Given the the vectors $a,b,c \in \mathbb{R}^5$:
$a = [180, 70, 10, 0, 4]$$b = [165, 55, 8, 1, 7]$$c = [175, 60, 9, 0, 3]$
(Hint: first find $(a-b)$)
The outcome of the two exercises should give you the same result. Reflect on the properties of inner products demonstrated in the second exercise.
Using your preferred formula find the vectors which are at the lowest Euclidean distance from each other.
You are given the following dataset consisting of training inputs $x$ and training labels, $y$:
$x_1 = 2, y_1 = 5$$x_2 = 3, y_2 = 7$$x_3 = 4, y_3 = 9$Assume you are asked to evaluate two models $f$ and $g$ defined as:
$f(x) = 3x^2 - 2x + 1$$g(x) = 2x^2 + 4x + 3$In the following steps you have to calculate the least squares loss of the models $f$ and $g$ on the training data:
Loss Function:
$(\mathcal{L} = \frac{1}{N} \sum_{i=1}^{N} (y_i - f(x_i))^2)$$(\mathcal{L} = \frac{1}{N} \sum_{i=1}^{N} (y_i - g(x_i))^2)$Calculate the loss $\mathcal{L}_f$
Calculate the loss $\mathcal{L}_g$
Compare the calculated losses $(\mathcal{L}_f)$ and $(\mathcal{L}_g)$ and decide which model is the best performing one.
A) $(f_x(\sigma))$
B) $(\sigma)$
C) $(x)$
D) $(b)$
A) $(f_x(\sigma))$
B) $(\sigma)$
C) $(x)$
D) $(b)$
A) The transformed vector
B) The input vector
C) The parameters
D) The bias vector
A) Model parameters
B) An input variables
C) The output variable
D) A bias term
A) $(f(x, y, z) = 2x - 3y + 5z)$
B) $(f(x, y, z) = 7x - 3y + 5z)$
C) $(f(x, y, z) = 2x + 3y - 5z)$
D) $(f(x, y, z) = 2x - 3y + 5z - 7)$
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