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In machine learning, "metrics to monitor during training and testing" refer to the specific performance measurements or evaluation criteria used to assess the quality and effectiveness of a machine learning model. These metrics are crucial for understanding how well a model is learning from the data, making predictions, and generalizing to unseen examples. Monitoring these metrics helps you fine-tune your model, select the best model, and ensure it meets the desired objectives.

Here are some common metrics used during training and testing phases in machine learning:

1. Accuracy: This is the most straightforward metric and measures the fraction of correctly classified instances out of the total. It's suitable for balanced datasets but may not be the best choice when dealing with imbalanced datasets.

2. Precision: Precision is the ratio of true positives to the total predicted positives. It measures the model's ability to avoid false positives. It's important in applications where false positives are costly.

3. Recall (Sensitivity or True Positive Rate): Recall is the ratio of true positives to the total actual positives. It measures the model's ability to identify all relevant instances. It's essential in applications where false negatives are costly.

4. F1-Score: The F1-score is the harmonic mean of precision and recall. It balances precision and recall, making it useful when you need to consider both false positives and false negatives.

5. Area Under the Receiver Operating Characteristic Curve (AUC-ROC): ROC curve measures the trade-off between true positive rate (recall) and false positive rate as you adjust the model's decision threshold. AUC-ROC quantifies the overall performance of the model and is especially useful for binary classification problems.

6. Area Under the Precision-Recall Curve (AUC-PR): PR curve also evaluates the trade-off between precision and recall but focuses more on the positive class. AUC-PR is useful when dealing with imbalanced datasets.

7. Mean Absolute Error (MAE): MAE measures the average absolute difference between the predicted and actual values in regression problems. It's easy to interpret but less sensitive to outliers.

8. Mean Squared Error (MSE): MSE measures the average squared difference between the predicted and actual values in regression problems. It penalizes larger errors more than MAE and is sensitive to outliers.

9. Root Mean Squared Error (RMSE): RMSE is the square root of MSE and provides a measure of the error in the same units as the target variable.

10. R-squared (Coefficient of Determination): R-squared quantifies the proportion of variance explained by the model. It ranges from 0 to 1, where higher values indicate a better fit.

11. Log-Loss (Logarithmic Loss): Log-loss is commonly used in binary and multiclass classification tasks to measure the quality of predicted probabilities. It penalizes models for being overconfident or underconfident.

The choice of metrics depends on the specific problem you're addressing and the goals of your machine learning project. It's often a good practice to use multiple metrics to get a comprehensive understanding of your model's performance.

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Plot 2D (two features) map of probability distributions for a binary classification problem using a synthetic dataset for Naive Bayes.  Code:
         
         
       Output:    
         

In the script, we have:

1. It creates a grid of points in a 2D space using np.meshgrid. These grid points are evenly spaced across the x and y axes, creating a dense grid covering the entire 2D space.

2. The Gaussian Naive Bayes classifier (nb_classifier) is trained on some example data points (X and y). These example data points are generated using random values in the script but can be replaced with your own dataset.

3. The script calculates class probabilities for each point on the grid using the trained classifier. Specifically, it calculates the probability that each point belongs to class 1. These calculated probabilities are stored in the probs variable.

4. The dots are colored based on their class labels. Specifically:

   • Dots that are colored in red represent data points that belong to class 1.
   • Dots that are colored in blue represent data points that belong to class 0.

     The script uses the c parameter in the plt.scatter function to specify the colors for each data point based on their class labels (y values). The color mapping is chosen to be a red-to-blue colormap (cmap=plt.cm.RdBu), where red represents class 1 and blue represents class 0.

   • Here's the relevant line of code where the colors are specified: :

     plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.RdBu, edgecolor='k')  
                     

     In this line, X[:, 0] and X[:, 1] are the feature values for the x and y axes, y contains the class labels (0 or 1), and cmap=plt.cm.RdBu sets the color mapping. As a result, the dots on the plot are colored according to their class labels to help you visually distinguish between the two classes in your dataset.

   • Dots are assigned to class 1 if the sum of their feature values (feature 1 and feature 2) is greater than zero.
   • Dots are assigned to class 0 if the sum of their feature values is less than or equal to zero.
   • Here's the line of code where this rule is applied:

     y = (X[:, 0] + X[:, 1] > 0).astype(int)
     
                     

   In this line, X[:, 0] and X[:, 1] are the feature values, and y is assigned 1 for data points where X[:, 0] + X[:, 1] > 0 and 0 otherwise.

5. Finally, the script creates a heatmap using plt.contourf to visualize the class 1 probabilities. The heatmap color represents the probability value at each point on the grid.
6. To provide context and show the actual data distribution, the script scatters the example data points (X and y) on top of the heatmap. The color of each dot corresponds to the class label (0 or 1), allowing you to see how the data points are distributed within the probability distribution map.

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