Notes

visualization

5 min read

Data Visualization for Modelling

Definition

The use of graphical representations to explore data distributions, relationships, model diagnostics, and results during the modelling workflow.

Intuition

Humans process visual patterns far faster than numeric tables. Visualisation accelerates EDA, exposes model failure modes (e.g., residuals clustering by a feature), and communicates results to non-technical stakeholders. The right chart type depends on what you want to compare or reveal.

Formal Description

Chart Selection Guide

GoalChart type
Distribution of one numeric variableHistogram, KDE, box plot
Distribution of one categorical variableBar chart
Relationship between two numeric variablesScatter plot
Relationship between numeric and categoricalBox plot, violin plot, strip plot
Correlation among many variablesCorrelation heatmap
Change over timeLine plot
Proportion of a wholeStacked bar, pie (sparingly)
Model calibrationCalibration curve
Classification performanceROC curve, precision–recall curve, confusion matrix
Regression diagnosticsResiduals vs fitted, Q–Q plot

Distribution Plots

import matplotlib.pyplot as plt
import seaborn as sns
 
# Histogram + KDE
fig, axes = plt.subplots(1, 2, figsize=(12, 4))
sns.histplot(df['age'], kde=True, ax=axes[0])
sns.boxplot(x='target', y='age', data=df, ax=axes[1])
plt.tight_layout()

Q–Q plot to check normality:

from scipy.stats import probplot
probplot(df['residuals'], plot=plt)
plt.title('Q–Q Plot of Residuals')

Deviations from the diagonal indicate non-normality (heavy tails, skewness).

Correlation Heatmap

corr = df[num_cols].corr()
mask = np.triu(np.ones_like(corr, dtype=bool))  # upper triangle
 
sns.heatmap(corr, mask=mask, cmap='coolwarm', vmin=-1, vmax=1,
            annot=True, fmt='.2f', square=True)
plt.title('Feature Correlation Matrix')

Scatter Plots with Regression Line

sns.regplot(x='age', y='claim_amount', data=df, scatter_kws={'alpha': 0.3})
# Or: pairplot for multiple features
sns.pairplot(df[num_cols + ['target']], hue='target', corner=True)

Classification Diagnostics

from sklearn.metrics import RocCurveDisplay, PrecisionRecallDisplay, ConfusionMatrixDisplay
 
# ROC curve
RocCurveDisplay.from_estimator(model, X_test, y_test)
 
# Precision-Recall curve (better for imbalanced data)
PrecisionRecallDisplay.from_estimator(model, X_test, y_test)
 
# Confusion matrix
ConfusionMatrixDisplay.from_estimator(model, X_test, y_test, cmap='Blues')

Regression Diagnostics

y_pred = model.predict(X_test)
residuals = y_test - y_pred
 
fig, axes = plt.subplots(1, 2, figsize=(12, 5))
 
# Residuals vs fitted
axes[0].scatter(y_pred, residuals, alpha=0.3)
axes[0].axhline(0, color='red', linestyle='--')
axes[0].set_xlabel('Fitted values'); axes[0].set_ylabel('Residuals')
axes[0].set_title('Residuals vs Fitted')
 
# Residuals distribution
sns.histplot(residuals, kde=True, ax=axes[1])
axes[1].set_title('Residual Distribution')

A random scatter around 0 in the residuals-vs-fitted plot indicates a good fit. Patterns suggest heteroscedasticity or a missing feature.

Calibration Plots

from sklearn.calibration import CalibrationDisplay
CalibrationDisplay.from_estimator(model, X_test, y_test, n_bins=10)

A well-calibrated model lies on the diagonal: if it predicts 0.7 probability, about 70% of such cases are positive.

