Formally justified and modular Bayesian inference for probabilistic programs

Probabilistic modelling offers a simple and coherent framework to describe the real world in the face of uncertainty. Furthermore, by applying Bayes' rule it is possible to use probabilistic models to make inferences about the state of the world from partial observations. While traditionally probabilistic models were constructed on paper, more recently the approach of probabilistic programming enables users to write the models in executable languages resembling computer programs and to freely mix them with deterministic code. It has long been recognised that the semantics of programming languages is complicated and the intuitive understanding that programmers have is often inaccurate, resulting in difficult to understand bugs and unexpected program behaviours. Programming languages are therefore studied in a rigorous way using formal languages with mathematically defined semantics. Traditionally formal semantics of probabilistic programs are defined using exact inference results, but in practice exact Bayesian inference is not tractable and approximate methods are used instead, posing a question of how the results of these algorithms relate to the exact results. Correctness of such approximate methods is usually argued somewhat less rigorously, without reference to a formal semantics. In this dissertation we formally develop denotational semantics for probabilistic programs that correspond to popular sampling algorithms often used in practice. The semantics is defined for an expressive typed lambda calculus with higher-order functions and inductive types, extended with probabilistic effects for sampling and conditioning, allowing continuous distributions and unbounded likelihoods. It makes crucial use of the recently developed formalism of quasi-Borel spaces to bring all these elements together. We provide semantics corresponding to several variants of Markov chain Monte Carlo and Sequential Monte Carlo methods and formally prove a notion of correctness for these algorithms in the context of probabilistic programming. We also show that the semantic construction can be directly mapped to an implementation using established functional programming abstractions called monad transformers. We develop a compact Haskell library for probabilistic programming closely corresponding to the semantic construction, giving users a high level of assurance in the correctness of the implementation. We also demonstrate on a collection of benchmarks that the library offers performance competitive with existing systems of similar scope. An important property of our construction, both the semantics and the implementation, is the high degree of modularity it offers. All the inference algorithms are constructed by combining small building blocks in a setup where the type system ensures correctness of compositions. We show that with basic building blocks corresponding to vanilla Metropolis-Hastings and Sequential Monte Carlo we can implement more advanced algorithms known in the literature, such as Resample-Move Sequential Monte Carlo, Particle Marginal Metropolis-Hastings, and Sequential Monte Carlo squared. These implementations are very concise, reducing the effort required to produce them and the scope for bugs. On top of that, our modular construction enables in some cases deterministic testing of randomised inference algorithms, further increasing reliability of the implementation.Engineering and Physical Sciences Research Council, Cambridge Trust, Cambridge-Tuebingen programm

Comparative analysis of React, Next and Gatsby programming frameworks for creating SPA applications

This article presents a performance analysis of some of the most popular development frameworks based on the React library. The aim of the study was to show which of the technologies used to create the visual parts of web applications is the most efficient. The research was conducted with the use of 3 applications representing the same research content but based on the above-mentioned frontend technologies. In order to evaluate the performance, web browser development tools and React library were used, which proved that vanilla React is the most efficient for rendering pages with a lot of data

Deep Probabilistic Surrogate Networks for Universal Simulator Approximation

We present a framework for automatically structuring and training fast, approximate, deep neural surrogates of existing stochastic simulators. Unlike traditional approaches to surrogate modeling, our surrogates retain the interpretable structure of the reference simulators. The particular way we achieve this allows us to replace the reference simulator with the surrogate when undertaking amortized inference in the probabilistic programming sense. The fidelity and speed of our surrogates allow for not only faster "forward" stochastic simulation but also for accurate and substantially faster inference. We support these claims via experiments that involve a commercial composite-materials curing simulator. Employing our surrogate modeling technique makes inference an order of magnitude faster, opening up the possibility of doing simulator-based, non-invasive, just-in-time parts quality testing; in this case inferring safety-critical latent internal temperature profiles of composite materials undergoing curing from surface temperature profile measurements

Video Killed the HD-Map: Predicting Driving Behavior Directly From Drone Images

The development of algorithms that learn behavioral driving models using human demonstrations has led to increasingly realistic simulations. In general, such models learn to jointly predict trajectories for all controlled agents by exploiting road context information such as drivable lanes obtained from manually annotated high-definition (HD) maps. Recent studies show that these models can greatly benefit from increasing the amount of human data available for training. However, the manual annotation of HD maps which is necessary for every new location puts a bottleneck on efficiently scaling up human traffic datasets. We propose a drone birdview image-based map (DBM) representation that requires minimal annotation and provides rich road context information. We evaluate multi-agent trajectory prediction using the DBM by incorporating it into a differentiable driving simulator as an image-texture-based differentiable rendering module. Our results demonstrate competitive multi-agent trajectory prediction performance when using our DBM representation as compared to models trained with rasterized HD maps

Amortized Rejection Sampling in Universal Probabilistic Programming

Existing approaches to amortized inference in probabilistic programs with unbounded loops can produce estimators with infinite variance. An instance of this is importance sampling inference in programs that explicitly include rejection sampling as part of the user-programmed generative procedure. In this paper we develop a new and efficient amortized importance sampling estimator. We prove finite variance of our estimator and empirically demonstrate our method's correctness and efficiency compared to existing alternatives on generative programs containing rejection sampling loops and discuss how to implement our method in a generic probabilistic programming framework

Fabular: regression formulas as probabilistic programming

Regression formulas are a domain-specific language adopted by several R packages for describing an important and useful class of statistical models: hierarchical linear regressions. Formulas are succinct, expressive, and clearly popular, so are they a useful addition to probabilistic programming languages? And what do they mean? We propose a core calculus of hierarchical linear regression, in which regression coefficients are themselves defined by nested regressions (unlike in R). We explain how our calculus captures the essence of the formula DSL found in R. We describe the design and implementation of Fabular, a version of the Tabular schema-driven probabilistic programming language, enriched with formulas based on our regression calculus. To the best of our knowledge, this is the first formal description of the core ideas of R's formula notation, the first development of a calculus of regression formulas, and the first demonstration of the benefits of composing regression formulas and latent variables in a probabilistic programming language.Adam Ścibior received travel support from the DARPA PPAML programme. Marcin Szymczak was supported by Microsoft Research through its PhD Scholarship Programme.This is the author accepted manuscript. The final version is available from the Association of Computer Machinery via http://dx.doi.org/10.1145/2837614.283765