[ML] 2. Introduction to neural networks

Training an algorithm involes four ingredients:

Data
Model
Objective function: We put data input a Model and get output out of it. The value we call it as 'lost'. We want to minimize the 'lost' value.
Optimization algorithm: For example the linear model, we will try to optimize y = wx + b, 'w' & 'b' so that it will minimize the 'lost' value.

Repeat the process...

Three types of machine learning:

Supervised: Give feedback

Classification: outputs are categories: cats or dogs
Regression: output would be numbers.

Unsupervised: No feedback, find parttens

Reinforcement: Train the algorithm to works in a enviorment based on the rewords it receives. (Just like training your dog)

Linear Model:

f(x) = x * w + b

x: input

w: coefficient / weight

b: intercept / bias

Linear Model: Multi inputs:

x, w are both vectors:

x: 1 * 2

w: 2 * 1

f(x): 1 * 1

Notice that the lienar model doesn't chage, it is still:

f(x) = x * w + b

Lienar Model: multi inputs and multi outputs:

For 'W', the first index is always the same as X; the second index is always the same as ouput Y.

If there is K inputs and M outputs, the number of Weigths would be K * M

The number of bias is equal to the number of ouputs: M.

N * M = (N * K) * (K * M) + 1 * M

Each model is determined by its weights and biases.

Objection function:

Is the measure used to evaluate how well the model's output match the desired correct values.

Loss function: the lower the loss function, the higher the level of accuracy (Supervized learning)
Reward function: the hight of the reward function, the higher the level of accuracy (Reubfircement learning)

Loss functions for Supervised learning:

Regression: L2-NORM

Classification: CROSS-ENTROPY

Expect cross-entropy should be lower.

Optimization algorithm: Dradient descent

Until one point, the following value never update anymore.

The picture looks like this:

Generally, we want the learning rate to be:

　　High enough, so we can reach the closest minimum in a rational amount of time

　　Low enough, so we don't oscillate around the minimum