6.3 Visualizations for ML

Introduction

Visualization is essential for understanding model behavior, debugging performance issues, and communicating results. For LLMs, visualizations help interpret attention patterns, token distributions, and embedding spaces.

1. Decision Boundaries

Decision boundaries show how a classifier divides the feature space into class regions. For a binary classifier $ f: \mathbb{R}^2 \rightarrow \{0, 1\} $, the decision boundary is: $$\{x \in \mathbb{R}^2 : P(y=1|x) = 0.5\}$$

Interactive: Decision Boundary Visualization

Compare decision boundaries of different classifiers:

Classifier: k: {{kValue}}

Interpretation: Colors show predicted class regions

Accuracy: {{accuracy | number:1}}%

2. Confusion Matrix

The confusion matrix shows the performance of a classification model:

		Predicted
		Positive	Negative
Actual	Positive	TP (True Positive)	FN (False Negative)
Actual	Negative	FP (False Positive)	TN (True Negative)

Interactive: Confusion Matrix

Adjust the classification threshold and see how the confusion matrix changes:

Decision Threshold: {{threshold | number:2}} Class Imbalance: {{classBalance | number:1}}

Accuracy: {{confusionMetrics.accuracy | number:3}}

Precision: {{confusionMetrics.precision | number:3}}

Recall: {{confusionMetrics.recall | number:3}}

F1-Score: {{confusionMetrics.f1 | number:3}}

3. ROC Curve

The Receiver Operating Characteristic (ROC) curve plots True Positive Rate vs False Positive Rate: $$\text{TPR} = \frac{TP}{TP + FN}, \quad \text{FPR} = \frac{FP}{FP + TN}$$ The Area Under the Curve (AUC) measures overall performance: AUC = 1 is perfect, AUC = 0.5 is random.

Interactive: ROC Curve

See how model quality affects the ROC curve:

Model Quality:

AUC: {{aucValue | number:3}}

Interpretation: {{aucInterpretation}}

4. Learning Curves

Learning curves show how model performance changes with training data size. They help diagnose:

Underfitting: Both training and validation error are high
Overfitting: Large gap between training and validation error
Good Fit: Both errors are low and converge

Interactive: Learning Curves

Simulate different learning scenarios:

Scenario:

Diagnosis: {{learningDiagnosis}}

Recommendation: {{learningRecommendation}}

5. Attention Heatmap (for LLMs)

Attention mechanisms in transformers show which tokens the model focuses on. For query $ Q $, key $ K $, and value $ V $: $$\text{Attention}(Q, K, V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V$$ The attention weights $ \text{softmax}(QK^T/\sqrt{d_k}) $ can be visualized as a heatmap.

Interactive: Attention Pattern Visualization

Visualize how tokens attend to each other:

Attention Pattern:

Pattern: {{attentionDescription}}

6. Feature Importance

Feature importance shows which features contribute most to predictions. For tree-based models: $$\text{Importance}(f) = \sum_{t \in \text{splits on } f} \Delta \text{Impurity}_t \cdot n_t$$ where $ \Delta \text{Impurity}_t $ is the impurity reduction and $ n_t $ is the number of samples at node $ t $.

Interactive: Feature Importance

Compare feature importances across different models:

View Type: Models:

Top 3 Features: {{topFeatures}}

Explanation: Radar view normalizes each model's importances to its max for multi-model comparison.

Visualization Best Practices

Choose the Right Plot: Match visualization to the question you're answering
Use Color Wisely: Sequential for continuous, diverging for positive/negative, categorical for classes
Label Everything: Axes, legends, titles make plots self-explanatory
Show Uncertainty: Include confidence intervals, error bars when relevant
Interactive is Better: Allow users to explore data dynamically
Keep it Simple: Don't overcomplicate; clarity over complexity

Common Visualization Types

Visualization	Use Case	Key Insight
Scatter Plot	Relationships between variables	Correlation, clusters, outliers
Histogram	Distribution of single variable	Shape, center, spread, skewness
Box Plot	Compare distributions across groups	Median, quartiles, outliers
Heatmap	Matrix data, correlations	Patterns, clusters, relationships
Line Plot	Trends over time/sequence	Temporal patterns, convergence
Bar Chart	Compare quantities across categories	Rankings, comparisons