Variational Inference¶
Variational inference is a family of approximate inference techniques for computing posterior distributions in probabilistic models where exact inference is intractable. The core idea is to optimize an approximate distribution to be close (in KL divergence) to the true posterior while maintaining a tractable form.
The key technical contribution is the Evidence Lower Bound (ELBO), which provides a principled objective for optimization. For a probabilistic model with parameters \(\theta\) and latent variables \(z\), the ELBO is:
The first term is the KL divergence between the approximate posterior \(q_\phi(z|x)\) and the true posterior, and the second term is the marginal likelihood (intractable). Minimizing the KL divergence is equivalent to maximizing the ELBO.
Key papers¶
- AIGC Survey — covers the historical development of variational methods within the broader AI generation landscape
Related topics¶
- Generative Models — variational inference powers many generative modeling approaches
- Probabilistic Graphical Models — classical domain where variational inference is applied
- Deep learning — modern variational methods combine inference with deep neural networks
Notes¶
The shift from mean-field variational inference with hand-designed families to learned approximate posteriors with neural networks (as in VAEs) was transformative for deep generative modeling. Modern variational methods remain central to probabilistic machine learning and enable efficient inference in complex high-dimensional models.