1.1 A historical example

A historical example with real data from more than 100 years ago

Before we delve into how a neural network is trained and can therefore learn on its own, let's take a look at a neural network that has already been trained. We don't have to understand everything yet, but we can nonetheless explore it as a representative of many other similarly structured neural networks. The neural network used in this example is able to predict with an accuracy of 80 percent who survived the sinking of the famous Titanic in 1912 and who did not. Following a collision with an iceberg, the ship, which was considered unsinkable at the time, went under, and there were not enough lifeboats for all passengers. Out of more than 2200 people, only about 700 survived.

The data of 1300 of the 2200 passengers from the accident over 100 years ago could be reconstructed and compiled into a data set, which is often used as a starting example and will also be used here.^[1] The neural network shown below has already been fully trained with this data. The network can now use the learnt data to predict whether a passenger would survive or not. In this first step, we don’t need to understand how exactly this works; this will be explained later. For now, it is sufficient to know that the neural network learns during training how it can best convert the input data (in this case, eight numerical values) into the desired output data (survived, not survived).

Try for yourself: Who survived the sinking of the Titanic?

Fill in all eight fields with values of your choice and click Calculate. The input fields are converted into numerical values and sent to the already trained neural network. From there, the numbers “flow” from left to right through the neural network and ensure that one of the two so-called output neurons is activated at the end: either the one that represents “survived”, or the one that represents “not survived”.

*Number of relatives A: number of siblings or spouse. E. g. 2 for a child travelling with two siblings, 1 for a woman travelling with a husband.
*Number of relatives B: number of children or parents. E. g. 2 for a child travelling with mother and father, 4 for a woman travelling with four children.
*Price: Average ticket prices ranged between £8 and £500 at the time, depending on (corresponding) cabin class.

Try entering the data of real passengers to see if the network predicts their survival correctly:

• Mrs Stengel, 1st class, female, aged 43, booked with husband and no children in cabin section C for £55, boarded in Cherbourg (survived)
• Mr Lovell, 3rd class, male, aged 20, travelling alone, booked in cabin section A for £7.25, boarded in Southampton (did not survive)

For the above data, the network should correctly predict whether these passengers survived or not, as these two data sets belong to the 80 percent of the total of 1300 data sets that the network predicts correctly. Now enter the following real data which the network unfortunately gets wrong:

• Mrs Mack, 2nd class, female, aged 57, travelling alone, booked in cabin section E for £10.50, boarded in Southampton (did not survive)
• Mr Pickard, 3rd class, male, aged 32, travelling alone, booked in cabin section E for £8.05, boarded in Southampton (survived)

Why does the network not work perfectly?

Why does the network make errors? This is because the network is not a database. Also, there is no memory in which the original data can somehow be stored and from which it could be retrieved. There are not even as many connections (in which information could be stored in the form of a number) as there are people in the data set. In fact, the network only has a total of 118 numerical values (“parameters”) which can be changed during training and must be adjusted in such a way that the network makes as many correct predictions as possible. But there were 1300 x 8 = 10,400 input data-items, which is why the network makes an error in every fifth prediction (20%) on average. However, there are enough scenarios in which an accuracy rate of 80 per cent could already be important. After all, an 80% probability of dying with a low-cost 3rd class ticket is quite significant.

Overall, the network does not reproduce the real chance of survival on the Titanic perfectly, but it does tend to do so quite well. Due to the shortage of lifeboats at the time, women and children, especially in 1st and 2nd class, were prioritised for evacuation. For structural and organisational reasons, among other things, 3rd class passengers had poorer access to the lifeboats, which is why many of them drowned. Men in 2nd class had the lowest survival rate in percentage terms, presumably because they let women and children evacuate first. This and more information can be found here.^[2]