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-2
votes
1answer
163 views

AI / Machine Learning related to high/modern/front mathematics [closed]

I major math and cs. and i'm interested in ai/machine learning/data mining. so i want to know what math subjects are used in frontier of these technology. especially, high mathematical tool, like ...
5
votes
1answer
395 views

Is there a mistake in Vapnik's “Basic Lemma”?

I have a concern about the "Basic Lemma" which Valdimir Vapnik states and proves in his 1998 book Statistical Learning Theory (ch. 14.3, pp. 574–76): It seems like a certain coefficient should have ...
1
vote
2answers
241 views

A machine learning application question

I am familiar with basic probabilities, random processes but not so much of machine learning methods. This is the problem I am trying to solve. I want to predict the nature of user activity on a ...
0
votes
1answer
112 views

What is the Bahadur-Anderson Algorithm?

What is the Bahadur-Anderson Algorithm, and which book could one read to learn it?
1
vote
2answers
248 views

A sampling and learning question

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 sampled according to ...
0
votes
0answers
445 views

Gradient Descent for Primal Kernel SVM with Soft-Margin(Hinge) Loss

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 being the number of ...
1
vote
0answers
61 views

Vertex cover for hamming graphs representing sets of bounded VC dimension

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 vector and two ...
0
votes
0answers
159 views

VC dimension and boolean hypercube subgraphs

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.
3
votes
2answers
460 views

Vapnik-Chervonenkis dimension of lines in the plane

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 the plane, define a ...
0
votes
0answers
204 views

can someone please help me with this optimization problem

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 paper ...
4
votes
1answer
916 views

Monotonicity of the hard EM algorithm.

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 that the soft EM ...
2
votes
0answers
474 views

Classical Multidimensional Scaling

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 space which best ...
7
votes
4answers
1k views

Reference request for manifold learning

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 manifold learning I mean ...
1
vote
5answers
2k views

Nodes clusters with a distance matrix

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 60 60 60 100 120 ...
2
votes
3answers
5k views

The Polynomial Kernel

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,y) = (x \cdot y + ...
2
votes
1answer
92 views

Ranking sources at variable(random) frequencies

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 less frequent ...
9
votes
3answers
325 views

disconnected or poorly connected graphs in sport ratings systems

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 is a lot of ...