The formula of loss function uses '(i)' as power of expected and real variables. What does that mean?

Question

The formula of loss function uses '(i)' as power of expected and real variables. What does that mean?

Alex Javarotti

2021年11月2日 10:54

In the formula below, could one understand $y^{(i)}$ as $y_i$ ? If not, what is the fundamental difference ?

$$ j(\theta_0, \theta_1) = \frac{1}{2m}\sum_{i=1}^m(h_{\theta}(x^{(i)})-y^{(i)})^2 $$

Topic mathematics cost-function loss-function

Category Data Science

Oxbowerce · Accepted Answer · 2021年11月2日 10:54

You are correct, the $i$ superscript simply denotes an index of a single observation/sample in the dataset. $y^{(i)}$ then refers to the output/label of a single sample and $h_\theta(x^{(i)})$ is the model's prediction for a specific input.

The formula of loss function uses '(i)' as power of expected and real variables. What does that mean?

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