Problems tagged with regression

Problems tagged with "regression"

Problem #176

Tags: multiple outputs, lecture-16, regression

A neural network with 3 output nodes is trained to predict temperature, humidity, and wind speed simultaneously. The network uses the multi-target regression loss:

\[\ell(\vec h, \vec y) = \|\vec h - \vec y\|^2 = \sum_{k=1}^{3}(h_k - y_k)^2 \]

For a particular data point, the network's predictions are $\vec h = (5, 3, 7)$ and the true values are $\vec y = (3, 4, 5)$. Compute the loss.

Solution

$9$.

$$\begin{align*}\ell(\vec h, \vec y) &= (5 - 3)^2 + (3 - 4)^2 + (7 - 5)^2 \\&= 4 + 1 + 4 \\&= 9 \end{align*}$$