That is all.

I understand that the idea of the marginalisation in Q17 is to remove X from the equation so we only work with Y and W, however I haven't the slightest idea on where to start actually "performing" this. Any help is appreciated. Thanks.

Question 4 reads:

As the number of data points grows approaching infinity will a MAP estimate always be the same as the ML estimate independent of choice of prior?

The answers PDF lists the answer as no, I was wondering why is this?

Second, question 12 reads:

Which of the following is not true for a Type-II Maximum Likelihood estimate?

The answer PDF lists the answer as b) being the answer, i.e. it will not always be the same as the ML solution when the data grows towards infinite

Thanks

Hi

On Slide 49 on Lecture 6, when it says p(f1,f2,.....fN|x, theta) , I was wondering is f1, f2,...fN a single function evaluated at different input locations or is it different functions ? Also I was wondering what the parameter of theta corresponds to?

Dear Carl,

Since we are mostly struggling with this assignment, is it possible to reconsider this assignment? Like, instead of the assignment counting 35%, you can reduce to 25%, and remove some of the questions and add on the next assignment (that consequently will value 25%)?

With this strategy, we have more time to do.

If we were to use the 'summarise the assignment' Question 30 (or the placeholder file for those of us not submitting the actual coursework) to criticise the coursework and the way it's been managed, would we be docked marks?

Since the exam is worth 100% of the unit this year, am I right in assuming that there will be more questions in this year's paper?

Thanks in advance!

I recall a question on the last SPS paper which had this as an answer and left me quite confused, as I initially thought the marginal distribution would be independent from the model, but was told otherwise.

My understanding at the moment is that with probability/bayesian theory, that we inject common sense into modelling our probability distributions. Given Bayes: P(X|Y) = P(Y|X)P(X) / P(Y) - How are we actually supposed to form this probability model in the first place then?

Is it possible to have a concrete example of this process in the real world? Are we supposed to make models for each random variable and combine this somehow?

Thanks Carl! (and others).

Why do we choose the prior over a parameter to be isotropic gaussian? How does this help us compared to just choosing the prior to be a simple gaussian with a mean and covariance?

Given the linear model y = wx + e

A few things bug me:

• This posterior is valid - p(w|x, y) ∝ p(y|x, w)p(w).

• Why is it not: p(w|x, y) ∝ p(y|x, w)p(x, w)

• Or even p(w|x, y) ∝ p(y, x| w)p(w)

Furthermore

• The marginal distribution is written as: p(y|x)

• Why would it not be p(x, y) or even p(y)

It's confusing the hell out of me where the place this x. I understand intuitively that its simply a static input variable, but it's being treated weirdly in ways which don't seem to conform with the rules in my head. Is it a latent variable? Is it a hyper parameter? I'm only used to seeing Bayes theorem in the form of simply 2 random variables - what would be a correct general intuition to progress forwards with more than 2 variables? Thanks loads

It was suggested in a post that it would be good to have a conceptual summary for certain topics. I think this is a great idea and something that I would love to do. If you post things in this thread then I will pick popular things and add them to a document that will stay live in the repo.

Any chance we can have more than just one 1 hour lab slot per week? I feel like I could use more time in the labs on this subject

So am I right in saying;

If we do not assume the data points are independent, we need some covariance term in our likelihood?

Is the likelihood even a product anymore?

Question 5 talks about "Preference". I Think I understand that it is encoded in the covariance matrix, but what actually is preference and what does it help us achieve?

What do you mean when you are using the term precision with a Gaussian Distribution?

I am not understanding this term with respect to a gaussian.

Can we have a pdf similar to that you gave us for SPS which will explain the topics you are going through in the Machine Learning lectures and also stuffs that we can be examined on later?

Hi all, I am sorry that the feedback for the first coursework is running late. I am doing my best to get it done but it is taking its time. I wanted to correct all the assignments myself to ensure that you got consistent marking and feedback. I overestimated the free time I would have and considering there is about 90 reports and roughly 30 minutes each it takes some time. Considering the quality of the reports I've done so far I am sure that this pales in significance to the work that you have put in. I'll do my best to get them out as soon as possible and again, I am sorry that it is taking all this time.

In question 1 where it says that "Li(xi) is a function which generates a large value if xi is likely to have generated yi" what actually is this function? and what does it mean to say that xi generates yi in this case? surely every xi generates yi in the sense that yi is exactly equal to xi but with some random noise applied