Demand Prediction

Introduction

To illustrate how neural networks work, let's start with an example. We'll use an example from demand prediction in which you look at the product and try to predict, will this product be a top seller or not?

Example: Predicting T-shirt Sales

Let's take a look. In this example, you're selling T-shirts and you would like to know if a particular T-shirt will be a top seller, yes or no. You have collected data of different T-shirts that were sold at different prices, as well as which ones became a top seller. This type of application is used by retailers today to plan better inventory levels and marketing campaigns.

Input Feature: Price

The input feature ( x ) is the price of the T-shirt, and that's the input to the learning algorithm.

Logistic Regression

If you apply logistic regression to fit a sigmoid function to the data, it might look like:

$$f(x) = 1 / (1 + e^{-wx + b})$$

In previous examples, we wrote this as ( f(x) ) as the output of the learning algorithm.

Transition to Neural Networks

To set us up to build a neural network, I'm going to switch the terminology a little bit and use the term ( a ) to denote the output of this logistic regression algorithm.

Activation

The term ( a ) stands for activation, and it's a term from neuroscience. It refers to how much a neuron sends a high output to other neurons downstream.

Simplified Neuron Model

We can think of logistic regression units as a very simplified model of a single neuron in the brain.

Building a Neural Network

Building a neural network requires taking a bunch of these neurons and wiring them together.

Example: Demand Prediction with Multiple Features

Let's now look at a more complex example of demand prediction. In this example, we're going to have four features to predict whether or not a T-shirt is a top seller.

Features of the Model

1. Price
2. Shipping Costs
3. Marketing Amount
4. Material Quality

Understanding the Features

• Affordability: Function of price and shipping costs.
• Awareness: Function of marketing.
• Perceived Quality: Function of price and material quality.

Neural Network Layers

We group neurons together into what's called a layer.

Layer Structure

• A layer can have multiple neurons or a single neuron.
• The output layer outputs the probability predicted by the neural network.

Activations

Affordability, awareness, and perceived quality are activations. These activations represent the degree to which the neural network predicts each factor.

Simplifying the Network

Rather than manually deciding which neurons take which features as inputs, each neuron in a layer can access all features from the previous layer.

Neural Network Representation

A neural network uses a vector of features as inputs and computes activation values through its layers.

Input, Hidden, and Output Layers

• Input layer: The vector of features.
• Hidden layer: Intermediate computations (affordability, awareness, and perceived quality).
• Output layer: Final prediction.

Hidden Layers

The hidden layer is so named because the values for the intermediate features are hidden in the training data.

Logistic Regression and Feature Learning

The neural network builds upon logistic regression but can learn its own features, making it more powerful.

Manual Feature Engineering vs Neural Networks

In previous methods, we manually combined features. Neural networks, however, learn to create their own features, reducing the need for manual engineering.

Example of a Multi-Layer Neural Network

Here's an example of a neural network with multiple hidden layers:

Deciding the Structure of a Neural Network

When building a neural network, you must decide:

1. How many hidden layers to use.
2. How many neurons per hidden layer.