Bayesian Estimation in Machine Learning

Bayesian estimation is a probabilistic approach in machine learning that incorporates prior knowledge into parameter estimation using Bayes' Theorem. It provides a systematic way to update beliefs as new data is observed.

Bayes' Theorem:

P(θX)=P(Xθ)P(θ)P(X)P(\theta | X) = \frac{P(X | \theta) P(\theta)}{P(X)}

where:

  • P(θX)P(\theta | X) is the posterior probability (updated belief after observing data).

  • P(Xθ)P(X | \theta) is the likelihood (probability of data given parameters).

  • P(θ)P(\theta) is the prior (initial belief about parameters).

  • P(X)P(X) is the evidence (normalizing factor).

Role of Bayesian Estimation in Machine Learning

  1. Parameter Estimation:

    • Unlike Maximum Likelihood Estimation (MLE), which only maximizes likelihood, Bayesian estimation balances prior knowledge with observed data.

    • Example: Estimating mean and variance of a Gaussian distribution.

  2. Regularization and Uncertainty Handling:

    • Bayesian methods prevent overfitting by incorporating prior distributions (e.g., Gaussian priors in Bayesian linear regression).

    • Provides uncertainty estimation, useful in medical diagnosis and risk prediction.

  3. Bayesian Learning Models:

    • Naïve Bayes Classifier: Uses Bayes’ rule for probabilistic classification.

    • Bayesian Neural Networks (BNNs): Introduces probabilistic weights to improve robustness.

Advantages:

  • Handles small datasets efficiently.

  • Provides probabilistic predictions rather than point estimates.

Bayesian estimation is widely used in classification, regression, reinforcement learning, and AI-driven decision-making where uncertainty plays a crucial role.

Post a Comment

0 Comments