Almost every problem in ML and data science starts with the same ingredients:

• The dataset \( \mathbf{x} \) (could be some observable quantity of the system we are studying)
• A model which is a function of a set of parameters \( \mathbf{\alpha} \) that relates to the dataset, say a likelihood function \( p(\mathbf{x}\vert \mathbf{\alpha}) \) or just a simple model \( f(\mathbf{\alpha}) \)
• A so-called cost function \( \mathcal{C} (\mathbf{x}, f(\mathbf{\alpha})) \) which allows us to decide how well our model represents the dataset.

We seek to minimize the function \( \mathcal{C} (\mathbf{x}, f(\mathbf{\alpha})) \) by finding the parameter values which minimize \( \mathcal{C} \). This leads to various minimization algorithms. It may surprise many, but at the heart of all machine learning algortihms there is an optimization problem.