## Overview#

Cost function is the average of the Loss function of the entire Training dataset.The desire is to find the parameters 𝑤 𝑎𝑛𝑑 𝑏 that minimize the overall Cost function.

Where:

- w is the weight a Vector
- b is the bias a Scalar
- L is the Loss function
- m is number of examples in the Training dataset
- 𝑦̂ is the Predictor variable output vector. It can also be denoted a^(number of layers)
- y is the truth from Training dataset

Cost function sum of Loss functions over your training dataset plus some model complexity penalty.

A loss function is a part of a Cost function which is a type of an objective function.

Cost function is generally represented by "J" and

The entire concept of "Training a Artificial Neural network is minimizing the Cost function
Normally, you must optimise the Training dataset and the weights on the synapses as you will **NOT** be able to control over the input data

### Common Examples:#

- Mean Squared Error (MSE): MSE(θ)=1N∑Ni=1(f(xi|θ)−yi)2MSE(θ)=1N∑i=1N(f(xi|θ)−yi)2
- SVM cost function: SVM(θ)=‖θ‖2+C∑Ni=1ξiSVM(θ)=‖θ‖2+C∑i=1Nξi

(there are additional constraints connecting ξiξi with CC and with Training dataset) - J = ∑1/2(y-yHat)exp(2)

### Category#

Artificial Intelligence