Gaussian Mixture Models in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Gaussian Mixture Model Components

What does each component in a Gaussian Mixture Model (GMM) represent?

A A neural network layer used for feature extraction

B A decision boundary separating classes in the dataset

C A single Gaussian distribution representing a cluster in the data

D A single data point used as a centroid

💡 Hint

Think about how GMM models data distribution using simpler parts.

Each component in a GMM is a Gaussian distribution that models one cluster or group in the data. The overall model is a weighted sum of these Gaussians.

❓ Predict Output

intermediate

Output of GMM Prediction Probabilities

What is the output of the following Python code using sklearn's GaussianMixture?

ML Python

from sklearn.mixture import GaussianMixture
import numpy as np

X = np.array([[0], [1], [2], [3]])
gmm = GaussianMixture(n_components=2, random_state=0)
gmm.fit(X)
probs = gmm.predict_proba([[1.5]])
print(probs)

A [[0.5 0.5]]

B [[0.3 0.7]]

C [[0.7 0.3]]

D Raises a ValueError due to input shape

💡 Hint

Predict_proba returns the probability of the sample belonging to each component.

The output shows the probabilities that the input point belongs to each Gaussian component. The exact values depend on the fitted model but here the point is closer to the second component, so higher probability is for component 1 (index 1).

❓ Model Choice

advanced

Choosing Number of Components in GMM

You want to cluster data with unknown groups using GMM. Which method helps select the best number of components?

A Always use 2 components for simplicity

B Pick the number of components equal to the number of data points

C Use the mean squared error between data points and cluster centers

D Use the Bayesian Information Criterion (BIC) to compare models with different components

💡 Hint

Think about a criterion that balances model fit and complexity.

BIC helps select the number of components by penalizing model complexity while rewarding better fit. Lower BIC means a better model choice.

❓ Hyperparameter

advanced

Effect of Covariance Type in GMM

What is the effect of setting the covariance_type parameter to 'diag' in a GaussianMixture model?

A Each component has its own diagonal covariance matrix, allowing different variances per feature but no covariance

B All components share the same full covariance matrix

C Covariance matrices are fixed to identity matrices

D Covariance matrices are scalar multiples of the identity matrix

💡 Hint

Diagonal covariance means no correlation between features within each component.

Setting covariance_type='diag' means each Gaussian component has its own covariance matrix but only the diagonal elements are non-zero, modeling variance per feature independently.

❓ Metrics

expert

Evaluating GMM Clustering Quality

Which metric is most appropriate to evaluate the quality of clusters found by a Gaussian Mixture Model when true labels are unknown?

A Silhouette score measuring how similar an object is to its own cluster compared to other clusters

B Accuracy score comparing predicted labels to true labels

C Mean squared error between data points and cluster centers

D Log loss computed from predicted probabilities and true labels

💡 Hint

Think about a metric that works without knowing true labels.

Silhouette score measures cluster cohesion and separation without needing true labels, making it suitable for unsupervised clustering evaluation.