0
votes
1answer
15 views

InformationGain on Two Continuos classes instead on inary

I've a problem regarding an excersise with information gain. I can't seem to get the right answer, because the excersises differs from what we learned. Usually, a target class is a binary variable ...
2
votes
1answer
40 views

How can I plot this?

Given a bunch of data $x_i$ , $y_i$, how do I plot $$f(\theta_2,\theta_2)= \frac{1}{2M} \sum_{i=1}^{M} (\theta_1\cdot x_i -\theta_2 y_i)^2$$ in matlab? I know it should be parabolic, but my code ...
0
votes
1answer
111 views

Perceptron exercise

I wonder how to find a solution to the following questions: Q: Design a two-input perceptron that implements the boolean function A ∧¬ B? Q: Design a two-layer network of perceptrons that ...
0
votes
0answers
56 views

Factor graphs: HMM

A friend of mine and me are struggling for a while now on how to start with this example that we have to work out. There is a 10x10 map which an agent is randomly placed on. The single tiles of ...
2
votes
1answer
107 views

expectation of norm of orthogonal projector

The question has to do with calculating the expected squared norm of a random projection. We have a 2D subspace $T := span\{U1, U2\}$ where $U1$ is a random vector uniformly distributed over unit ...
0
votes
1answer
121 views

Multi layer perceptron activation function

How can you show that the Fourier series approximation of a function (so $f(x)=\sum\limits_{n=0}^{\infty} (a_n cos(nx) + b_n sin(nx))$ can be approximated to arbitrary precision by a feedforward ...
0
votes
0answers
47 views

Please help me about conjugate gradient method

As I know, the error function of neural network is the sum of difference between actual output and the target value. But in conjugate gradient method, they use quadratic function: $E(w) = \frac{1}{2} ...
1
vote
1answer
114 views

Linear algebra: finding a Tikhonov regularizer matrix

A more general soft constraint is the Tikhonov regularization constraint $$ \mathbf{w}^\text{T}\Gamma^\text{T}\Gamma\mathbf{w} \leq C $$ which can capture relationships among the $w_i$ (the matrix ...
1
vote
1answer
74 views

Probability of observed data in a HMM [duplicate]

Possible Duplicate: Probability of an observation message In a given Gaussian mixture model with observed continues variables $Y$ and latent discrete variables $X$ I want to apply the ...
2
votes
1answer
565 views

Minimizing L1 Regularization

I have given a high dimensional input $x \in \mathbb{R}^m$ where $m$ is a big number. Linear regression can be applied, but in generel it is expected, that a lot of these dimensions are actually ...
1
vote
0answers
141 views

Understanding Linear Regressions with Least Squares

I am currently trying to understand the linear regression fit by least squares for my machine learning homework, where I implement it and have to plot the result: I have given two data sets, ...
1
vote
1answer
291 views

Consensus in Discrete-Time and Matrix Theory [closed]

I have an $N \times N$ adjacency matrix $A_{ij}$ for nodes $i$ and $j$, numbered 1 through $N$. Each node $i$ starts with a scalar value $x_i(0)$ between 0 and 1. At each non-negative integral time ...
3
votes
1answer
332 views

Boltzmann “soft max” distribution

Formula is here: $$ p(i)=\frac{e^\frac{f(i)}{T}}{\displaystyle \sum_j e^\frac{f(j)}{T}} $$ Prove: 1) Each $p(i)$ is a number between $0$ and $1$, no matter what the fitness is (positive or ...