Now we will look closer at prediction. A neural network requires a lot of data to accurately predict. Similar to how a human would learn. We can build a neural network that can predict based on a single input. It takes the input and adjust its parameter or weight to produce an output (prediction).

def neural_network(input, weight):
  prediction = input * weight
  return prediction

Through trial and error this neural network can tweak the weight to achieve a higher probability of being right. While one data point is good to get started, the more the better to come up with more accurate predictions.

weights = [0.1, 0.2, 1]
def neural_network(input, weight):
  prediction = weighted_sum(input, weights)
  return prediction

The weighted_sum maps each weight to a data point allowing us to adjust each data points weight individually.

To make accurate predictions it is important to build neural networks that combine multiple inputs at the same time. We still multiply all data points with the respective weights. What changes is that we have to sum the predictions, also called waited sum of the input or waited sum or dot product.

The need for multiple inputs requires a vector or a list of numbers. Any time we perform a mathematical operation on two factors of equal length we do an element wise operation. That is why the order matters.

import numpy as np

weights = np.array([0.1, 0.2, 0])
def neural_network(input, weight):
  prediction = input.dot(weight)
  return prediction

A neural network can also make multiple predictions with a single input. We multiply the input with different weights. In the same way, a neural network makes predictions with multiple inputs and multiple outputs. For this to work, we have to put all our weights in a matrix or a list of vectors. We can use vector matrix multiplication to multiply it with the input matrix. What makes neural networks interesting is that you can stack neural networks. The output of one neural network can be feed into another neural network essentially doing two consecutive vector matrix multiplications. This is especially important for matrix multiplication which are too complex for a single weight matrix.

Numpy is a great tool for working with vectors and matrices. When creating a matrix keep in mind that rows come before columns.

The columns of the left matric must equal the rows on the right matrix, (a,b).dot(b,c) = (a,c)