The learning-theory tag has no wiki summary.

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### Probability of ongoing experiment [migrated]

Suppose, I do a experiment where I have an event 'a' true 1000 times in 1000 trials. So, the probability becomes 1000/1000 = 1.
If I am going to do another trial, my prediction about event 'a's ...

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224 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 ...

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**1**answer

98 views

### What is the Bahadur-Anderson Algorithm?

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

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**2**answers

243 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 ...

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403 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 ...

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59 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 ...

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149 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.

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**2**answers

432 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 ...

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199 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 ...

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**1**answer

755 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 ...

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398 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 ...

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**4**answers

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### 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 ...

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**5**answers

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### 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 ...

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**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 + ...

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**1**answer

91 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 ...

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**3**answers

324 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 ...