Practical probabilistic programming with monads

Abstract

The machine learning community has recently shown a lot of interest in practical probabilistic programming systems that target the problem of Bayesian inference. Such systems come in different forms, but they all express probabilistic models as computational processes using syntax resembling programming languages. In the functional programming community monads are known to offer a convenient and elegant abstraction for programming with probability distributions, but their use is often limited to very simple inference problems. We show that it is possible to use the monad abstraction to construct probabilistic models for machine learning, while still offering good performance of inference in challenging models. We use a GADT as an underlying representation of a probability distribution and apply Sequential Monte Carlo-based methods to achieve efficient inference. We define a formal semantics via measure theory. We demonstrate a clean and elegant implementation that achieves performance comparable with Anglican, a stateof-the-art probabilistic programming system.

Cost analysis of nondeterministic probabilistic programs

“…generation of random values according to a predefined probability distribution, leads to the class of probabilistic programs [45]. Probabilistic programs are shown to be powerful models for a wide variety of applications, such as analysis of stochastic network protocols [40,65,88], machine learning applications [26,44,81,83], and robot planning [91,92], to name a few. There are also many probabilistic programming languages (such as Church [42], Anglican [93] and WebPPL [43]) and automated analysis of such programs is an active research area in formal methods and programming languages (see [1,16,18,22,37,66,67,74,96]).…”

Probabilistic Smart Contracts: Secure Randomness on the Blockchain

“…Probabilistic programs are very widely studied (e.g. see [9,[17][18][19][20][21]) and have many applications in different fields, such as machine learning [22][23][24][25], randomized algorithms [26], and analyzing stochastic networks [27][28][29]. Probability vs Non-determinism.…”

Deployable probabilistic programming

“…The need for integration between probabilistic programs and the surrounding software environment is well understood in the literature [7,51]. Probabilistic programming languages are often implemented as embedded domainspecific languages [11,42,51] and include a mechanism of calling functions from libraries of the host languages. Our work goes a step further in this direction: since the language of implementation of probabilistic models coincides with the host language, any library or user-defined function of the host language can be directly called from the probabilistic model, and model methods can be directly called from the host language.…”

“…Hence, efficiency of inference in general is affected by an efficient implementation of logSumExp (this can also be confirmed by profiling). To save on the cost of a differentiated call and speed up gradient computation, logSumExp is implemented as an elemental (lines [36][37][38][39][40][41][42][43]. The hand-coded gradient is supplied for logSumExp (lines 45-54) to make automatic differentiation work.…”