For questions 1 and 4, please include a PDF with your answers.
Please also include a submission.py that can run your code for questions 2 and 3.
Question 1: Our Mars rover has been out collecting samples, and it needs to return to the charging station as quickly as possible.
It knows that over rocky terrain it can go 2 km/h. Over sandy terrain it can go 3 km/h, and over smooth terrain it can go 5 km/h.
There are three routes it might choose from. Unfortunately, our terrain data for the three routes is incomplete, so we only have estimates.
Route 1 is 2 km long. There is a 20% chance it is sandy, 30% chance it is smooth, and a 50% chance it is rocky.
Route 2 is 1.8 km long. There is a 40% chance it is sandy, a 20% chance it is smooth, and a 40 % chance it is rocky.
Route 3 is 3.1 km long. There is a 50% chance it is sandy, a 40% chance it is smooth, and a 10% chance it is rocky.
(10 points) Which route should we pick? Show your work.
We have now found out some additional information.
Route 1 contains a crater. If the wall of the crater is intact, we can go through it. If the wall has been damaged, we will need to go around, which will add 45 minutes to our journey. There is a 30% chance that the wall is damaged.
Route 2 contains a bridge. If that bridge is damaged, we will need to repair it, which will add 1 hour to our time. There is a 60% chance that the bridge is out.
(10 points) Now which route should we pick? Show your work.
(10 points) Now suppose that we can use a satellite to find out whether the terrain in route 3 is smooth. Is this helpful? What is the value of this information? Expressed differently, how long are we willing to wait for this information from the satellite?
(5 points) Now put this problem into ChatGPT. Is it able to solve it correctly? If not, where does it make mistakes?
Part 2: Hidden Markov Models
(Note: this is derived from an assignment in AAAI's Model Assignments workshop)
In this assignment you'll be implementing two algorithms associated with Hidden Markov Models.
You'll be building off of the code presented in HMM.py. There's also some included data to use. The first set of files are called two-english.trans and two-english.emit. These represent a two-state HMM that was learned from English words. This HMM has two states: Consonant and Vowel. It's here for practice. Since it only has two states, it's not going to be very accurate.
The first set of files are .trans files. They contain the transition probabilities. two_english models the transition between 'C' for Consonant and 'V' for Vowel in English. There's also a '#' which is used to represent the starting state.
The second set of files are .emit files. These contain the probability of emitting a particular output from that state. These are learned from data, and so contain errors (especially two_english).
The second set of .trans/.emit files are for the Brown corpus. These represent an HMM for recognizing parts of speech. This problem is larger, with 12 states and lots of possible emissions.
The last pair of files is ambiguous_sents.obs and ambiguous_sents.tagged.obs. This is what you'll test your Viterbi implementation on.
(5 points). Use the included code to implement load. Use two_english as a sample file to work with. You should be able to do:
model = HMM() model.load('two_english')
You should store the transitions and emissions as dictionaries of dictionaries. e.g. {'#': {'C': 0.814506898514, 'V': 0.185493101486}, 'C': {'C': 0.625840873591, 'V': 0.374159126409}, 'V': {'C': 0.603126993184, 'V': 0.396873006816}}
(10 points) Implement generate. It should take an integer n, and return a random observation of length n. To generate this, start in the initial state and repeatedly select successor states at random, using the probability as a weight, and then select an emission, again using the probability as a weight. You may find either numpy.random.choice or random.choices very helpful here. Be sure that you are using the transition probabilities to determine the next state, and not a uniform distribution!
You should be able to run it with the pre-trained probabilities for the Brown corpus, like so:
python hmm.py partofspeech.browntags.trained --generate 20
which generates 20 random observations.
Here are two sample observations:
DET ADJ . ADV ADJ VERB ADP DET ADJ NOUN VERB ADJ NOUN
the semi-catatonic , quite several must of an western bridge cannot spectacular analyses
DET NOUN ADP NOUN CONJ DET VERB DET NOUN NOUN NOUN ADP DET NOUN
whose light for wall and the learned the hull postmaster trash in his peters
(10 points) Next, implement the forward algorithm. This tells us, for a sequence of observations, the most likely final state. You should be able to run this like so:
python hmm.py partofspeech.browntags.trained --forward ambiguous_sents.obs
(15 points) Next, implement Viterbi. This tells us, for a sequence of observations, the most likely sequence of states. You should be able to run this like so:
python hmm.py partofspeech.browntags.trained --viterbi ambiguous_sents.obs
This uses the HMM parameters in partofspeech.browntags.trained.{trans,emit} to compute the best sequence of part-of-speech tags for each sentence in ambiguous_sents.obs, and prints the results.
You might find it helpful to use a numpy array to hold the matrix.
You can compare your results to ambiguous_sents.tagged.obs.
Problem 3: Belief networks.
For this problem, you'll be using the pgmpy library for probabilistic inference. To begin, you'll want to install this.
To start, take a look at the pgm_alarm.py file, which encodes the earthquake example from class. At the bottom is an example of how to query the network to find the probability that John calls given Earthquake.
(5 points) 1. Modify this query to determine:
- the probability of Mary Calling given that John called
- The probability of both John and Mary calling given Alarm
- the probability of Alarm, given that Mary called. Include each of your queries in pgm_alarm.py
(10 points) 2. Next, consider the carnet.py file. This contains the Bayesian netowrk represeting the car starting problem. To begin, ask the following queries:
- Given that the car will not move, what is the probability that the battery is not working?
- Given that the radio is not working, what is the probability that the car will not start?
- Given that the battery is working, does the probability of the radio working change if we discover that the car has gas in it?
- Given that the car doesn't move, how does the probability of the ignition failing change if we observe that the car dies not have gas in it?
- What is the probability that the car starts if the radio works and it has gas in it? Include each of your queries in carnet.py
(10 points) 3. Last, we will add an additional node to the network, called KeyPresent, that indicates whether or not we have the key for the car. This is a Categorical variable with two state values, yes and no. The prior for 'yes' is 0.7.
KeyPresent should only affect Starts. Add an edge to starts and update the CPD to indicate that:
P(starts | gas, ignition, keyPresent) = 0.99 P(starts | gas, !ignition, keyPresent) = 0.01 P(starts | !gas, ignition, keyPresent) = 0.01 P(starts | gas, ignition, !keyPresent) = 0.01 P(starts | !gas, !ignition, keyPresent) = 0.01 P(starts | !gas, ignition, !keyPresent) = 0.01 P(starts | gas, !ignition, !keyPresent) = 0.01 P(starts | !gas, !ignition, !keyPresent) = 0.01
(Problem 4 - grad students only)
AINow is a research institute that produces policy analysis addressing the concentration of power in the tech industry. They have recently published a landscape report assessing the state of the AI industry and making policy rcommendations.
Please read the executive summary and answer the following questions:
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What are the three dimensions along which Big Tech has an advantage in AI?
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Why does AI Now think it's important to focus on Big Tech?
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Priority 1 discusses Algorithmic Accountability. What does this mean? Why is it important to shift responsibility for detecting harm on companies themselves?
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What are the windows for action that are identified? Which do you personally think are the most effective or promising?
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The executive summary contains this quote:
"These are only a handful of examples, and what they make clear is that there is nothing about artificial intelligence that is inevitable. Only once we stop seeing AI as synonymous with progress can we establish popular control over the trajectory of these technologies and meaningfully confront their serious social, economic, and political impacts—from exacerbating patterns of inequality in housing, credit, healthcare, and education to inhibiting workers’ ability to organize and incentivizing content production that is deleterious to young people’s mental and physical health."
Do you agree with this assessment? How might we rethink our relationship with AI and with technology in order to avoid these potential negative outcomes?
Now paste this last question into ChatGPT and include its response. How do you compare its output to your own?