Task

Build an MLP classifier using the sklearn wine dataset, split data (80/20), scale data, perform hyperparameter optimization with cross-validation (cv=5) using GridSearchCV or RandomizedSearchCV for hidden_layer_sizes, alpha, and learning_rate_init, plot the optimization results using a seaborn relplot, train the final model with the best parameters, evaluate on the test set (accuracy), print the classification report, and plot the confusion matrix as a seaborn heatmap.

Load and split the data

Subtask:

Load the wine dataset from sklearn and split it into training (80%) and test (20%) sets.

Reasoning: Import the necessary dataset and split the data into training and testing sets as per the instructions.

from sklearn.datasets import load_wine
from sklearn.model_selection import train_test_split

# Load the dataset
wine = load_wine()
X = wine.data
y = wine.target

# Split the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42, stratify=y)

print("Data loaded and split successfully.")
print(f"Training data shape: {X_train.shape}")
print(f"Testing data shape: {X_test.shape}")

Data loaded and split successfully.
Training data shape: (142, 13)
Testing data shape: (36, 13)

Scale the data

Subtask:

Scale the training and test data using an appropriate scaler.

Reasoning: Import the necessary scaler, instantiate it, and scale both the training and test data.

from sklearn.preprocessing import StandardScaler

# Instantiate a StandardScaler object
scaler = StandardScaler()

# Fit the scaler to the training data and transform both training and testing data
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

print("Data scaled successfully.")
print(f"Scaled training data shape: {X_train_scaled.shape}")
print(f"Scaled testing data shape: {X_test_scaled.shape}")

Data scaled successfully.
Scaled training data shape: (142, 13)
Scaled testing data shape: (36, 13)

Define the model and hyperparameter space

Subtask:

Define the MLPClassifier model from sklearn and the search space for hyperparameter optimization, including hidden_layer_sizes, alpha, and learning_rate_init.

Reasoning: Import the necessary class and define the hyperparameter grid for the MLPClassifier.

from sklearn.neural_network import MLPClassifier

# Define the hyperparameter search space
param_grid = {
    'hidden_layer_sizes': [(50,), (100,), (50, 50), (100, 50)],
    'alpha': [0.0001, 0.001, 0.01, 0.1],
    'learning_rate_init': [0.001, 0.01, 0.1]
}

# Define the MLPClassifier model (with a fixed random state for reproducibility)
mlp = MLPClassifier(random_state=42, max_iter=1000)

print("MLPClassifier model and hyperparameter grid defined.")

MLPClassifier model and hyperparameter grid defined.

Hyperparameter optimization

Subtask:

Implement hyperparameter optimization using GridSearchCV or RandomizedSearchCV with cross-validation (cv=5) to find the best hyperparameters.

Reasoning: Implement hyperparameter optimization using GridSearchCV with cross-validation (cv=5) to find the best hyperparameters and store the best parameters and score.

from sklearn.model_selection import GridSearchCV

# Instantiate GridSearchCV
grid_search = GridSearchCV(mlp, param_grid, cv=5)

# Fit GridSearchCV to the scaled training data
grid_search.fit(X_train_scaled, y_train)

# Store the best hyperparameters
best_params = grid_search.best_params_

# Store the best cross-validation score
best_score = grid_search.best_score_

print("Hyperparameter optimization completed.")
print(f"Best parameters found: {best_params}")
print(f"Best cross-validation accuracy: {best_score:.4f}")

Hyperparameter optimization completed.
Best parameters found: {'alpha': 0.0001, 'hidden_layer_sizes': (50,), 'learning_rate_init': 0.01}
Best cross-validation accuracy: 0.9931

Plot optimization results

Subtask:

Plot the relationship between the hyperparameters and the cross-validation score using a seaborn relplot to visualize the results of the optimization.

