About Machine Learning ( Part 2: Linear Regression )
Dataset
In prediction tasks, we often use independent features to predict a dependent variable. If we have a dataset:
$$
{ x_d^{(i)}, t^{(i)} }
$$
where:
- $x_d^{(i)}$: The $d$-th feature of the $i$-th instance in the dataset.
- $t^{(i)}$: The target value (dependent variable) for the $i$-th instance.
- $i = 1, \dots, N$: $i$ indexes the instances, and $N$ is the total number of instances in the dataset. ( Here $i$ is not power )
- $d = 1, \dots, D$: $d$ indexes the features, and $D$ is the total number of independent features.
Each feature in the dataset can be expressed as:
$$
x_d^{(i)}
$$
For simplicity, the following focuses on a single feature $x$, meaning $D = 1$.