Probabilistic Programming System Research Articles

The application of probabilistic programming in statistics

This article focuses on three aspects of Probabilistic reasoning systems for applications, including Predict future events, Infer the cause of events, and learn from past events to better predict future events. In addition, the article explains that the data will become more accurate as the number of samples increases, and finally, the article describes the application of Turing-Completed Systems in statistics, a kind of probabilistic programming system. This article starts with a soccer competition as an example, then will explain the concepts in depth behind the example.

Curve Fitting Algorithm of Functional Radiation-Response Data Using Bayesian Hierarchical Gaussian Process Regression Model

We present a nonparametric Bayesian hierarchical (NBH) model and develop a variational approximation (VA) algorithm for the curve fitting of the functional radiation response data. The NBH model is based on a Bayesian hierarchical (BH) model with a Gaussian-Inverse Wishart process (G-IWP) prior, which simultaneously smooths multiple functional observations and estimates mean-covariance functions. We use the automatic differentiation variational inference (ADVI) algorithm with a Gaussian distribution as the variational distribution for approximating the posterior distribution of parameters of interest, which is applicable to a wide class of probabilistic models and can also be implemented in Stan (a probabilistic programming system). Using the NBH model and the Gaussian ADVI algorithm, we fit a dataset for the semiconductor obtained from the radiation response map (RRM) of South Korea.

ZhuSuan: design and implementation of differentiable probabilistic programming libraries

Probabilistic models provide a set of powerful tools to deal with uncertainty that is pervasive in machine learning applications. Probabilistic programming utilizes computer programs to represent probabilistic models, and it supports the functions of sampling as well as probabilistic inference conditioned on arbitrary observations. Traditionally, the dependency relationship in probabilistic programming is mainly linear or generalized linear, which serves as the basis of many successful models and inference algorithms. However, such linearity also limits the expressiveness and flexibility of probabilistic programs. Differentiable probabilistic programming allows probabilistic programs to have nonlinear dependency under a proper parameterization form (e.g., neural networks) and can learn unknown parameters from data via gradient-based methods. This programming paradigm is easy to extend, largely avoids the tedious model selection process, and makes the deployment of probabilistic models possible in an end-to-end manner. This article presents ZhuSuan, an open-source library for differentiable probabilistic programming. Taking ZhuSuan as an example, we discuss the design and implementation of differentiable probabilistic programming systems.

Мethod of automated development of solutions for special cases in flight

The article develops a method of automated decision making in the framework of the creation of DSS air traffic controller. The method of automated decision-making for special cases in flight is being developed as one of the stages of information technology for the creation of decision support system for air traffic controllers. This is necessary to help decide on the option of terminating the flight in the event of a special case in flight on the example of engine failure on the aircraft. The developed method involves the use of probabilistic programming technology. It includes: construction of a probabilistic hierarchical model of emergency based on the Bayesian network taking into account the factors influencing the decision-making process, creating a sample of examples for learning the model to improve future situations models on examples using the Bayesian learning paradigm, the choice of inference algorithm to obtain a probabilistic conclusion. The proposed method is implemented in the probabilistic programming system Figaro, which is free and available under an open source license. The program code is written in Scala. The set of training data was formed based on the results of the investigation of aviation accidents and catastrophes and contained fifty-two cases of forced landing at the aerodrome and on the site with different consequences. The learning process was learning the parameters of the model on the data and was performed on thirty- six examples. Other cases (sixteen) were used to test the prediction quality of the created model. The Bayesian learning paradigm is used to teach the model, which does not require a special learning algorithm and is performed using the inference algorithm. The Metropolis-Hastings approximation algorithm is used as the derivation algorithm. The developed method showed high accuracy of forecasting. The error between the actual result and the estimate obtained using the Bayesian network was 10%. Further research will be aimed at developing information technology for the creation of DSS air traffic controller for special cases in flight.

Using SWISH to Realize Interactive Web-based Tutorials for Logic-based Languages

AbstractProgramming environments have evolved from purely text based to using graphical user interfaces, and now we see a move toward web-based interfaces, such as Jupyter. Web-based interfaces allow for the creation of interactive documents that consist of text and programs, as well as their output. The output can be rendered using web technology as, for example, text, tables, charts, or graphs. This approach is particularly suitable for capturing data analysis workflows and creating interactive educational material. This article describes SWISH, a web front-end for Prolog that consists of a web server implemented in SWI-Prolog and a client web application written in JavaScript. SWISH provides a web server where multiple users can manipulate and run the same material, and it can be adapted to support Prolog extensions. In this article we describe the architecture of SWISH, and describe two case studies of extensions of Prolog, namely Probabilistic Logic Programming and Logic Production System, which have used SWISH to provide tutorial sites.

