This chapter provides an introduction to variational inference, and reviews its applications to a range of geophysical problems, including petrophysical inversion, travel time tomography, and full-waveform inversion. We demonstrate that variational inference is an efficient and scalable method which can be...
This chapter provides an introduction to variational inference, and reviews its applications to a range of geophysical problems, including petrophysical inversion, travel time tomography, and full-waveform inversion. We demonstrate that variational inference is an efficient and scalable method which can be...
Introduction (1) Problem of Probabilistic Inference H : set of hidden nodes E : set of evidence nodes P(E) : likelihood Provide satisfactory solution to inference and learning cases where time or space complexity is unacceptable Introduction (2) Variational Method provide approach to the design of...
我们现在已经得到了关于潜在变量Z的优化分布的表达形式: 其中: 所以现在我们可以得到Z的期望: 另外对于Z还值得一提的是,我们从其优化分布的表达式中可以看出,各个Z的组成部分之间还是相互耦合的,所以需要一个迭代的求解方式。 解决了关于Z的一些遗留的问题,我们可以继续讨论如何求解余下的参数。同样的...
An Introduction to Variational Methods (5.1) 在这篇文章中,我引用Bishop书中的一个例子,来简单介绍一下Variational Methods的应用。想要更详细地理解这个例子,可以参考Bishop的书Pattern Recongnition and Machine Learning的第十章。 这个例子应用于一个混合高斯分布,我们先来看一看这个混合高斯分布的图模型,见图3,...
Variational Inference for LDALDA的变分推理 Gaussian Graphical Models Graphical Models Exponential Families and Variational Inference - Martin J. Wainwright and Michael I. Jordan - 2008 Graphical Models in a Nutshell Introduction to graphical modelling 因果推断和因果模型-Causal inference and Causal graphical...
This article gives a basic introduction to the principles of Bayesian inference in a machine learning context, with an emphasis on the importance of marginalisation for dealing with uncertainty. We begin by illustrating concepts via a simple regression t
Introduction Understanding phenotype-to-genotype relationships is one of the most fundamental problems of current biological research with profound translational implications for questions ranging from human healthcare to biotechnological crop improvement. Genome-wide association studies (GWAS) statistically associa...
Retrosynthesis is a crucial task in drug discovery and organic synthesis, where artificial intelligence (AI) is increasingly employed to expedite the process. However, existing approaches employ token-by-token decoding methods to translate target molecul
An Introduction to Variational Methods (5.3) 从之前的文章中,我们已经得到了所有需要求解的参数的优化分布的形式,分别为: 但是,我们从这些分布的表达式中(参见之前的文章),可以发现这些式子并不能够直接求解。这是因为各个参数之间相互耦合,从而导致得到的不是一个直接可以得到的解,所以我们需要进行迭代求解,...