Reasoning: Create a pandas DataFrame from the cv_results_ attribute of the grid_search object and prepare it for plotting by extracting relevant columns and creating a combined hyperparameter string.

import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt

# Create a DataFrame from cv_results_
cv_results_df = pd.DataFrame(grid_search.cv_results_)

# Extract relevant columns
cv_results_df = cv_results_df[['param_hidden_layer_sizes', 'param_alpha', 'param_learning_rate_init', 'mean_test_score']]

# Create a combined hyperparameter string
cv_results_df['hyperparameter_combination'] = cv_results_df.apply(lambda row: f"HL:{row['param_hidden_layer_sizes']}, A:{row['param_alpha']}, LR:{row['param_learning_rate_init']}", axis=1)

# Display the first few rows of the prepared DataFrame
display(cv_results_df.head())

	param_hidden_layer_sizes	param_alpha	param_learning_rate_init	mean_test_score	hyperparameter_combination
0	(50,)	0.0001	0.001	0.978818	HL:(50,), A:0.0001, LR:0.001
1	(50,)	0.0001	0.010	0.993103	HL:(50,), A:0.0001, LR:0.01
2	(50,)	0.0001	0.100	0.993103	HL:(50,), A:0.0001, LR:0.1
3	(100,)	0.0001	0.001	0.985961	HL:(100,), A:0.0001, LR:0.001
4	(100,)	0.0001	0.010	0.985961	HL:(100,), A:0.0001, LR:0.01

Reasoning: Use seaborn's relplot to visualize the relationship between the hyperparameter combinations and the mean test score.

# Plot the relationship between hyperparameters and cross-validation score using relplot
plt.figure(figsize=(15, 8)) # Adjust figure size for readability
sns.relplot(data=cv_results_df, x='hyperparameter_combination', y='mean_test_score', kind='line', height=6, aspect=2)
plt.xticks(rotation=90) # Rotate x-axis labels for better readability
plt.title('Cross-Validation Score vs. Hyperparameter Combinations')
plt.xlabel('Hyperparameter Combination (Hidden Layers, Alpha, Learning Rate)')
plt.ylabel('Mean Test Score')
plt.tight_layout() # Adjust layout to prevent labels overlapping
plt.show()

<Figure size 1500x800 with 0 Axes>

Train the final model

Subtask:

Train the MLPClassifier with the best hyperparameters found in the previous step using the entire training set.

Reasoning: Instantiate a new MLPClassifier model with the best hyperparameters and train it on the entire scaled training data.

from sklearn.neural_network import MLPClassifier

# Instantiate the final model with the best hyperparameters
final_model = MLPClassifier(hidden_layer_sizes=best_params['hidden_layer_sizes'],
                            alpha=best_params['alpha'],
                            learning_rate_init=best_params['learning_rate_init'],
                            random_state=42,
                            max_iter=1000)

# Fit the final model to the entire scaled training data
final_model.fit(X_train_scaled, y_train)

print("Final model trained successfully with the best hyperparameters.")

Final model trained successfully with the best hyperparameters.

Evaluate the model

Subtask:

Evaluate the trained model on the test set by calculating accuracy.

Reasoning: Use the trained model to make predictions on the test set and calculate the accuracy.

from sklearn.metrics import accuracy_score

# Make predictions on the scaled test data
y_pred = final_model.predict(X_test_scaled)

# Calculate the accuracy of the model
accuracy = accuracy_score(y_test, y_pred)

# Print the calculated accuracy
print(f"Accuracy on the test set: {accuracy:.4f}")

Accuracy on the test set: 0.9444

Print classification report

Subtask:

Print the full classification report showing metrics for all three classes.

Reasoning: Import the classification_report function and print the classification report using the true and predicted labels.

from sklearn.metrics import classification_report

# Print the classification report
print(classification_report(y_test, y_pred))

              precision    recall  f1-score   support

           0       0.92      1.00      0.96        12
           1       0.93      0.93      0.93        14
           2       1.00      0.90      0.95        10

    accuracy                           0.94        36
   macro avg       0.95      0.94      0.95        36
weighted avg       0.95      0.94      0.94        36

Plot confusion matrix

Subtask:

Plot the 3x3 confusion matrix as a heatmap using seaborn to visualize the performance of the classifier in detail.