Bayesian synthesis of probabilistic programs for automatic data modeling

We present new techniques for automatically constructing probabilistic programs for data analysis, interpretation, and prediction. These techniques work with probabilistic domain-specific data modeling languages that capture key properties of a broad class of data generating processes, using Bayesian inference to synthesize probabilistic programs in these modeling languages given observed data. We provide a precise formulation of Bayesian synthesis for automatic data modeling that identifies sufficient conditions for the resulting synthesis procedure to be sound. We also derive a general class of synthesis algorithms for domain-specific languages specified by probabilistic context-free grammars and establish the soundness of our approach for these languages. We apply the techniques to automatically synthesize probabilistic programs for time series data and multivariate tabular data. We show how to analyze the structure of the synthesized programs to compute, for key qualitative properties of interest, the probability that the underlying data generating process exhibits each of these properties. Second, we translate probabilistic programs in the domain-specific language into probabilistic programs in Venture, a general-purpose probabilistic programming system. The translated Venture programs are then executed to obtain predictions of new time series data and new multivariate data records. Experimental results show that our techniques can accurately infer qualitative structure in multiple real-world data sets and outperform standard data analysis methods in forecasting and predicting new data.

Functional programming for modular Bayesian inference

We present an architectural design of a library for Bayesian modelling and inference in modern functional programming languages. The novel aspect of our approach are modular implementations of existing state-of-the-art inference algorithms. Our design relies on three inherently functional features: higher-order functions, inductive data-types, and support for either type-classes or an expressive module system. We provide a performant Haskell implementation of this architecture, demonstrating that high-level and modular probabilistic programming can be added as a library in sufficiently expressive languages. We review the core abstractions in this architecture: inference representations, inference transformations, and inference representation transformers. We then implement concrete instances of these abstractions, counterparts to particle filters and Metropolis-Hastings samplers, which form the basic building blocks of our library. By composing these building blocks we obtain state-of-the-art inference algorithms: Resample-Move Sequential Monte Carlo, Particle Marginal Metropolis-Hastings, and Sequential Monte Carlo Squared. We evaluate our implementation against existing probabilistic programming systems and find it is already competitively performant, although we conjecture that existing functional programming optimisation techniques could reduce the overhead associated with the abstractions we use. We show that our modular design enables deterministic testing of inherently stochastic Monte Carlo algorithms. Finally, we demonstrate using OCaml that an expressive module system can also implement our design.

Incremental inference for probabilistic programs

We present a novel approach for approximate sampling in probabilistic programs based on incremental inference. The key idea is to adapt the samples for a program P into samples for a program Q , thereby avoiding the expensive sampling computation for program Q . To enable incremental inference in probabilistic programming, our work: (i) introduces the concept of a trace translator which adapts samples from P into samples of Q , (ii) phrases this translation approach in the context of sequential Monte Carlo (SMC), which gives theoretical guarantees that the adapted samples converge to the distribution induced by Q , and (iii) shows how to obtain a concrete trace translator by establishing a correspondence between the random choices of the two probabilistic programs. We implemented our approach in two different probabilistic programming systems and showed that, compared to methods that sample the program Q from scratch, incremental inference can lead to orders of magnitude increase in efficiency, depending on how closely related P and Q are.

Symbolic conditioning of arrays in probabilistic programs

Probabilistic programming systems make machine learning more modular by automating inference . Recent work by Shan and Ramsey makes inference more modular by automating conditioning . Their technique uses a symbolic program transformation that treats conditioning generally via the measure-theoretic notion of disintegration . This technique, however, is limited to conditioning a single scalar variable. As a step towards modular inference for realistic machine learning applications, we have extended the disintegration algorithm to symbolically condition arrays in probabilistic programs. The extended algorithm implements lifted disintegration , where repetition is treated symbolically and without unrolling loops. The technique uses a language of index variables for tracking expressions at various array levels. We find that the method works well for arbitrarily-sized arrays of independent random choices, with the conditioning step taking time linear in the number of indices needed to select an element.

Automatic differentiation variational inference

Probabilistic modeling is iterative. A scientist posits a simple model, fits it to her data, refines it according to her analysis, and repeats. However, fitting complex models to large data is a bottleneck in this process. Deriving algorithms for new models can be both mathematically and computationally challenging, which makes it difficult to efficiently cycle through the steps. To this end, we develop automatic differentiation variational inference (ADVI). Using our method, the scientist only provides a probabilistic model and a dataset, nothing else. ADVI automatically derives an efficient variational inference algorithm, freeing the scientist to refine and explore many models. ADVI supports a broad class of models--no conjugacy assumptions are required. We study ADVI across ten modern probabilistic models and apply it to a dataset with millions of observations. We deploy ADVI as part of Stan, a probabilistic programming system.

Practical probabilistic programming with monads

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 state-of-the-art probabilistic programming system.