Approximate inference and Bayesian decision theory

求解决策问题是一个两步的过程：首先，进行推理以获得近似的后验分布，然后使用该后验分布来求解所述决策问题。以这种方式分解贝叶斯决策理论的美妙之处在于，这两个步骤可以独立实现。然而，在现实中，推理步骤只能以近似的方式进行；因此，第二步将取决于第一步近似的性质。因此，这两个步骤是耦合的。我们建议对这种耦合进行研究。该项目旨在研究贝叶斯决策理论背景下的近似推理。我们希望将贝叶斯决策理论与成熟的近似推理方案相结合；定性和定量地识别由于执行近似推理而导致的决策偏差；并开发减轻这些偏见的技术。

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.