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# System prepended metadata

title: Lec 01 - The Learning Problem

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# Lec 01 - The Learning Problem

#### Machine Learning can be applied, when

* a pattern exists
* we cannot pin it down mathematicaly
* We have data

### How is learning applied?

We have a viewer, a movie and a rating.

We apply learning by e.g. changing the weights, so that the inner product of movie and viewer relate to the rating.

### More general:

Input: $x$

Output: $y$

target function: $f: X\rightarrow Y$ (target function will remain unknown)

Data: $(x_1,y_1), ...$

Hypothesis: $g: X\rightarrow Y$ ($g$ approximates $f$, $g\approx f$)

Hypothesis set: $H$ (set of candidate formulas, e.g. Neural Network) $H={h},\,  g\in H$

Learning Algorithm (e.g. Backpropagation)

![](https://i.imgur.com/Ec6gmKI.png)


#### Perceptron

Approve credit:

$\sum_{i=1}^d w_i x_i > treshold$

Deny credit:

$\sum_{i=1}^d w_i x_i < treshold$

Linear formulation $h\in H$

$h(x)=sign((\sum_{i=1}^d w_i x_i) - treshold)$

$treshold = w_0, \, x_0=1$

$h(x)=sign\sum_{i=0}^d w_i x_i = sign(w^T x)$

Weights are changed if misclassified ($sign(w^T x) \neq y_n$):

$w\leftarrow w + y_n\cdot x_n$



