[Data Science] Note on lbfgs solver + objects to pickle

docs/data-science/algorithms/supervised/classification.md

@@ -236,7 +236,7 @@ Now that we have our training data, we can train the logistic regression model.
 ```python
 from sklearn.linear_model import LogisticRegression
 
-model = LogisticRegression(random_state=42, max_iter=3_000)  # (1)!
+model = LogisticRegression(random_state=42, max_iter=5_000)  # (1)!
 model.fit(X_train, y_train)
 ```
 
@@ -261,12 +261,27 @@ print(f"Model weights: {model.coef_}")
 ```
 
 ```title=">>> Output"
-Model weights: [[ 0.98293997  0.22667548 -0.36956971  0.02637225 ... ]]
+Model weights: [[ 0.98208299  0.22519686 -0.36688444  0.0262268 ... ]]
 ```
 
 The `coef_` attribute contains the weight for each feature. 
 [As discussed](#deja-vu-linear-regression), the weights are real numbers.
 
+???+ warning "You might not have the exact same results"
+
+    Your model weights might differ slightly from the ones shown above. 
+    This is completely normal and happens because:
+
+    **Numerical precision**: The default optimization solver 
+    (`#!python "lbfgs"`) behind `LogisticRegression` encounters tiny 
+    hardware-specific variations. The underlying libraries handle 
+    floating-point arithmetic differently across hardware platforms. During the
+    iterative optimization, these tiny rounding differences  accumulate, 
+    causing the solver to converge to slightly different solutions.
+
+    :fontawesome-solid-lightbulb: These small differences don't affect your 
+    model's predictions or accuracy.
+
 Now, it's your turn to look at the bias.
 
 ???+ question "Model bias"

docs/data-science/data/preprocessing.md

@@ -66,9 +66,10 @@ we provide a distilled version of the code from
 Again, we urge you to use a virtual environment which by now, should be second 
 nature anyway.
 
-???+ info "Create a new notebook"
+???+ info
 
-    To follow along, create a new Jupyter notebook within your project.
+    To follow along, create a new script or Jupyter notebook within your 
+    project.
 
 ## Missing values
 

docs/data-science/practice/end-to-end.md

@@ -228,6 +228,20 @@ To get our prediction process working, we need to save all objects involved:
 - `encoder`
 - `forest`
 
+???+ warning "Critical: Save ALL preprocessing objects!"
+
+    **You must save every single object** used in the prediction pipeline, not
+    just the model!
+
+    Missing even one object will break your predictions:
+
+    - Missing `impute` → Cannot handle new missing values
+    - Missing `preprocessor` → Cannot transform features correctly
+    - Missing `encoder` → Cannot convert predictions back to original labels
+    - Missing `forest` → Cannot make predictions
+
+    **The model is useless without its preprocessing pipeline!** :warning:
+
 We can save all these objects in one file using a simple `#!python dict`:
 
 ```python
@@ -242,6 +256,10 @@ with open("bank-model.pkl", "wb") as file:
     pickle.dump(model, file)
 ```
 
+Bundling all objects in a dictionary ensures you never accidentally 
+forget a component. When you load `bank-model.pkl`, you have **everything** 
+needed for predictions in one place.
+
 ???+ question "Load the model"
 
     Create a new script or notebook which we will use to test the saved model.