Feature Importance Visualisation

import pandas as pd
 
importance = pd.Series(model.feature_importances_, index=feature_names)
importance.sort_values().tail(20).plot(kind='barh', figsize=(8, 8))
plt.title('Top 20 Feature Importances')

Learning Curves

Learning curves plot training and validation performance as a function of training set size — the primary visual tool for diagnosing the bias-variance tradeoff.

from sklearn.model_selection import LearningCurveDisplay
 
LearningCurveDisplay.from_estimator(
    model, X_train, y_train,
    train_sizes=np.linspace(0.1, 1.0, 10),
    scoring='roc_auc',
    cv=5,
    n_jobs=-1
)
plt.title('Learning Curve')

Interpretation:

  • High bias (underfitting): both training and validation scores are low and converge to a similar low value. Adding more data won’t help — increase model complexity.
  • High variance (overfitting): training score is high, validation score is much lower, and a gap persists. Adding more data may help; also try regularisation.
  • Good fit: training and validation scores are close and both high.

Embedding Visualisation (t-SNE / UMAP)

High-dimensional embeddings (e.g., from neural network layers, sentence transformers, or feature matrices) can be projected to 2-D for visual inspection.

from sklearn.manifold import TSNE
import umap
import matplotlib.pyplot as plt
 
# t-SNE (better for local cluster structure)
reducer = TSNE(n_components=2, perplexity=30, random_state=42, init='pca')
Z = reducer.fit_transform(X)  # X: (n_samples, d)
 
# UMAP (faster, preserves global structure better)
reducer = umap.UMAP(n_components=2, random_state=42)
Z = reducer.fit_transform(X)
 
# Plot coloured by label
plt.figure(figsize=(8, 6))
scatter = plt.scatter(Z[:, 0], Z[:, 1], c=y, cmap='tab10', alpha=0.6, s=10)
plt.colorbar(scatter, label='Class')
plt.title('UMAP Embedding')
plt.tight_layout()

Use cases: checking whether classes are linearly separable, visualising cluster quality, debugging representations before a downstream task. Caveat: distances in t-SNE output are not interpretable; only cluster membership is meaningful.

SHAP Summary Plot

SHAP (SHapley Additive exPlanations) summary plots show feature impact across the entire dataset — a global explanation built from local attributions.

import shap
 
explainer = shap.TreeExplainer(model)   # or shap.Explainer(model, X_train)
shap_values = explainer.shap_values(X_test)
 
# Beeswarm plot: feature importance + direction of effect
shap.summary_plot(shap_values, X_test, feature_names=feature_names)
 
# Bar chart: mean absolute SHAP values (magnitude only)
shap.summary_plot(shap_values, X_test, feature_names=feature_names, plot_type='bar')

Each dot represents one prediction; colour indicates feature value (red = high). Points to the right increase the prediction; points to the left decrease it.

See PDP, ICE, and ALE for marginal effect alternatives.

Interactive Visualisation with Plotly

import plotly.express as px
 
fig = px.scatter(df, x='age', y='claim_amount', color='target',
                 hover_data=['policy_id'], opacity=0.4)
fig.show()

Plotly is preferred for exploratory reports and dashboards; matplotlib/seaborn for publication-quality static figures.

Applications

  • Identifying that residuals increase with fitted value → heteroscedasticity → consider log-transforming target.
  • Showing stakeholders that the model is well-calibrated at a steering committee.
  • Spotting a bimodal age distribution → investigate whether two distinct customer segments should be modelled separately.

Trade-offs

  • Interactive visualisations (Plotly, Bokeh) are better for exploration but harder to embed in PDFs; use matplotlib for reports.
  • Pair plots are — intractable for many features; use correlation heatmap or PCA visualisation instead.

References

  • Tufte, E. R. (2001). The Visual Display of Quantitative Information (2nd ed.). Graphics Press.
  • Wickham, H. (2010). “A Layered Grammar of Graphics.” Journal of Computational and Graphical Statistics.
  • Lundberg & Lee (2017). “A Unified Approach to Interpreting Model Predictions.” NeurIPS. (SHAP)

Graph View

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