Improve regression example

[laggui]

Pull Request Template

Checklist

• Confirmed that run-checks all script has been executed.
• Made sure the book is up to date with changes in this PR.

Related Issues/PRs

Fixes #2401

Changes

The previous example had some issues regarding input and feature normalization, and the model did not converge well.

I have adapted the simple regression example to use a more simple dataset (in terms of features and target variable): the California housing dataset.

The model remains pretty much the same, but I changed some minor details for the training config.

I've also added the code for inference and display a nice little graph for 1000 samples (predicted vs expected). The console looks like this (minus the colorized points) when the example completes:

Train Dataset Size: 16640
Valid Dataset Size: 2000
======================== Learner Summary ========================
Model:
RegressionModel {
  input_layer: Linear {d_input: 8, d_output: 64, bias: true, params: 576}
  output_layer: Linear {d_input: 64, d_output: 1, bias: true, params: 65}
  activation: Relu
  params: 641
}
Total Epochs: 100


| Split | Metric | Min.     | Epoch    | Max.     | Epoch    |
|-------|--------|----------|----------|----------|----------|
| Train | Loss   | 0.435    | 100      | 3.481    | 1        |
| Valid | Loss   | 0.589    | 51       | 5.093    | 1        |

Predicted vs. Expected Median House Value (in 100,000$)
⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 5.0
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⢀⠈⠀⠁⠠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⢀⡁⡀⠐⢤⠀⠀⣊⠐⠸⡉⢄⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⣂⠐⠒⠾⠂⠈⠙⡐⠒⡐⠎⠂⠐⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠂⠀⠢⡂⢁⠤⡆⢪⣼⡳⡾⢧⢂⡄⠿⠇⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢄⠅⠌⠀⡀⡡⡂⡦⡹⠮⡮⣫⡵⢐⠈⡃⠔⠚⠀⠠⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢂⣧⢃⢂⡚⣃⢲⣖⢞⡧⣶⣚⡽⡫⢮⣳⣟⠅⡉⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢧⣸⣂⣹⠻⣽⣺⣯⣻⣿⣣⢯⣿⣟⡖⡉⡴⠄⢄⠄⢀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⡀⣨⢧⢊⡸⡺⣴⣟⣞⡿⣽⣙⣽⡷⣣⢷⡽⠣⢊⡂⠈⡂⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡁⠀⠀⢼⠆⣮⣧⣵⢝⣽⡿⡿⣿⣳⡫⡏⠛⠋⠇⡟⠛⠈⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡤⠆⠟⠛⠛⠽⠊⠛⠙⠟⠉⠓⠈⠁⠈⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁ 0.0
0.0                                                      5.0

Predicted 2.1703506 Expected 2.158

Testing

Tested the example with all feature flags.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 85.25%. Comparing base (80c831b) to head (2385e91).
Report is 6 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2405      +/-   ##
==========================================
- Coverage   85.26%   85.25%   -0.01%     
==========================================
  Files         792      792              
  Lines      104516   104552      +36     
==========================================
+ Hits        89115    89140      +25     
- Misses      15401    15412      +11     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.