What’s the difference between a generative and discriminative model?

In machine learning, generative and discriminative models are two broad categories that differ in their approach to modeling and solving a problem.

1. Generative Models:
   • Generative models learn the joint probability distribution $P(X,Y)$ of the input features $X$ and the corresponding labels $Y$.
   • Once the joint distribution is learned, it can be used to generate new samples that resemble the training data.
   • Examples of generative models include Naive Bayes, Gaussian Mixture Models (GMM), Hidden Markov Models (HMM), and Generative Adversarial Networks (GANs).
2. Discriminative Models:
   • Discriminative models learn the conditional probability distribution $P(Y|X)$, i.e., the probability of labels given the input features.
   • These models directly learn the boundary between different classes or categories in the input space.
   • Discriminative models aim to directly model the decision boundary between classes rather than modeling the distribution of individual classes.
   • Examples of discriminative models include Logistic Regression, Support Vector Machines (SVM), Decision Trees, and Neural Networks (specifically when used for classification).

Key Differences:

• Objective: Generative models aim to understand the data distribution and generate new samples, while discriminative models focus on learning the decision boundary between classes.
• Usage: Generative models can be used for tasks such as generating new data samples, imputing missing values, or data augmentation. Discriminative models are typically used for classification or regression tasks.
• Complexity: Generative models often require modeling a more complex joint distribution $P(X,Y)$, which can make them computationally more demanding compared to discriminative models that directly model $P(Y|X)$.
• Robustness: Discriminative models can sometimes be more robust when the class distribution is imbalanced or when there’s a large amount of irrelevant features, as they focus directly on the decision boundary.

In an interview setting, it’s important to articulate these differences clearly and provide examples to demonstrate understanding.