Download cs344-endsem-25apr13-partial-sol

CS344
25/04/13
Introduction to Artificial Intelligence
Endsem-Examination
02.30 PM-05.30 AM
(Clarity and readability of answers are of utmost importance. Printout of class notes
allowed)
Question-1
(a) Recall “Maslow’s Hierarchy of Human Needs” discussed in the class. Some of
the human needs are d-needs or deficiency needs, in the sense that their nonfulfillment is acutely felt, but their fulfillment is not something special. There are
other needs which are exactly opposite, in that their fulfillment is noticed and
lauded, but their non-fulfillment is not critical. Mention the specific needs in these
two classes? Place them in Maslow’s hierarchy by drawing the hierarchy.
(2+2=4)
Ans:
The needs upto the 3rd layer are d-needs (survival, food+rest+shelter, social-acceptance).
Their non-fulfilment is critically felt, but fulfillment is so universal that that is hardly a
big deal. The needs 3rd layer upward are rare, and their fulfillment is noticed, but their
non-fulfillment is not critical.
(b) What do you think the left and right parts of the brain (of a right-handed
individual) do in case of the following activities:
a. Listening to a song
b. Quarreling
c. Cuddling a pet
d. Speaking and listening in a 2-person conversation
e. Speaking and listening in a crowd
(Write your answer as: Left Brain: <XYZ>; Right Brain: <PQR>)
(5 X2=10)
Ans (flexibility and variation expedcted ; apply your judgement):
General principle :
Left brain- concerned with details, organization, symbol-processing, verbal part
Right brain- concerned with gestalt, holistic aspects, emotion, overall and big picture
Listening to a song- left brain : rythm, words ; right brain : tune, emotion
Quarreling- left brain : words and body language ; right brain : level of anger, frustration
Cuddling a pet- left brain : pet’s physical condition, position with respect to the cuddler’s
body; right brain : affection towards and concern for the pet
Speaking and listening in a 2-person conversation- left brain : other party’s words and
body language ; right brain : emotional content of the conversation, overall profile
including user model of the other party
Speaking and listening in a crowd- left brain: individuals’ words and body language,
where to focus attention on; right brain : overall crowd sentiment, overall crowd profile
(logical, emotional, supporting the cause or opposing it)
Question-2
(a) Prove rigorously that if h=0, bidirectional A* search will always produce the
optimal path (the arc costs in the search graph need not be uniform). The
termination of the algorithm happens by the “meeting” of the searches from two
directions at a node, i.e., both searches expanding a node.
(8)
(b) Now prove by counter example that the path need not be optimal, if h>0. Give an
insight into why this is the case.
(4+3=7)
Question-3
(a) Additional knowledge helps an AI system. In the two coin EM algorithm, if we
have additional knowledge in the form of the ratio of the number of times coin1 is
chosen to the number of times coin2 is chosen, will the algorithm perform better?
That is, will it find better estimates of the parameters? Or will it terminate faster?
Establish your argument mathematically or by clear examples.
(10)
(b) Derive the expressions of Baum Welch algorithm from first principles. That is,
a. Set up the Maximum Likelihood Expression (MLE)
b. Introduce the constants of the problem using Lagrange multipliers
c. Differentiate the resulting expression to get the expressions of the
parameters (i.e., arc probabilities, the M-step) and the hidden variables (Estep)
(5+5+3+3=16)
Question-4
(a) What is the least number hidden neurons that will be required to compute XOR?
The multilayer perceptron (MLP) for this computation should be a feedforward
network, that is, the connections can be from any layer to any layer towards the
output neuron, but never backward. Draw the network, giving all the weights and
thresholds.
(5)
(b) Now give the most number of hidden neurons for the same task, i.e., computing
XOR. No neuron in the MLP should be “jobless”, that is doing nothing. (5)
(c) Give a “Universal” Boolean Function computer in the form of a multilayer
perceptron, obeying the following constraints:
a. There should be N input neurons (corresponding to N-ary Boolean
function)
b. There should be single output neuron
c. There should be a single hidden layer, if any
d. The connections should be feedforward from the input layer to the hidden
layer and from the hidden layer to the output neuron
e. The architecture of the MLP will not change from one function to another
(there are 2^(2^N) Boolean functions). That is the number of hidden layer
neurons will remain constant for all Boolean functions
f. Only the parameter values- weights of connections and threshold of
neurons- will change from one function to another.
As an example, if you have a 2-input, there are 16 Boolean functions, and each of
them will have the same MLP computing the function. Only the weight and threshold
values will change from AND to OR to NOR to NAND and so on.
(10)
Each neuron in the hidden layer represents the each possible min-term. Each neuron has
different combination of input weights depending upon the min-term. The weight is 1 for
the variable without complementation and -1 for the variable with complementation.
E.g., X0 X1 X2 will have weights (1,1,-1)
The weights W1, W2, …… will be either 1 or -1 depending on the formula.
========Paper Ends=======