Assignment 11 Machine Learning COMS 4771

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Consider the Chessboard City scenario of Assignment 10, Q3 (the 18 blocks at or adjacent to City Hall
Neighborhood are observed to be uncontaminated). In addition, you have stationed 8 sensors that detect
the epidemic pathogen. 4 of them are at the city corners a1,h1,a8,h8 and the other 4 are at the approximate
border midpoints e1,h5,d8,a4. Assume the entire Bayes Net of Chessboard City is resampled i.i.d (windbased infection occurs instantaneously, and every timepoint resets resets all the blocks afresh.
1) Perform exact inference using the Junction Tree Algorithm implemented by the Bayes Net Toolbox,
to learn to get the marginal probabilities of each of respective your sensors to indicate contamination.
function [ marginal ] = GetMarginals()
%GetMarginals
% compute marginal probabilities for ChessBoardCity sensors
% returns a vector of 8 real values that have the marginal probabilities
% of respective blocks a1,e1,h1,a4,h5,a8,d8,h8 to be contaminated
Note that this function needs to create the Chessboard City Bayes net inside the function.
[20pt]
2) Perform exact inference using the Junction Tree Algorithm implemented by the Bayes Net Toolbox,
to learn to get the marginal probabilities of each of respective your sensors to indicate contamination,
given information on one of the blocks.
function [ marginal ] = GetMarginalsGiven1(node)
%GetMarginalsGiven1
% compute marginal probabilities for ChessBoardCity sensors
% input:
% node number to marginalize over (integer in 1..64, where 1=a1, 8=a8,
% 64=h8)
% Output:
% marginal: a 8×2 matrix of real values, the i-th column of which
% has the marginal probabilities
% of respective blocks a1,e1,h1,a4,h5,a8,d8,h8 to be contaminated,
% given that node is observed to be i
Note that this function also needs to create the Chessboard City Bayes net inside the function. If the
input node is a sensor, the probabilities for that sensor would be 0 or 1.
[20pt]
3) Perform exact inference using the Junction Tree Algorithm implemented by the Bayes Net Toolbox,
to learn to get the marginal probabilities of each of respective your sensors to indicate contamination,
given information on several of the blocks.
function [ marginal ] = GetMarginalsGivenSeveral( nodes)
%GetMarginalsGivenSeveral
% compute marginal probabilities for Chessboard City sensoors
% Input: the set of nodes n1,n2,…,nk
% to be marginalized over ( a vector of integers,
% all in 1..64 , where 1=a1, 8=a8, 64=h8)
% returns a 8x2x2…x2 matrix of real values, the (i1,i2,…,ik)-th column of
% which
% has the marginal probabilities
% of respective blocks a1,e1,h1,a4,h5,a8,d8,h8 to be contaminated,
% given that node n1 is observed to be i1,
% node n2 is observed to be i2, …
% node nk is observed to be ik
Note that this function also needs to create the Chessboard City Bayes net inside the function. If the
input nodes include one or more sensors, the probabilities for such sensors would be 0 or 1.
[20pts]
4) Use the above to figure out a Bayes net with 8 nodes corresponding to the 8 sensors, that describes
the joint distribution over the sensors. This would involve running the marginal inference functions
above several times to compute conditional probabilities. Submit a matlab script run_me.m that
prints the conditional probabilities that you may need, and a description read_me.pdf of the
Bayes net [50pt]
Good luck!