Recent content by NATURE.M

Homework Statement Consider f = wT x, where p(w) ∼ N (w|0, Σ). Show that p(f|x) is Gaussian. The Attempt at a Solution [/B] So there are apparently two approaches to this problem using either the linearity of f in terms of w or moment generating functions. But I'm having a lot of trouble...

So I think I resolved my troubles using a few properties outlined in the matrix cookbook.

Okay so rewriting with exponents of -1/2 (for the gaussian) and repeating the operation we would have: $$C\exp[f(\mu,\Sigma_k)]\left[-\frac{1}{2}|\Sigma_k|^{\frac{-3}{2}}\frac{\partial |\Sigma_k|}{\partial \Sigma_k}+|\Sigma_k|^{\frac{-1}{2}}\frac{\partial}{\partial...

I don't understand how you got $$C\Sigma_{k}^{-1}$$ In the multivariate gaussian we have $$\frac{1}{|\Sigma_{k}|}$$ How did you convert that determinant into an inverse ? Maybe you meant the same thing but forgot the determinant sign ?

So looking through my notes I can't seem to understand how to get from one step to the next. I have attached a screenshot of the 2 lines I'm very confused about. Thanks. BTW: The equations are for the log likelihood in a mixture of gaussians model EDIT: To elaborate I am particularly...

Interesting, well this would confirm that there are only trivial solutions that exist to the original equation. But the original problem is as stated, that is 7.2.2

Right now I'm thinking the only possible solutions are when a=c, b=d or when a=d, b=c. So this is what I have, but it doesn't use a heap. I'm still not entirely sure what I would want to store in the heap. for (i : 1,...,n) ...for(j : 1,...,n) ...insert into array (i, j, i, j) ...if (i != j)...

Homework Statement We have four integers a,b,c,d each of which are >= 1 and <= n, and are asked to write an algorithm to find all possible solutions to the following equation: a7 + b7 = c7 + d 7 The algorithm should use a heap of at most n elements, and should have worst case runtime of O(n2...

Yeah I agree. I think this happens to be the case in many disciplines, physics being fairly notorious for this.

So basically, I'm sure many of you have watched the new tv show Mr. Robot. I'll be the first to say that the show is incredible and quite possibly one of my favourites ever. And if you haven't watched it you should. But that's besides the point. It seems the show has inspired many non-tech...

So what I take is that: for some t, s∈N, we have tm = sn = c. This would express any multiple of c. I'm wondering how to express the smallest common multiple. And in the larger scheme of things, I feel the loop invariant condition isn't particularly helpful as I don't see any uses of it. Is...

I feel like it would be better to use a decreasing sequence of natural numbers and use a corollary from well ordering principle that states any decreasing sequence of natural number is finite. At least, that's what I've typically seen looking through many proofs of correctness on iterative...

Okay so here is what I have: For i∈N, we define P(i): If there are at least i iterations, then i = k + l - 2 and mn(i+2) = na + mb. Proof of LI: Base Case: From the code when i=0 we see a=m, b=n, k=1, l=1. Then, k+l-2 = 1 + 1 -2 = 2-2 = 0 = i and mn(0+2) = 2mn = nm + mn = na + mb, as desired...

Okay so if I just substitute we have i = a/m + b/n - 2. I'm not sure what you mean by simplify (or how this equation can be simplified). I'm sure that a and b should be written in terms of i but don't know how to do so. Otherwise the above statement is equivalent to i = k + l -2.

Okay so I'm able to see the relationship i = k + l - 2 where i is the number of iterations but I'm still having difficulty trying to relate a and b to i, m and n.