 I 1 Mary Calls P(M) 70 01 Answer the following questions about this network, where the random variables are denoted by their initial. a. Prove that P(A | B,E,J,M) = P(A | B,E,J). b. If P(B|E,A,M,J ) = P(B | f(B) ), where f(B) = {E,A,M,J},what is the smallest value f(B) could have and why? c. Write a formula for the joint distribution P(B,M) given the network above. d. Write and justify a formula to calculate the conditional probability P(A | B, E) from the known joint distributions P(A,B,E) and P(B,E) Write down all values of the distribution P(B, E). 5. Bayesian Networks (30 points) Consider the following Bayesian network: 61 D b at node a: Prob(a) 0.7 ab 0 0 at node e: 01 100.7 1 0.9 1 e at node d: 0 1 e at node e: 0 Prob(c) 0.1 0.6 Prob(d) 0.6 0.8 10.7 Prob(e) 0.1 d Prob(g) at node g: 00.15 1 0.75 3 at node b: f Prob(h) at node h: 0 0.25 1 0.65 Prob(b) 0.8 c at node f: 0 Prob(f) 0.8 10.3 f at node i: 0 0.35 1 0.55 (e) (5 pts) Compute P(a = 1 | f = 1). Show your work. (f) (5 pts) Compute P(c = 1 | g = 1, h = 1). Show your work. Prob(i) (a) (5 pts) Compute P(f = 1 | a = 1). Show your work. (b) (5 pts) Compute P(f=1 | c = 0). Show your work. (c) (5 pts) Compute P(f =1 | a = 1, b = 1). Show your work. (d) (5 pts) Compute P(f=1| a = 1,b = 1,c= 1). Show your work. Figure 1 is a diagram of a small convolutional neural network that converts a 16 16 image into 6 output values. The network has the following layers/operations from input to output: convolution with 4 filters, max pooling, ReLu, and finally a fully- connected layer. For this network we will not be using any bias/offset parameters. Please answer the following questions about this network. 16x16 4@12x12 Convolution 4 filters 5x5 Stride 1 4@6x6 max pooling 2x2 Stride 2 6x1 fully- connected Figure 1: A small CNN network. (a) How many weights in the convolutional layer do we need to learn? (b) How many ReLu operations are performed on the forward pass? (c) How many weights do we need to learn for the entire network? [2 marks] [2 marks] [2 marks] (d) True or false: A fully-connected neural network with the same size layers as the above network (16 x 16 4 x12 x 12 4 x6 x 6 6 x1) can represent any classifier that the above convolutional network can represent. [2 marks] (e) What is the disadvantage of a fully-connected neural network compared to a convolutional neural network with the same size layers? [2 marks] Question# 01: Consider the following Bayesian Belief Network conditional probability table (CPT), and compute answers the following questions: P(B-T) P(B-F) 0.001 0.999 A P(AC-T) P(AC-F) T 0.90 0.10 F 0.05 0.95 Burglary Ali Calls Alarm Earthquake Veli Calls P(E=T) P(E=F) 0.002 0.998 BE|P(AT) P(A=F) TT 0.95 0.05 TF 0.94 0.06 FT 0.29 0.71 FF 0.001 0.999 A| P(VC=T) P(VC=F) T 0.70 0.30 F 0.01 0.99 c) What is the probability that there is a burglary given that Veli calls? d) What is the probability that there is earthquake given that Ali calls? I Question# 01: Consider the following Bayesian Belief Network conditional probability table (CPT), and compute answers the following questions: P(B-T) P(B-F) 0.001 0.999 A P(AC-T) P(AC-F) T 0.90 0.10 F 0.05 0.95 Burglary Ali Calls Alarm Earthquake Veli Calls P(E=T) P(E=F) 0.002 0.998 BE|P(A=T) P(A=F) TT 0.95 0.05 TF 0.94 0.06 FT 0.29 0.71 FF 0.001 0.999 A| P(VC=T) P(VC=F) T 0.70 0.30 F 0.01 0.99 c) What is the probability