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# Chapter 5. Neural Networks in a Nutshell

In Chapter 2, we briefly touched on the topic of neural networks in our exploration of the machine learning landscape. A neural network is a set of equations that we use to calculate an outcome. They aren’t so scary if we think of them as a brain made out of computer code. In some cases, this is closer to reality than we should expect from such a cartoony example. Depending on the number of features we have in our data, the neural network almost becomes a “black box.” In principle, we can display the equations that make up a neural network, but at a certain level, the amount of information becomes too cumbersome to intuit easily.

Neural networks are used far and wide in industry largely due to their accuracy. Sometimes, there are trade-offs between having a highly accurate model, but slow computation speeds, however. Therefore, it’s best to try multiple models and use neural networks only if they work for your particular dataset.

# Single-Layer Neural Networks

In Chapter 2, we looked at the development of an AND gate. An AND gate follows logic like this:

````x1` `<-` `c``(``0``,` `0``,` `1``,` `1``)`
`x2` `<-` `c``(``0``,` `1``,` `0``,` `1``)`
`logic` `<-` `data.frame``(``x1``,` `x2``)`
`logic``\$``AND` `<-` `as.numeric``(``x1` `&` `x2``)`
`logic````
````##   x1 x2 AND`
`## 1  0  0   0`
`## 2  0  1   0`
`## 3  1  0   0`
`## 4  1  1   1````

If you have two 1 inputs (both TRUE), your output is 1 (TRUE). However, if either of them, or both, are 0 (FALSE), your output is also 0 (FALSE). This computation is somewhat similar to our analysis of logistic regression. In ...

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