Reasoning: Import necessary libraries and calculate the confusion matrix, then create and display the heatmap.

from sklearn.metrics import confusion_matrix
import seaborn as sns
import matplotlib.pyplot as plt

# Calculate the confusion matrix
cm = confusion_matrix(y_test, y_pred)

# Create a heatmap of the confusion matrix
plt.figure(figsize=(8, 6))
sns.heatmap(cm, annot=True, fmt='d', cmap='Blues', xticklabels=['Class 0', 'Class 1', 'Class 2'], yticklabels=['Class 0', 'Class 1', 'Class 2'])
plt.xlabel('Predicted Label')
plt.ylabel('True Label')
plt.title('Confusion Matrix')
plt.show()

Summary:

Data Analysis Key Findings

• The wine dataset was successfully loaded and split into training (142 samples) and testing (36 samples) sets with stratification to maintain class distribution.
• The training and test data were successfully scaled using StandardScaler.
• Hyperparameter optimization using GridSearchCV with 5-fold cross-validation was performed on the training data to tune hidden_layer_sizes, alpha, and learning_rate_init.
• The best hyperparameters found were {'alpha': 0.0001, 'hidden_layer_sizes': (50,), 'learning_rate_init': 0.01}.
• The best cross-validation accuracy achieved during the optimization was approximately 0.9931.
• A seaborn relplot visualizing the mean cross-validation score for each hyperparameter combination was generated.
• The final MLPClassifier model was trained using the entire scaled training set with the best hyperparameters.
• The accuracy of the trained model on the scaled test set is 0.9444.
• The classification report shows good performance across all three classes on the test set, with high precision, recall, and f1-scores.
• The confusion matrix heatmap visualizes the model's predictions versus the true labels on the test set, showing the distribution of correct and incorrect classifications.

Insights or Next Steps

• The MLP classifier achieved high accuracy on the test set after hyperparameter tuning, indicating good generalization performance on this dataset.
• Further analysis could involve exploring a wider range of hyperparameters or different network architectures to potentially improve performance or reduce model complexity, although the current results are already very strong.

Prompt

Construye un regresor MLP en sklearn usando un dataset de regresión de sklearn, divide los datos en conjuntos de entrenamiento (80%) y prueba (20%), escala los datos apropiadamente, implementa optimización de hiperparámetros usando GridSearchCV o RandomizedSearchCV con validación cruzada (cv=5), encuentra los mejores hiperparámetros para el MLP (incluyendo hidden_layer_sizes, alpha, learning_rate_init), grafica la mejor combinación de hiperparámetros en un relplot de seaborn mostrando la relación entre los parámetros y el score de validación cruzada, entrena el modelo final con los mejores parámetros, evalúa en el conjunto de prueba calculando MSE, RMSE, MAE y R², y grafica un scatterplot de los valores observados vs predichos para el conjunto de prueba.

Task

Implement a MLP regressor in sklearn using a sklearn regression dataset, split the data into training (80%) and test (20%) sets, scale the data appropriately, implement hyperparameter optimization using GridSearchCV or RandomizedSearchCV with cross-validation (cv=5), find the best hyperparameters for the MLP (including hidden_layer_sizes, alpha, learning_rate_init), plot the best hyperparameter combination in a seaborn relplot showing the relationship between parameters and cross-validation score, train the final model with the best parameters, evaluate on the test set calculating MSE, RMSE, MAE, and R², and plot a scatterplot of observed vs predicted values for the test set.

Cargar y dividir los datos

Subtask:

Cargar un conjunto de datos de regresión de sklearn (por ejemplo, load_boston, load_diabetes) y dividirlo en conjuntos de entrenamiento (80%) y prueba (20%).

Reasoning: Import the necessary dataset and split the data into training and testing sets.

from sklearn.datasets import load_diabetes
from sklearn.model_selection import train_test_split

# Load the dataset
diabetes = load_diabetes()
X = diabetes.data
y = diabetes.target

# Split the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

print("Data loaded and split successfully.")
print(f"Training data shape: {X_train.shape}")
print(f"Testing data shape: {X_test.shape}")

Data loaded and split successfully.
Training data shape: (353, 10)
Testing data shape: (89, 10)

Escalar los datos

Subtask:

Escalar los datos de entrenamiento y prueba usando un escalador apropiado (por ejemplo, StandardScaler).

Reasoning: Import the necessary scaler, instantiate it, and scale both the training and test data.

from sklearn.preprocessing import StandardScaler

# Instantiate a StandardScaler object
scaler = StandardScaler()

# Fit the scaler to the training data and transform both training and testing data
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

print("Data scaled successfully.")
print(f"Scaled training data shape: {X_train_scaled.shape}")
print(f"Scaled testing data shape: {X_test_scaled.shape}")

Data scaled successfully.
Scaled training data shape: (353, 10)
Scaled testing data shape: (89, 10)

Definir el modelo y el espacio de hiperparámetros

Subtask:

Definir el modelo MLPRegressor de sklearn y el espacio de búsqueda para la optimización de hiperparámetros (incluyendo hidden_layer_sizes, alpha, learning_rate_init).

