General Concepts In Machine Learning

    import torchvision.models as models
    ...
    res_model = models.resnet34(pretrained=True)
    ```
    He then applies the following algorithm, entitled xxx on the image.
    ```python
    import math
    def xxx(arr):
        mod = 0.0
        for i in arr:
            mod += i * i
        mag = math.sqrt(mod)
        for i in range(len(arr)):
            arr[i] /= mag
    # Example usage:
    arr = [1.0, 2.0, 3.0]
    xxx(arr)
    print(arr)
    ```
Which results in this list:
<table align='center'>
<tr>
    <td align="center">
    <img src="img/similarity-1.png" style="max-width:70%;" />
    </td>
</tr>
</table>
Name the algorithm that he used and explain in detail why he used it.

Algo 1 Data: Two vectors v1 and v2 are provided Apply algorithm xxx on the two vectors Run algorithm 2 Algo 2

def algo2(v1, v2):
    mul = 0.0
    for i in range(len(v1)):
        mul += v1[i] * v2[i]
    if mul < 0:
        return 0
    return mul

1. Name the algorithm algo2 that he used and explain in detail what he used it for.
2. Write the mathematical formulae behind it.
3. What are the minimum and maximum values it can return?
4. An alternative similarity measures between two vectors is: $\text{simeuc}(v1, v2) = -\|v1 - v2\|$. Name the measure.

2. Explain the formulae in plain words.
3. Find the Jacard similarity given the sets.

The Kullback-Leibler divergence is a meas- ure of how different two probability distribution are. As noted, the KL divergence of the probability distributions P, Q on a set X is defined as shown in Equation 8.11. $D_{KL}(P \| Q) = \sum_{x \in X} P(x) \log\left(\frac{P(x)}{Q(x)}\right)$ Note however that since KL divergence is a non-symmetric information theoretical meas- ure of distance of P from Q, then it is not strictly a distance metric. During the past years, various KL based distance measures (rather than divergence based) have been introduced in the literature generalizing this measure. Name each of the following KL based distances: $D_{KLD1}(P \| Q) = D_{KL}(P \| Q) + D_{KL}(Q \| P)$ $D_{KLD2}(P \| Q) = \sum_{x \in X} (P(x) - Q(x)) \log(P(x))$ $D_{KLD3}(P \| Q) = \frac{1}{2} [D_{KL}\left(Q\|\right(\frac{P+Q}{2})) + D_{KL}\left(P\|\right(\frac{P+Q}{2})) ]$ $D_{KLD4}(P \| Q) = max(D_{KL}\left(Q\|\right(P)) + D_{KL}\left(P\|\right(Q)))$