Probabilistic computability and choice

Probabilistic Computability and Choice

We study the computational power of randomized computations on infinite objects, such as real numbers. In particular, we introduce the concept of a Las Vegas computable multi-valued function, which is a function that can be computed on a probabilistic Turing machine that receives a random binary sequence as auxiliary input. The machine can take advantage of this random sequence, but it always h...

Computable Functional Analysis and Probabilistic Computability

Computability, inference and modeling in probabilistic programming

We investigate the class of computable probability distributions and explore the fundamental limitations of using this class to describe and compute conditional distributions. In addition to proving the existence of noncomputable conditional distributions, and thus ruling out the possibility of generic probabilistic inference algorithms (even inefficient ones), we highlight some positive result...

Probabilistic programs, computability, and de Finetti measures

The complexity of probabilistic models, especially those involving recursion, has far exceeded the representational capacity of graphical models. Functional programming languages with probabilistic choice operators have recently been proposed as universal representations for statistical modeling (e.g., IBAL [Pfe01], λ◦ [PPT08], Church [GMR08]). The conditional independence structure of a probab...

Notions of Probabilistic Computability on Represented Spaces

We define and compare several probabilistic notions of computability for mappings from represented spaces (that are equipped with a measure or outer measure) into computable metric spaces. We thereby generalize definitions by [Ko 1991] and Parker (see [Parker 2003, Parker 2005, Parker 2006]), and furthermore introduce the new notion of computability in the mean. Some results employ a notion of ...