Along with your answer to each of these questions, please tell me roughly how long it took you to answer the question. This assignment is largely a reality check, to make sure you're comfortable with basic background and skills the course will require.
You beeped her out of the way so we could wented to school.Well, yes, ok, I did in fact beep my horn at the car in front of me on our way to school. Children tend to notice these things. But the light was green, and she wasn't moving! For the record, my horn beeping was what we call a "gentle tap", which is officially sanctioned, at least in Idaho.
From an NLP perspective, my son's sentence is chock full of interesting stuff. For each of the following terms or concepts, (a) briefly define what the term means, preferably in your own words, (b) discuss where the concept is illustrated in this example (if it is), and (c) where relevant, comment on any ways in which this sentence might be particularly challenging for an NLP system.
Question 2. Recall that Bayes's Rule is often used in "Bayesian updating", since it is used to take a prior probability distribution and update it on the basis of observed evidence to produce a posterior distribution. Before, after, hence updating; get it?
This notion of "Bayesian updating" is particularly useful when applied iteratively. Consider a scenario where we have a prior distribution P(H) over hypotheses, and then we observe evidence E1 and use Bayes's Rule to update our distribution to
P(E1 | H) P(H)
P(H | E1) = --------------
P(E1)
The distribution P(H|E1) can now be viewed as a new, more informed
prior. Therefore if we see a new piece of evidence E2, we can use
Bayes's Rule again to derive a new posterior. Since P(H|E1) is the
prior now, the result will take
the form
X P(H | E1)
P(H | E1,E2) = ------------
Y
Derive the simplest possible form of the full expression, i.e. fill in X and Y, assuming that E1 and E2 are independent. (Note that if you don't make that assumption, you won't get the right answer.)
Then, go to Wolfram Alpha and try typing the following things into the box at the top (and then hit Enter or click the "=" sign).
3(a) Look at the PDFs (probability density functions) for each one, and explain in plain English what each of these Beta distributions represents, when interpreted as a Bayesian prior for the probability of heads. (To keep things standard, let's all assume that the prior belief is about the probability of heads for a possibly-unfair coin.) What is your expectation about what the probability of heads will be, and how strongly do you think so?
3(b) Let's take the notion of "expectation" in (3a) a little more literally, as in expected value, also known as the mean of the distribution. Try typing BetaDistribution[α,β] for some other values of α and β, and look at the number Wolfram Alpha reports as the "mean". Can you figure out what the formula for the mean is, as a function of α and β? (If you can't give an exact formula, at least comment on some properties of the mean. If you already knew the formula, it's ok to tell me so. But don't just look up the mean of the Beta distribution and copy it down; what would you learn from that?!.)
extract-nonstoplist-bigrams-from-a-web-page-and-sort-by-frequencyby all means go ahead and use it. Ok, that probably doesn't exist, but if you want to use an existing toolkit, that's fine. Like the other questions on this assignment, this is a reality check: if you find it very challenging or time consuming, then we should probably talk about whether this course is right for you.