**How to build an objective function in machine learning**

Machine Learning and Artificial Intelligence can be generally described as using a combination of data, mathematics and software to get computers to make the best possible guesses (hence often also decisions) of what (“y”) will happen if “x” happens – very often better than humans do: this is done by effectively finding a function H which matches best an input vector (X) with an observation vector (Y), for a given collection of (X,Y) combinations:

**Y = H(X)**

For example, one can forecast the sales of ice creams (Y) for a given temperature (X).

The goal is to find the **most (appropriately) simple H **which predicts Y using X as inputs **for a given prediction accuracy**, on a given data set.

The performance of H in matching X with Y is called the “Objective function”.

Usually, the quality of H is measured by two terms: the **matching error **(L) and the **regularization (or “complexity control”) term **(W):

**Obj(H) = L(H) + **W**(H)**

**L **is an estimate of the **fitting error **over the available data sets, and W is a measure of the **complexity **of H. For both terms, **the lower the better**.

Machine learning, in this context, consists in **minimizing the objective function Obj(H) **as the **best potential compromise **between** ****fitting accuracy **on past data sets and **complexity**.

This turns out – mathematically provable under general conditions, and empirically observed – to be the best way to predict the Y for future X’s.

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