Variational Inference
Variational inference turns the problem of inference into an optimization problem. Instead of sampling from the posterior distribution, it approximates the distribution by a simpler distribution and optimizes the parameters of this distribution to be as close as possible to the true posterior.
The steps involved are:
- Choose a Family of Distributions: Select a family of distributions parameterized by variational parameters.
- Define the Variational Objective: Typically, this is the Evidence Lower Bound (ELBO), which is optimized to make the approximate distribution close to the true posterior.
- Optimize the ELBO: Use gradient descent or other optimization techniques to find the best parameters.
Mathematically, the ELBO is defined as:
[Tex]ELBO=E_{q(z)} [\log p(x,z)− \log q(z)] [/Tex]
where q(z) is the approximate posterior, and p(x,z) is the joint probability of the observed data x and latent variables z.
In VAEs, variational inference is used to approximate the posterior distribution of latent variables given observed data, facilitating the generation of new, similar data points.
Approximate Inference in Bayesian Networks
Bayesian Networks (BNs) are powerful frameworks for modeling probabilistic relationships among variables. They are widely used in various fields such as artificial intelligence, bioinformatics, and decision analysis. However, exact inference in Bayesian Networks is often computationally impractical for large or complex networks due to the exponential growth of computational requirements. Approximate inference methods provide a feasible alternative, offering probabilistic estimates with significantly reduced computational costs.
This article explores the key concepts, methods, challenges, and applications of approximate inference in Bayesian Networks.
Table of Content
- Need for Approximate Inference
- Approximate Inference Techniques
- Monte Carlo Methods
- Variational Inference
- Loopy Belief Propagation
- Challenges in Approximate Inference
- Application Examples of Approximate Inference in Bayesian Networks
- Conclusion