论文标题
分类随机过程和可能性
Categorical Stochastic Processes and Likelihood
论文作者
论文摘要
在这项工作中，我们对概率建模和功能近似之间的关系进行类别理论观点。我们首先将功能组成的两个扩展定义为随机过程从属：一个基于ComOnad（Omega X-）下的Co -Kleisli类别，另一个基于具有律师理论的类别的参数化。我们展示了这些扩展与类别Stoch和其他Markov类别的关系。接下来，我们将PARA构造应用于参数化统计模型，并定义了一种组成这些模型的可能性函数的方法。我们以演示最大似然估计过程的证明为结论，从统计模型类别定义了对象对象的身份函数到学习者类别。可以在本文附带的代码上找到https://github.com/dshieble/categorical_stochastic_processes_and_likelihoods
In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood
