自动生成julia(贝叶斯)推理算法代码

ForneyLab.jl is a Julia package for automatic generation of (Bayesian) inference algorithms. Given a probabilistic model, ForneyLab generates efficient Julia code for message-passing based inference. It uses the model structure to generate an algorithm that consists of a sequence of local computations on a Forney-style factor graph (FFG) representation of the model. For an excellent introduction to message passing and FFGs, see The Factor Graph Approach to Model-Based Signal Processing by Loeliger et al. (2007). Moreover, for a comprehensive overview of the underlying principles behind this tool, see A Factor Graph Approach to Automated Design of Bayesian Signal Processing Algorithms by Cox et. al. (2018).

We designed ForneyLab with a focus on flexible and modular modeling of time-series data. ForneyLab enables a user to:

• Conveniently specify a probabilistic model;
• Automatically generate an efficient inference algorithm;
• Compile the inference algorithm to executable Julia code.

The current version supports belief propagation (sum-product message passing), variational message passing and expectation propagation.

The ForneyLab project page provides more background on ForneyLab as well as pointers to related literature and talks. For a practical introduction, have a look at the demos.

相关论文：

Abstract:

Accurate evaluation of Bayesian model evidence for a given data set is a fundamental problem in model development. Since evidence evaluations are usually intractable, in practice variational free energy (VFE) minimization provides an attractive alternative, as the VFE is an upper bound on negative model log-evidence (NLE). In order to improve tractability of the VFE, it is common to manipulate the constraints in the search space for the posterior distribution of the latent variables. Unfortunately, constraint manipulation may also lead to a less accurate estimate of the NLE.

Thus, constraint manipulation implies an engineering trade-off between tractability and accuracy of model evidence estimation. In this paper, we develop a unifying account of constraint manipulation for variational inference in models that can be represented by a (Forney-style) factor graph, for which we identify the Bethe Free Energy as an approximation to the VFE. We derive well-known message passing algorithms from first principles, as the result of minimizing the constrained Bethe Free Energy (BFE). The proposed method supports evaluation of the BFE in factor graphs for model scoring and development of new message passing-based inference algorithms that potentially improve evidence estimation accuracy.

Keywords: Bayesian inference; Bethe free energy; factor graphs; message passing; variational free energy; variational inference; variational message passing