What Is Machine Learning? F(X) = Y, Explained

Machine learning reduces to one expression: F(X) = Y. A model F takes input data X and produces output Y. Everything else, the cost of a project, the type of problem it solves, the way it fails, follows from what you know about each of those three terms before training starts. The cost of machine learning articles uses this expression to break down budgets; here, we will explain what the field is doing rather than what it costs.

The four types of machine learning are usually presented as a list to memorise. They’re more legible as four answers to one question: at training time, which of X and Y do you actually have?

Supervised learning: X and Y both known

The standard case. You have input data and the correct output for each example, an email and whether it’s spam, a photo and what’s in it, a transaction and whether it was fraudulent. Training is the process of adjusting F until it maps X to Y as closely as possible across the whole dataset. Almost every production ML system in commercial use is supervised, because it’s the only type where “correct” is defined by data you already have rather than by a process you have to design.

Unsupervised learning: only X known

No labels. You have input data and no defined output, and the task is to find structure in X itself, clusters of similar customers, the underlying dimensions in a set of measurements, which transactions look unlike the rest. There is no F(X) = Y to fit, because there is no Y to fit over. What comes out is a description of the data’s structure, not a prediction against a known answer.

Semi-supervised learning: Y known for a small subset

The common real-world case. Labelling, as covered in why labels are the primary artefact, is expensive, so most projects end up with a small labelled subset and a much larger unlabelled set. Semi-supervised methods use the labelled portion to anchor what “correct” looks like, then extend that understanding across the unlabelled data. It sits between the other two, using the small known Y to make sense of the much larger unknown one.

Reinforcement learning: Y isn’t fixed at all

The equation resists this one, which is itself informative. There’s no static correct output to learn from. Instead, an agent takes actions against an environment and receives a reward signal after the fact, and Y is generated by that interaction over time rather than known in advance. F(X) = Y still describes the agent’s policy at any given moment, mapping a state to an action, but Y itself is a moving target the agent is learning to produce rather than a label sitting in a dataset waiting to be matched.

The equation is a starting point, not a complete description, the same caveat that applies to using it as a cost model. What it does well is turn “what type of machine learning problem is this” into a concrete question: what do you actually know, and when do you know it. Most problems that get miscategorised in early planning turn out to have been miscategorised on that question specifically, not on the technical approach.