Reasoning: Import the necessary class and define the hyperparameter grid for the MLPRegressor.

from sklearn.neural_network import MLPRegressor

# Define the hyperparameter search space
param_grid = {
    'hidden_layer_sizes': [(50,), (100,), (50, 50), (100, 50)],
    'alpha': [0.0001, 0.001, 0.01, 0.1],
    'learning_rate_init': [0.001, 0.01, 0.1]
}

# Define the MLPRegressor model (with a fixed random state for reproducibility)
mlp = MLPRegressor(random_state=42, max_iter=1000)

print("MLPRegressor model and hyperparameter grid defined.")

MLPRegressor model and hyperparameter grid defined.

Optimización de hiperparámetros

Subtask:

Implementar la optimización de hiperparámetros usando GridSearchCV o RandomizedSearchCV con validación cruzada (cv=5) para encontrar la mejor combinación de hiperparámetros.

Reasoning: Implement hyperparameter optimization using GridSearchCV with cross-validation (cv=5) to find the best hyperparameters and store the best parameters and score.

from sklearn.model_selection import GridSearchCV

# Instantiate GridSearchCV
grid_search = GridSearchCV(mlp, param_grid, cv=5, scoring='neg_mean_squared_error')

# Fit GridSearchCV to the scaled training data
grid_search.fit(X_train_scaled, y_train)

# Store the best hyperparameters
best_params = grid_search.best_params_

# Store the best cross-validation score (which is the mean of the test scores across folds)
# Note: GridSearchCV with scoring='neg_mean_squared_error' returns negative MSE.
# To get the actual MSE or a positive score for interpretability, we can negate the best_score.
best_score = grid_search.best_score_

print("Hyperparameter optimization completed.")
print(f"Best parameters found: {best_params}")
# Print the best cross-validation score (negated to show positive MSE)
print(f"Best cross-validation negative mean squared error: {best_score:.4f}")

/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(

Hyperparameter optimization completed.
Best parameters found: {'alpha': 0.0001, 'hidden_layer_sizes': (50, 50), 'learning_rate_init': 0.001}
Best cross-validation negative mean squared error: -3355.7790

/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(

Graficar los resultados de la optimización

Subtask:

Graficar la relación entre los hiperparámetros y el score de validación cruzada usando un relplot de seaborn para visualizar los resultados de la optimización.

Reasoning: Create a pandas DataFrame from the cv_results_ attribute of the grid_search object and prepare it for plotting by extracting relevant columns and creating a combined hyperparameter string.

import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt

# Create a DataFrame from cv_results_
cv_results_df = pd.DataFrame(grid_search.cv_results_)

# Extract relevant columns
cv_results_df = cv_results_df[['param_hidden_layer_sizes', 'param_alpha', 'param_learning_rate_init', 'mean_test_score']]

# Create a combined hyperparameter string
cv_results_df['hyperparameter_combination'] = cv_results_df.apply(lambda row: f"HL:{row['param_hidden_layer_sizes']}, A:{row['param_alpha']}, LR:{row['param_learning_rate_init']}", axis=1)

# Display the first few rows of the prepared DataFrame
display(cv_results_df.head())

	param_hidden_layer_sizes	param_alpha	param_learning_rate_init	mean_test_score	hyperparameter_combination
0	(50,)	0.0001	0.001	-4050.374697	HL:(50,), A:0.0001, LR:0.001
1	(50,)	0.0001	0.010	-3784.831913	HL:(50,), A:0.0001, LR:0.01
2	(50,)	0.0001	0.100	-4219.399957	HL:(50,), A:0.0001, LR:0.1
3	(100,)	0.0001	0.001	-3428.543741	HL:(100,), A:0.0001, LR:0.001
4	(100,)	0.0001	0.010	-3726.358704	HL:(100,), A:0.0001, LR:0.01

Reasoning: Use seaborn's relplot to visualize the relationship between the hyperparameter combinations and the mean test score.

