### Model Preliminaries

Machine Learning often involves minimising a cost/objective function, which is a function that measures the error of our model, consisting of several parameters(variables). We use methods from differential calculus for finding the minimum of cost functions. (Or maximum of reward functions).

There are several ways to think about calculus

• the study of the relationship between variables and their rates of change.
• a set of tools for analysing the relationship between function and their inputs. Typically we want to find the parameter values which enable a function to best match the data.
• a set of tools for helping us navigate in high-dimensional spaces.

The following posts link mathematical concepts in calculus with Optimization and Machine Learning.

1. Derivatives and functions
2. Gradients, partial derivatives, directional derivatives and gradient descent
3. Jacobian, Chain rule and backpropagation
4. Hessian, second derivatives, function convexity, saddle points
5. Taylor Series, Newtonâ€™s method
6. Lagrange Multipliers and Constrained Optimization
7. Limits, delta-epsilon and theoretical guarantees