Approximate inference and Bayesian decision theory

解决决策问题是一个分两步进行的过程：首先进行推理，得到近似的后验分布，然后利用该后验分布来求解决策问题。以这种方式分解贝叶斯决策理论的好处在于，这两个步骤可以独立实施。然而，在现实中，推理步骤只能以近似的方式执行；因此，第二步将取决于第一步中的近似的属性。因此，这两个步骤变得相互耦合。本课题旨在研究贝叶斯决策理论背景下的近似推理。我们希望能够将贝叶斯决策理论与成熟的近似推理方案结合起来应用；定性和定量地识别由于进行近似推理而导致的决策中的偏差；并开发出减轻这些偏差的技术。

Solving a decision problem is a two-step procedure: firstly, one performs inference to obtain the approximate posterior distribution, which, secondly, is used to solve said decision problem. The beauty of breaking down Bayesian decision theory in this way, it is usually lectured, is that the two steps can be implemented independently. In reality, however, the inference step can only be performed in an approximate manner; as a consequence, the second step will depend on properties of the approximation in the first step. hence the two steps become coupled. We propose to investigate this coupling.The project aims to research approximate inference in the context of Bayesian decision theory. We hope to enable the application of Bayesian decision theory in combination with well-established approximate-inference schemes; to qualitatively and quantitatively identify biases in decisions due to performing inference approximately; and to develop techniques that alleviate these biases.