Explain the difference between discriminative and generative models.

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Discriminative and generative models are two fundamental approaches in machine learning, particularly in classification tasks:

1. Discriminative Models:
   These models learn the decision boundary between classes. They model the conditional probability $P(y|x)$, which means they focus on predicting the label $y$ given the input $x$. Discriminative models don't try to understand how the data was generated—just how to distinguish between classes.

• Examples: Logistic Regression, Support Vector Machines (SVM), Neural Networks, Random Forests.

• Use Case: Best when the goal is accurate classification.

2. Generative Models:
   Generative models learn the joint probability distribution $P(x, y)$, or often $P(x|y)$ and $P(y)$. They try to model how the data is generated for each class, allowing them to generate new samples similar to the training data. They can also perform classification by applying Bayes’ theorem:

$$P(y|x) = \frac{P(x|y)P(y)}{P(x)}$$

• Examples: Naive Bayes, Hidden Markov Models, Gaussian Mixture Models, Generative Adversarial Networks (GANs).

• Use Case: Useful when you need to generate data, handle missing data, or model underlying data structure.

Key Difference:

• Discriminative = Predicts labels

• Generative = Models data distribution and can generate new data

In summary, discriminative models are usually more accurate for classification, while generative models offer broader capabilities, including synthesis and unsupervised learning.

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