VARIATIONAL BAYESIAN METHODS Meaning and
Definition
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Variational Bayesian methods, also known as Variational Inference, are computational techniques used to approximate complex and often intractable posterior probability distributions. In Bayesian inference, the goal is to estimate the posterior distribution of model parameters given some observed data. However, in many cases, the exact posterior distribution cannot be analytically computed, especially with complicated models.
Variational Bayesian methods offer an alternative approach to approximate the posterior distribution by formulating it as an optimization problem. The idea is to find the closest possible approximation to the true posterior distribution by minimizing a divergence metric, typically the Kullback-Leibler divergence, between the true distribution and an approximating distribution from a predefined family of distributions. This family of distributions is often chosen to be more tractable, such as the mean-field family where the variables are assumed to be independent.
The optimization problem is solved iteratively using techniques like coordinate ascent or stochastic gradient descent. At each iteration, the approximating distribution is refined, moving closer to the true posterior distribution. By iteratively updating the approximation, a variational Bayesian method can find an increasingly accurate representation of the posterior distribution.
Variational Bayesian methods have gained popularity in machine learning and statistics due to their ability to handle high-dimensional data and complex models efficiently. They offer a trade-off between computational complexity and accuracy and are widely used in applications like probabilistic graphical models, latent variable models, and Bayesian neural networks.
