CS 57100: Artificial Intelligence

Assignment 6: Bayesian Inference, AI Ethics

Due 11:59pmEDT Wednesday, 30 November 2022

Please turn in a PDF through Gradescope. ITaP provides these instructions. Make sure that you mark the start/end of each question in Gradescope. Assignments will be graded based on what you mark as the start/end of each question. Please typeset your answers (LaTex/Word/OpenOffice/etc.)

1. Bayesian Inference

(2 points) Consider a Bayes net over the random variables A, B, C, D, with full joint distribution P(A, B, C, D). Assume that we are given the observation A=a. Draw the minimal Bayes net that is guaranteed to be able to represent the distribution P(B, C, D | A=a).

2. Bayesian Inference

SPIN wants to keep track of where scooters are on campus. They have a (sometimes accurate) location from a built-in GPS G, an also somewhat accurate location U where the user's cell phone says the scooter was left. The actual location is modeled as a random variable L.

1. (2 points) Draw a fragment of an HMM for this problem (t-1 to t+1). Note that the current location X_t is dependent on the prior location X_t-1, and that the reported locations G_t and U_t depend on the current location X_t.
2. (2 points) Give the forward update expression for P(x_t|u_1:t, g_1:t)

3. Structural Causal Modeling

Consider the following supervised learning task. Doctors prescribe two different treatments (A and B) to patients with kidney stones. Our goal is to predict which treatment we should ascribe to a patient. Let X ∈ {A,B} denote the prescribed treatment, and Y ∈ {0,1} be the success (1) or failure (0) of the treatment. In our dataset, we have 700 patients ascribed treatment, equally balanced between A and B.
(The numbers provided in the table are just for your reference. Do not use them in the equations.)

The dataset shows:

1. (2 points) Use structural causal model equations describing how this data is generated in the most general way possible. Hint: You must describe the exogenous variables (and if they are dependent or independent). An easy way is to use a single background variable source U and divide it into U_X and U_Y. Use f_X the deterministic function that gives X from its background variable, and f_Y as the deterministic function that gives Y from its background variable.
2. (2 points) Investigating further, we find that doctors consider treatment A more invasive and tend to only prescribe it in more severe cases. Adding severity to the data gives the following:
   

   	Size of kidney stone
   	Small		Large
   	Treat. A	Treat. B	Treat. A	Treat. B
   Y=1	(94%) 82	(87%) 234	(73%) 192	(70%) 56
   Y=0	5	36	71	24

   
   Clearly, treatment A is a more effective treatment for kidney stones than B, regardless of kidney stone size. Let S ∈ {small, large} be the random variable that describes the size of the kidney stone. Rewrite the equations in item 1 to include S, but now assume the exogenous variables are independent.

4. AI Ethics

We have seen several examples of how AI systems can exhibit racial, gender, cultural, or other types of harmful bias.

1. (2 points) Without discussing this with your project team, identify a form of harmful bias that could potentially be an outcome of your final project; if you don't think this is possible, explain why. This should be 1-2 paragraphs.
2. (1 point) Once you and your team members have written your answer to part 1, discuss your answer with your team members. Note any interesting differences in your answers, in particular, if you came up with different answers, do you see a reason why?

If your team members have not all finished before you turn in your assignment, just note the discussions you were able to have; if none, just note this and hold the discussion after they have completed (you will get credit anyway.)

5. AI Ethics

(3 points) There are several options for copyright or patent protection for AI-generated creations/inventions. Some are:

• Allow an AI system to hold a patent or copyright, just like a human.
• Allow the developer of an AI system to hold patent or copyright for things created by the AI system.
• Treat creations of an AI system as public domain (cannot be patented or copyrighted.)

Choose either copyright or patent, and one of the above options, and briefly (1-2 paragraphs, no more than a page) argue either for or against that option. You should have at least one reference that either supports your argument or provides additional information that you use in making the argument.

6. Robot Motion Planning

Envision a 2-arm robot, with each arm 1M long (the lower arm attaches to and pivots at the base). This is mounted in a space with a 0.9M ceiling:

1. (3 points) Draw the configuration space / obstacles for this robot. You don't need to get angles exact, giving a rough idea of the shape of the space and obstacles (floor and ceiling) will do.
2. (1 point) Note that if I started with the arm to the left (θ_s > 90, θ_e < 90), I could get to exactly the same point as shown in the figure, but the overall space I could reach would be different. Is this captured in your answer to Part 1? Why or why not?