Suppose there is an oracle that returns a number $b \in \mathbb{Z}_{n}$ whenever I press the button. We have $b = a + e$, where $a \in \mathbb{Z}_n$ is a fixed number and $e$ is s …

whats the relation between an input space and the VC dimension of a family of classifers on that space? as in, if H is the set of classifers, and H is defined on a really small i …

Given the primal objective $$F({\bf a})=L\sum_{i,j}a_{i}a_{j}k(x_i,x_j) + \sum_{i}max(0, 1-y_i \sum_{j}a_jk(x_i,x_j)$$ for the soft margin SVM, where ${\bf a}=(a_1,...,a_N)$, N be …

I'm having some problems with this problem concerning VC dimensions ( http://en.wikipedia.org/wiki/VC_dimension ), I hope for some helping input. Given a set $L$ of $n$ lines in t …

Are there any well studied graph theoretic properties that are common to all subgraphs of the boolean hypercubes that have a given VC dimension d.

Let $S$ be a set of binary vectors (in $\lbrace 0,1 \rbrace^m $) whose VC dimension is $d$. Let $H$ be the Hamming graph generated from this set where each node represents a binary …

Consider the problem where we want to find a maximum likelihood estimate of $\theta$, given $X$ and $$P_\theta(Y) = \sum_z P_\theta(Y,x)$$ where $x$ is a latent variable. I know t …

Hi, I have a (symmetric) matrix $M$ that represents the distance between each pair of nodes. For example, A B C D E F G H I J K L A 0 20 20 20 40 …

Hi all, I'm a CS major and don't quite understand the mathematics behind a optimization problem coming from a machine learning algorithm. The algorithm is in Section 5 of the pape …

I am interested in learning about manifold learning (no pun intended) and would like to know of some references that discuss the subject from a more geometric perspective. By mani …

I have a set of n samples, each associated with a set of x observations (real numbers) and y probabilities of outcomes (0 to 1 for each). I want to find subsets of observations tha …

Hi, I am doing an MDS with a distance matrix coming from geodesic distances between points X on a 3d mesh (ie., not euclidean distances), and try to find points Y in euclidean spac …

I Have seen two versions of the Polynomial Kernel during my time learning Kernel Methods for things such as regression analysis. 1) $\kappa_d(x,y) = (x \cdot y)^d$ 2) $\kappa_d(x …

I've briefly read about rating systems that provide rankings to players based only on their performance wrt other players, in the context of chess. (for example, elo). When there i …

Hi, I have this math modeling problem that I need help with. If I have 3 data sources, each being updated at different frequencies, what would be the best way to rank them so the …