that there is a burglary given that Veli calls? d) What is the probability that there is earthquake given that Ali calls? I Question 2 Answer the questions based on the given network diagram. PC1 172.17.10.21 VLAN 10 PC2 172.17.20.22 VLAN 20 F0/11 F0/18 F0/6 S2 PC3 172.17.30.23 VLAN 30 GO/1 GO/1 S1 GO/2 GO/2 FO/11 S3 FO/18 F0/6 Phone0 PC6 172.17.30.26 VLAN 30 5 Marks PC4 172.17.10.24 VLAN 10 PC5 172.17.20.25 VLAN 20 a. If the switches in the network are able to carry traffic of different subnets, comment on the network type. b. Can PC1 and PC4 communicate each other? Justify your answer. c. What is your observation about G0/1, G0/2 links of $1? d. Write the command for adding VLAN 20 to $2. e. What techniques may be used for PC5 and PC3 to communicate each other? do a1 0.1 0.9 P(A) ao. bo ao,b bo b 0.4 0.6 do 0.9 0.7 d 0.1 0.3 fo fi do 0.8 0.2 d 0.3 0.7 p(B) p(F|D) p(D|A, B) p(EC, D) Use pomegranate to write a program for this Bayesian network. Use this program to compute the following probabilities. Please keep four digits after the decimal point. (6 marks, 2 marks for the last question) a1, bo 0.6 0.4 a1, b 0.1 0.9 (d) p(E =e A = ao, B = bo) (e) p(A= ao, B=bo E = ) Co C1 0.3 0.7 p(C) (a) p(E = co) (b) p(A= ao, B=b,C=co, D = d, E = o, F = f) (c) p(A= ao\F= fo) eo 0.9 e1 0.1 co, do Condi 0.8 0.2 0.7 0.3 C1, do C, di 0.1 0.9 do a1 0.1 0.9 P(A) ao. bo ao,b bo b 0.4 0.6 do 0.9 0.7 d 0.1 0.3 a1, bo 0.6 0.4 a1, b 0.1 0.9 fo fi do 0.8 0.2 d 0.3 0.7 p(B) p(F|D) p(D|A, B) p(EC, D) Use pomegranate to write a program for this Bayesian network. Use this program to compute the following probabilities. Please keep four digits after the decimal point. (6 marks, 2 marks for the last question) (d) p(E=eA = ao, B = bo) (e) p(A= ao, B =bo E =e) Co C1 0.3 0.7 p(C) (a) p(E = co) (b) p(A = do, B =b,C=co, D = d, E=co, F = f) (c) p(A= ao|F = fo) eo 0.9 e1 0.1 co, do Condi 0.8 0.2 0.7 0.3 C1, do C, d 0.1 0.9 Q2 Consider the Bayesian network from Chapter 14 of the AIMA text shown below P(B) 001 P(E) 002 Burglary e. Alarm A P(J) JohnCalls t 90 05 Earthquake B E P(A) 1 f 95 1 f 94 f 29 001 I 1 Mary Calls P(M) 70 01 Answer the following questions about this network, where the random variables are denoted by their initial. a. Prove that P(A | B,E,J,M) = P(A | B,E,J). b. If P(B|E,A,M,J ) = P(B | f(B) ), where f(B) = {E,A,M,J},what is the smallest value f(B) could have and why? c. Write a formula for the joint distribution P(B,M) given the network above. d. Write and justify a formula to calculate the conditional probability P(A | B, E) from the known joint distributions P(A,B,E) and P(B,E) Write down all values of the distribution P(B, E). 5. Bayesian Networks (30 points) Consider the following Bayesian network: 61 D b at node a: Prob(a) 0.7 ab 0 0 at node e: 01 100.7 1 0.9 1 e at node d: 0 1 e at node e: 0 Prob(c) 0.1 0.6 Prob(d) 0.6 0.8 10.7 Prob(e) 0.1 d Prob(g) at node g: 00.15 1 0.75 3 at node b: f Prob(h) at node h: 0 0.25 1 0.65 Prob(b) 0.8 c at node f: 0 Prob(f) 0.8 10.3 f at node i: 0 0.35 1 0.55 (e) (5 pts) Compute P(a = 1 | f = 1). Show your work. (f) (5 pts) Compute P(c = 1 | g = 1, h = 1). Show your work. Prob(i) (a) (5 pts) Compute P(f = 1 | a = 1). Show your work. (b) (5 pts) Compute P(f=1 | c = 0). Show your work. (c) (5 pts) Compute P(f =1 | a = 1, b = 1). Show your work. (d) (5 pts) Compute P(f=1| a = 1,b = 1,c= 1). Show your work.