Tutorium | Machine Learning

anchored to 116.00_anchor_machine_learning

First tutorial

First Task1:

b: Shifting to right will cause issues because we completely change the vector that is representing the tempalte in the given character.

The difference between two images with a shifted template will compute a whole different distance hence it will obviously be completely different than the previous template.

d Using grids will average values over a large area of the image, hence a variation - like a shift - wont have much of an impact However detailed grids could cause finer details to be detected yet still

f maximizing the margin with an improved error function: $$\begin{array}{rl}& y^t,r^t\\ & y>0,r=1\wedge \text{ margin}>\to 0\\ & y<0,r=1\text{ margin}>\to 0\\ & \text{ else}\to \end{array}$$ we want the values within the margin to the function to have a loss of 1, while the ones outside the margin are not receiving any error value.

We can describe it as follows: $$y:g(x)=a{x}_1+b{x}_2+c$$ Where: $$L(y^t,r^t)=\{\begin{array}{llc}0& \text{ if }y& t{r}^t\ge 1\\ 1-y^t{r}^t& \text{ else}& \end{array}$$ If the distance of a point to our function/line is smaller than 1 we use the distance from the defined function to the point as possible loss! thats the part on the right

reasons to penalize points within the margin: We want the classifier to be accurate and if its closer to the margin - or within - then we have a value that seems to be close to the side where its maybe modifiying the result of our modell - because it might be too ambiguous?

Second tutorial

Bayes Theorem | Task C

After calculating the initial values about the probabilities for the red / blue machine we ought to update the probabilities:

This changed / improved evaluation can be written as: $$\begin{array}{r}{P}_{+}^{\sim }\end{array}$$