Recent content by hoffmann

beautiful! thank you!

yes, that is also not coming to me. if it helps, i know that this scoring metric is skewed when the sizes of the lists are large and their overlaps are small (only in comparison to the sizes of the lists, but still pretty large in comparison to smaller list/overlap sizes). it seems that i need...

Say I have two lists, List1 and List2 containing elements such as words. Some words are common two both List1 and List2. I want to create a distance metric that tells me how far apart the two lists are based on a similarity "score". The similarity score and distance metric are as follows...

basic statistics question: i have two variables, M1 and M2. i want to calculate how similar these two variables are using the odds ratio. M1 and M2 are lists of things, with some elements present in both lists. i also have a background list containing the things in M1 and M2, plus more...

basically the kkt conditions need to be satisfied if the solution is optimal. you have the two constraints as your functions (say g and h) -- both these and the objective function need to be stationary, dual and primal feasible, and satisfy complementary slackness. anyway, so i think there are...

what does it mean to write out the kkt conditions and find x* for the following problem: minimize f(x) = \sum x_i subject to \prod x_i = 1 and x_i \geq 0 for 1<= i <= n. the bounds on the sum and product are from i = 1 to n.

yep, that makes sense. why isn't x2, ..., xn-1 = 0 then? are you saying it should just be 1?

i'll write P as: P = x^{2}_{1} - 2x_{1} + 1 + x^{2}_{n} + (x_{n} - x_{n-1}) + ... + (x_{2} - x_{1}) and now differentiating P wrt x1, ..., xn: P^{'}_{x_{1}} = 2x_{1} -3 = 0, x_{1}= 3/2 P^{'}_{x_{2}} = -1 + 1= 0, x_{2}= 0 P^{'}_{x_{n}} = 2x_{n}+ 1 = 0, x_{n}= -1/2 so would the...

alright, so how would i do that within the summation notation?

i have the following problem: find the critical points of: P = (x_{1} - 1)^{2} + (x_{n})^{2} + \sum(x_{k+1} - x_{k}) the bounds of the sum are from i = 1 to n-1. so i differentiate P with respect to x and i set it equal to zero, and i eventually get the expression: \sum(x_{k+1} -...

ok, some help: 1) set this up with a variable (btw, better to call the starting point x0 rather than x, since it is fixed), an objective function and a set of equality constraints. Write them down. You should replace the objective function by something nicer: for example no square roots, since...

^^ i think you're on the right track, dafe. i think an analogy to this problem is, what is the shortest distance between a point in the xy plane and the x axis. it's just a line perpendicular to the x-axis. so in the context of the problem i asked, it's like...the dot product between the...

i think this question has something to do with the orthogonality of subspaces and is analogous to saying the shortest distance between a point and an axis is just a perpendicular line...

i think this question has something to do with the orthogonality of subspaces and is analogous to saying the shortest distance between a point and an axis is just a perpendicular line...

Does anyone know how to approach this problem? Let A be an m×n matrix of rank m, where m<n. Pick a point x in R^n, and let x∗ be the point in the nullspace of A closest to x. Write a formula for x∗ in terms of x and A. What exactly is the significance of the point x* in the nullspace of A?