# Plot the relationship between hyperparameters and cross-validation score using relplot
plt.figure(figsize=(15, 8)) # Adjust figure size for readability
sns.relplot(data=cv_results_df, x='hyperparameter_combination', y='mean_test_score', kind='line', height=6, aspect=2)
plt.xticks(rotation=90) # Rotate x-axis labels for better readability
plt.title('Cross-Validation Negative Mean Squared Error vs. Hyperparameter Combinations')
plt.xlabel('Hyperparameter Combination (Hidden Layers, Alpha, Learning Rate)')
plt.ylabel('Negative Mean Squared Error')
plt.tight_layout() # Adjust layout to prevent labels overlapping
plt.show()

<Figure size 1500x800 with 0 Axes>

Entrenar el modelo final

Subtask:

Entrenar el modelo MLPRegressor con los mejores hiperparámetros encontrados en el paso anterior usando todo el conjunto de entrenamiento.

Reasoning: Instantiate a new MLPRegressor model with the best hyperparameters and train it on the entire scaled training data.

from sklearn.neural_network import MLPRegressor

# Instantiate the final model with the best hyperparameters
final_model = MLPRegressor(hidden_layer_sizes=best_params['hidden_layer_sizes'],
                           alpha=best_params['alpha'],
                           learning_rate_init=best_params['learning_rate_init'],
                           random_state=42,
                           max_iter=1000)

# Fit the final model to the entire scaled training data
final_model.fit(X_train_scaled, y_train)

print("Final model trained successfully with the best hyperparameters.")

Final model trained successfully with the best hyperparameters.

/usr/local/lib/python3.12/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1000) reached and the optimization hasn't converged yet.
  warnings.warn(

Evaluar el modelo

Subtask:

Evaluar el modelo entrenado en el conjunto de prueba calculando métricas de regresión como MSE, RMSE, MAE y R².

Reasoning: Import necessary regression metrics, make predictions on the test set, calculate MSE, RMSE, MAE, and R², and print the results.

import numpy as np
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score

# Make predictions on the scaled test data
y_pred = final_model.predict(X_test_scaled)

# Calculate regression metrics
mse = mean_squared_error(y_test, y_pred)
rmse = np.sqrt(mse)
mae = mean_absolute_error(y_test, y_pred)
r2 = r2_score(y_test, y_pred)

# Print the calculated metrics
print(f"Mean Squared Error (MSE): {mse:.4f}")
print(f"Root Mean Squared Error (RMSE): {rmse:.4f}")
print(f"Mean Absolute Error (MAE): {mae:.4f}")
print(f"R-squared (R²): {r2:.4f}")

Mean Squared Error (MSE): 2830.0078
Root Mean Squared Error (RMSE): 53.1978
Mean Absolute Error (MAE): 41.6917
R-squared (R²): 0.4658

Graficar valores observados vs predichos

Subtask:

Graficar un scatterplot de los valores observados vs predichos para el conjunto de prueba para visualizar el rendimiento del modelo.

Reasoning: Create a scatter plot of observed vs predicted values and add a diagonal line for the ideal scenario.

import matplotlib.pyplot as plt

# Create a scatter plot of observed vs predicted values
plt.figure(figsize=(8, 6))
plt.scatter(y_test, y_pred, alpha=0.5)

# Add a diagonal line representing the ideal scenario
plt.plot([y_test.min(), y_test.max()], [y_test.min(), y_test.max()], 'k--', lw=2)

# Add labels and title
plt.xlabel("Observed Values")
plt.ylabel("Predicted Values")
plt.title("Observed vs. Predicted Values on Test Set")

# Add grid
plt.grid(True)

# Display the plot
plt.show()

Summary:

Data Analysis Key Findings

• The dataset was split into 80% for training (353 samples, 10 features) and 20% for testing (89 samples, 10 features).
• The data was successfully scaled using StandardScaler.
• Hyperparameter optimization using GridSearchCV with 5-fold cross-validation identified the best parameters as {'alpha': 0.0001, 'hidden_layer_sizes': (50, 50), 'learning_rate_init': 0.001}.
• The best cross-validation negative mean squared error achieved was approximately -3355.78.
• The final model trained with the best parameters achieved the following performance metrics on the test set: MSE = 2830.01, RMSE = 53.20, MAE = 41.69, and R² = 0.4658.

Insights or Next Steps

• The R² value of 0.4658 suggests that the model explains less than half of the variance in the target variable, indicating potential for improvement.
• Further steps could involve exploring a wider range of hyperparameters, increasing max_iter to address the observed convergence warnings, or trying more complex network architectures to potentially improve the model's performance.