Merge pull request #926 from evgenyigumnov/book-trainin-simplified

Book train simlified example

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+# Simplified
+
+## How its works
+
+This program implements a neural network to predict the winner of the second round of elections based on the results of the first round.
+
+Basic moments:
+
+1. A multilayer perceptron with two hidden layers is used. The first hidden layer has 4 neurons, the second has 2 neurons.
+2. The input is a vector of 2 numbers - the percentage of votes for the first and second candidates in the first stage.
+3. The output is the number 0 or 1, where 1 means that the first candidate will win in the second stage, 0 means that he will lose.
+4. For training, samples with real data on the results of the first and second stages of different elections are used.
+5. The model is trained by backpropagation using gradient descent and the cross-entropy loss function.
+6. Model parameters (weights of neurons) are initialized randomly, then optimized during training.
+7. After training, the model is tested on a deferred sample to evaluate the accuracy.
+8. If the accuracy on the test set is below 100%, the model is considered underfit and the learning process is repeated.
+
+Thus, this neural network learns to find hidden relationships between the results of the first and second rounds of voting in order to make predictions for new data.
+
+
+```rust,ignore
+{{#include ../simplified.rs:book_training_simplified1}}
+```
+
+```rust,ignore
+{{#include ../simplified.rs:book_training_simplified2}}
+```
+
+```rust,ignore
+{{#include ../simplified.rs:book_training_simplified3}}
+```
+
+
+## Example output
+
+```bash
+Trying to train neural network.
+Epoch:   1 Train loss:  4.42555 Test accuracy:  0.00%
+Epoch:   2 Train loss:  0.84677 Test accuracy: 33.33%
+Epoch:   3 Train loss:  2.54335 Test accuracy: 33.33%
+Epoch:   4 Train loss:  0.37806 Test accuracy: 33.33%
+Epoch:   5 Train loss:  0.36647 Test accuracy: 100.00%
+real_life_votes: [13, 22]
+neural_network_prediction_result: 0.0
+```