论文标题
贝叶斯编程的仿制单和懒惰结构
Affine Monads and Lazy Structures for Bayesian Programming
论文作者
论文摘要
我们表明，流和懒惰的数据结构是使用无限维贝叶斯方法（例如泊松过程，高斯流程，跳跃过程，dirichlet流程和beta过程）进行编程的自然习惯。受合成概率理论发展的启发的关键语义思想是与两个单独的单独的单独的概率合作：一种支持懒惰的概率仿真，并提供了一个交换性的，是措施的合理性，非承诺的措施单元。 （仿射意味着$ t（1）\ cong 1 $。）我们表明，从确定性的角度来看，分离很重要，并且最近的准空间空间模型支持这两个单子。 为了对这些示例进行贝叶斯的推断，我们引入了专门适合懒惰的新推论方法。通过参考大都会杂货法的方法，它们被证明是正确的。我们的理论发展被实施为Haskell库Lazyppl。
We show that streams and lazy data structures are a natural idiom for programming with infinite-dimensional Bayesian methods such as Poisson processes, Gaussian processes, jump processes, Dirichlet processes, and Beta processes. The crucial semantic idea, inspired by developments in synthetic probability theory, is to work with two separate monads: an affine monad of probability, which supports laziness, and a commutative, non-affine monad of measures, which does not. (Affine means that $T(1)\cong 1$.) We show that the separation is important from a decidability perspective, and that the recent model of quasi-Borel spaces supports these two monads. To perform Bayesian inference with these examples, we introduce new inference methods that are specially adapted to laziness; they are proven correct by reference to the Metropolis-Hastings-Green method. Our theoretical development is implemented as a Haskell library, LazyPPL.
