In the world of machine learning, understanding the core concepts of how models are trained is essential. One fundamental approach is supervised learning, where we provide the algorithm with a training set comprising input features and their corresponding output targets. The learning algorithm then processes this information and produces a function, which we'll denote as f.
Here's a quick breakdown:
f is the model or function.
x is the input or input features.
ŷ (y-hat) is the output of the model, representing the prediction or estimate for y.
The model's prediction, ŷ, is an estimate of the true value y. When we simply use the symbol y, we refer to the target value, which is the actual true value within the training set. It's crucial to note that ŷ is merely an estimate and might not always align perfectly with the actual true value y.
The Role of Parameters w and b
It's important to understand that w and b are numbers, and the values chosen for them determine the prediction ŷ based on the input feature x. When we write f{w,b}(x), it means f is a function that takes x as input, and depending on the values of w and b, f will output some prediction ŷ. For simplicity, we'll often write f(x) without explicitly including w and b in the subscript, though it means the same thing as f{w,b}(x).
In simpler terms, this function f uses the input feature x to predict the output y.
Application: House Sizes and Prices
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