Probabilistic Graphical Models - Statistic Assignment Help

Assignment Task

Implement forward sampling for Bayesian networks specified using numpy like in the example above. The example specifies the conditional probability distributions (CPDs) in v0 – v4, and stores them in a list cpds, in the order that they should be processed during forward sampling.
There are also variables that list all parents of all nodes (parents), and the cardinality of each variable (cards), which means how many different values a variable can take.
Take the following steps:
1. Implement a function that returns a single sample, given a CPD and possibly some evidence. Follow the template in Listing 2 below. An example function call will then
look like this:
In [22]: sampleone(v2, [1, 0], [2, 2]) Out[22]: 1
In this example, we are drawing a sample from the CPD in v2, with evidence v0 = 1, v1 = 0. Cardinality of v0 and v1 is both 2, and the returned sample is 1.

2. Implement a function that forward-samples a whole Bayesian Network. Follow the template in Listing 3 below. An example function call will then look like this:
In [44]: forwardsample(cpds, parents, cards)
Out[44]: [0, 1, 2, 1, 0]
In this example, we get a list of values, with one value for each node in the Bayesian Network.

3. Implement a function that draws N samples from the Bayesian Network, and returns them in a list. Follow the example in Listing 4. An example function call to draw 3
samples will look like this:
In [47]: sample(3,cpds,parents,cards)
Out[47]: [[1, 0, 2, 0, 0], [0, 0, 2, 0, 0], [0, 0, 1, 0, 0]]

4. Implement rejection sampling using your methods from above, so that you can compute (estimate) p(v4 | v3 = 1). Use your approach multiple times, with increasing number of samples (start with N=20, increase in steps of 20 up to N=1000). Plot a graph from your results, with N on the x-axis, and the estimated probability on the y. Describe your results in 2-3 sentences

This Statistic Assignment has been solved by our Statistic experts at My Uni Paper. Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+ Students in Australia, UK & US by helping them to score HD in their academics. Our Experts are well trained to follow all marking rubrics & referencing style.
Be it a used or new solution, the quality of the work submitted by our assignment experts remains unhampered. You may continue to expect the same or even better quality with the used and new assignment solution files respectively. There’s one thing to be noticed that you could choose one between the two and acquire an HD either way. You could choose a new assignment solution file to get yourself an exclusive, plagiarism (with free Turnitin file), expert quality assignment or order an old solution file that was considered worthy of the highest distinction.