笔者在入门VAE(Variational Autoencoder)的时候,发现几乎所有博客都会提到变分推断(Variational Inference)和ELBO(证据下界,Evidence Lower Bound),但是总是搞不明白具体是什么意思,方法是什么来源;以及经常被突然出现的Jensen不等式放缩唬住。笔者在学习之后有了大概的了解,遂写此文,兼作学习笔记
The ideas here extend the popular stochastic variational inference paradigm to a far larger family. The second topic of the thesis focuses on the theoretical properties of variational inference. Specifically, we discuss several variants of the variational approximation and show that some of these have...
确定近似中的一些方法对于大数据来说更为适用,拉普拉斯近似 (Laplace Approximation) 和变分推断 (Variational Inference) 就是确定近似方法 变分推断将推断问题转换为一个优化问题,使用一个简单分布来拟合复杂的分布变分推断将推断问题转换为一个优化问题,使用一个简单分布来拟合复杂的分布 简单的分布近似会带来更大的偏差...
It does so by minimizing a Monte Carlo approximation of the exponentiated upper bound, L = exp{n · CUBOn(λ)}. 4 Algorithm 1: χ-divergence variational inference (CHIVI) Input: Data x, Model p(x, z), Variational family q(z; λ). Output: Variational parameters λ. Initialize λ ...
Approximate solutions arise in variational inference by restricting the family of densities which can be used as a proxy for the exact conditional density. Typically, the mean field variational family is used where independence is assumed across the factors. Thus by specifying conjugate priors, approx...
As in variational inference, the bound in Eq. 4 is ex- act when r(λ | z; φ) matches the variational posterior q(λ | z; θ). From this perspective, we can view r as a recur- sive variational approximation. It is a model for the poste- rior q of the mean-field parameters ...
In variational inference (VI), coordinate-ascent and gradient-based approaches are two major types of algorithms for approximating difficult-to-compute probability densities. In real-world implementations of complex models, Monte Carlo methods are widely used to estimate expectations in coordinate-ascent ...
Active inference: A process theory 2017, Neural Computation Weight uncertainty in neural networks 2015, 32nd International Conference on Machine Learning, ICML 2015 The free-energy principle: A unified brain theory? 2010, Nature Reviews Neuroscience Predictive coding under the free-energy principle 2009...
Variational Inference 模型参数是\alpha \ \eta,求解目标是\theta\ \beta\ z,由于\theta\ \beta\ z之间的耦合性,需要使用变分假设,假设所有的隐藏变量都是通过各自的独立分布形成的(mean field theory),这样就去掉了隐藏变量之间的耦合关系。隐藏变量的概率分布为:p(\theta,\beta, z | w, \alpha, \eta) ...
The approximation is carried out with respect to the Kullback-Leibler functional DKL,minν∈ADKL(ν‖μ). Mean-field variational inference (MFVI) which corresponds to the case where A is a family of factorized probability measures (see section 2), has been applied to approximate the ...