What a ML Model Really Is (From a Mathematical Perspective)

When we talk about a model in machine learning, it helps to immediately drop all associations with “artificial intelligence” and complex abstractions. At its core, a model is simply a function. Nothing more, nothing less. It takes some input data and returns a result. The only difference is that this function isn’t fixed — it has parameters that can be adjusted. If you’re a PHP developer, this should feel very familiar. A model is essentially just a function or class method: it takes inputs performs some computation returns a value A Model as a Function In its most general form, a model looks like this: f(x) = ŷ x — input data ŷ — predicted output The “hat” on ŷ is intentional: it’s not the true value, just an estimate. Function as the Foundation of a Model Let’s make it concrete. Suppose we want to predict the price of an apartment based on its size. A simple linear model would look like this: ŷ = w * x + b This already is a complete model. It says: “The predicted price is the area mu