The learning-theory tag has no wiki summary.

**2**

votes

**1**answer

90 views

### Epsilon-approximations of set systems with finite VC-dimension

ECorollary 6.9 in A Guide to NIP theories by Pierre Simon proves the following
Theorem. For every positive integer $k$ and every positive real $\varepsilon$ there is an integer $n=n(k,\epsilon)$ ...

**0**

votes

**0**answers

41 views

### Recursive parameter estimation for partially observed Ito SDEs

I'm trying to get my head around online (recursive) maximum-likelihood parameter estimation in the language of stochastic processes and in the context of stochastic filtering, i.e. where we have a ...

**0**

votes

**0**answers

32 views

### Is it possible to distinguish between to edge orientation while learning a network structure?

I'm considering the case of learning bayesian network structure using a dataset $\mathcal{D}$ with scoring methods :
$$\mathcal{G}^*=\max_{\mathcal{G}}\text{Score}(\mathcal{G}, \mathcal{D})$$
I'm ...

**1**

vote

**0**answers

36 views

### assumptions on local rademacher complexities

A lot of the work on Local Rademacher complexities of Koltchinskii, and Bartlett for fast rates of convergence is based on Bousquet's version of Talagrand's inequality [1] (Theorem 2.11). However the ...

**0**

votes

**0**answers

49 views

### Orthogonalization technique after cosparse dictionary update

I'm trying to adapt the cosparse dictionary learning (DL) approach described in Analysis K-SVD to a DL method that creates the dictionary as a union of orthonormal blocks (UONB).
For this I apply the ...

**-2**

votes

**1**answer

320 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

**1**answer

408 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

**2**answers

258 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

**1**answer

132 views

### What is the Bahadur-Anderson Algorithm?

What is the Bahadur-Anderson Algorithm, and which book could one read to learn it?

**1**

vote

**2**answers

253 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 ...

**1**

vote

**0**answers

62 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

**0**answers

178 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

**2**answers

506 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 ...

**4**

votes

**1**answer

1k 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

**0**answers

591 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 ...

**8**

votes

**4**answers

2k 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

**5**answers

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

**3**answers

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

**1**answer

93 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 ...

**10**

votes

**3**answers

330 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 ...