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:
where:
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is the posterior probability (updated belief after observing data).
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is the likelihood (probability of data given parameters).
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is the prior (initial belief about parameters).
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is the evidence (normalizing factor).
Role of Bayesian Estimation in Machine Learning
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Parameter Estimation:
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Unlike Maximum Likelihood Estimation (MLE), which only maximizes likelihood, Bayesian estimation balances prior knowledge with observed data.
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Example: Estimating mean and variance of a Gaussian distribution.
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Regularization and Uncertainty Handling:
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Bayesian methods prevent overfitting by incorporating prior distributions (e.g., Gaussian priors in Bayesian linear regression).
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Provides uncertainty estimation, useful in medical diagnosis and risk prediction.
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Bayesian Learning Models:
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Naïve Bayes Classifier: Uses Bayes’ rule for probabilistic classification.
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Bayesian Neural Networks (BNNs): Introduces probabilistic weights to improve robustness.
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Advantages:
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Handles small datasets efficiently.
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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.
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