Probabilistic programming languages (PPLs) are powerful modelling tools which allow to formalise our knowledge about the world and reason about its inherent uncertainty. Inference methods used in PPL can be computationally costly due to significant time burden and/or storage requirements; or they can lack theoretical guarantees of convergence and accuracy when applied to large scale graphical models. To this end, we present the Universal Marginaliser (UM), a novel method for amortised inference, in PPL. We show how combining samples drawn from the original probabilistic program prior with an appropriate augmentation method allows us to train one neural network to approximate any of the corresponding conditional marginal distributions, with any separation into latent and observed variables, and thus amortise the cost of inference. Finally, we benchmark the method on multiple probabilistic programs, in Pyro, with different model structure.
Probabilistic programming is a powerful abstraction for statistical machine learning. Applying static analysis methods to probabilistic programs could serve to optimize the learning process, automatically verify properties of models, and improve the programming interface for users. This field of static analysis for probabilistic programming (SAPP) is young and unorganized, consisting of a constellation of techniques with various goals and limitations. The primary aim of this work is to synthesize the major contributions of the SAPP field within an organizing structure and context. We provide technical background for static analysis and probabilistic programming, suggest a functional taxonomy for probabilistic programming languages, and analyze the applicability of major ideas in the SAPP field. We conclude that, while current static analysis techniques for probabilistic programs have practical limitations, there are a number of future directions with high potential to improve the state of statistical machine learning.
Compute and memory constraints have historically prevented traffic simulation software users from fully utilizing the predictive models underlying them. When calibrating car-following models, particularly, accommodations have included 1) using sensitivity analysis to limit the number of parameters to be calibrated, and 2) identifying only one set of parameter values using data collected from multiple car-following instances across multiple drivers. Shortcuts are further motivated by insufficient data set sizes, for which a driver may have too few instances to fully account for the variation in their driving behavior. In this paper, we demonstrate that recent technological advances can enable transportation researchers and engineers to overcome these constraints and produce calibration results that 1) outperform industry standard approaches, and 2) allow for a unique set of parameters to be estimated for each driver in a data set, even given a small amount of data. We propose a novel calibration procedure for car-following models based on Bayesian machine learning and probabilistic programming, and apply it to real-world data from a naturalistic driving study. We also discuss how this combination of mathematical and software tools can offer additional benefits such as more informative model validation and the incorporation of true-to-data uncertainty into simulation traces.
Probabilistic programming is the idea of writing models from statistics and machine learning using program notations and reasoning about these models using generic inference engines. Recently its combination with deep learning has been explored intensely, leading to the development of deep probabilistic programming languages such as Pyro. At the core of this development lie inference engines based on stochastic variational inference algorithms. When asked to find information about the posterior distribution of a model written in such a language, these algorithms convert this posterior-inference query into an optimisation problem and solve it approximately by gradient ascent. In this paper, we analyse one of the most fundamental and versatile variational inference algorithms, called score estimator, using tools from denotational semantics and program analysis. We formally express what this algorithm does on models denoted by programs, and expose implicit assumptions made by the algorithm. The violation of these assumptions may lead to an undefined optimisation objective or the loss of convergence guarantee of the optimisation process. We then describe rules for proving these assumptions, which can be automated by static program analyses. Some of our rules use nontrivial facts from continuous mathematics, and let us replace requirements about integrals in the assumptions, by conditions involving differentiation or boundedness, which are much easier to prove automatically. Following our general methodology, we have developed a static program analysis for Pyro that aims at discharging the assumption about what we call model-guide support match. Applied to the eight representative model-guide pairs from the Pyro webpage, our analysis finds a bug in one of these cases, reveals a non-standard use of an inference engine in another, and shows the assumptions are met in the remaining cases.
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.
Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and further applying this identified surrogate to uncertainty analysis remains to be very challenging. A deep learning approach is presented to provide predictions based on limited and noisy data. To address noise perturbation, the Bayesian learning method that naturally facilitates an automatic updating mechanism is considered to quantify and propagate model uncertainties into predictive quantities. Specifically, hierarchical Bayesian modeling (HBM) is first adopted to describe model uncertainties, which allows the prior assumption to be less subjective, while also makes the proposed surrogate more robust. Next, the Bayesian inference is seamlessly integrated into the DL framework, which in turn supports probabilistic programming by yielding a probability distribution of the quantities of interest rather than their point estimates. Variational inference (VI) is implemented for the posterior distribution analysis where the intractable marginalization of the likelihood function over parameter space is framed in an optimization format, and stochastic gradient descent method is applied to solve this optimization problem. Finally, Monte Carlo simulation is used to obtain an unbiased estimator in the predictive phase of Bayesian inference, where the proposed Bayesian deep learning (BDL) scheme is able to offer confidence bounds for the output estimation by analyzing propagated uncertainties. The effectiveness of Bayesian shrinkage is demonstrated in improving predictive performance using contaminated data, and various examples are provided to illustrate concepts, methodologies, and algorithms of this proposed BDL modeling technique.
We consider probabilistic programming for birth-death models of evolution and introduce a new widely-applicable inference method that combines an extension of the alive particle filter (APF) with automatic Rao-Blackwellization via delayed sampling. Birth-death models of evolution are an important family of phylogenetic models of the diversification processes that lead to evolutionary trees. Probabilistic programming languages (PPLs) give phylogeneticists a new and exciting tool: their models can be implemented as probabilistic programs with just a basic knowledge of programming. The general inference methods in PPLs reduce the need for external experts, allow quick prototyping and testing, and accelerate the development and deployment of new models. We show how these birth-death models can be implemented as simple programs in existing PPLs, and demonstrate the usefulness of the proposed inference method for such models. For the popular BiSSE model the method yields an increase of the effective sample size and the conditional acceptance rate by a factor of 30 in comparison with a standard bootstrap particle filter. Although concentrating on phylogenetics, the extended APF is a general inference method that shows its strength in situations where particles are often assigned zero weight. In the case when the weights are always positive, the extra cost of using the APF rather than the bootstrap particle filter is negligible, making our method a suitable drop-in replacement for the bootstrap particle filter in probabilistic programming inference.
Probabilistic programming languages (PPLs) are receiving widespread attention for performing Bayesian inference in complex generative models. However, applications to science remain limited because of the impracticability of rewriting complex scientific simulators in a PPL, the computational cost of inference, and the lack of scalable implementations. To address these, we present a novel PPL framework that couples directly to existing scientific simulators through a cross-platform probabilistic execution protocol and provides Markov chain Monte Carlo (MCMC) and deep-learning-based inference compilation (IC) engines for tractable inference. To guide IC inference, we perform distributed training of a dynamic 3DCNN--LSTM architecture with a PyTorch-MPI-based framework on 1,024 32-core CPU nodes of the Cori supercomputer with a global minibatch size of 128k: achieving a performance of 450 Tflop/s through enhancements to PyTorch. We demonstrate a Large Hadron Collider (LHC) use-case with the C++ Sherpa simulator and achieve the largest-scale posterior inference in a Turing-complete PPL.
We propose design guidelines for a probabilistic programming facility suitable for deployment as a part of a production software system. As a reference implementation, we introduce Infergo, a probabilistic programming facility for Go, a modern programming language of choice for server-side software development. We argue that a similar probabilistic programming facility can be added to most modern general-purpose programming languages. Probabilistic programming enables automatic tuning of program parameters and algorithmic decision making through probabilistic inference based on the data. To facilitate addition of probabilistic programming capabilities to other programming languages, we share implementation choices and techniques employed in development of Infergo. We illustrate applicability of Infergo to various use cases on case studies, and evaluate Infergo's performance on several benchmarks, comparing Infergo to dedicated inference-centric probabilistic programming frameworks.
Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating data. However, the performance of inference algorithms can be dramatically affected by the parameterisation used to express a model, requiring users to transform their programs in non-intuitive ways. We argue for automating these transformations, and demonstrate that mechanisms available in recent modeling frameworks can implement non-centring and related reparameterisations. This enables new inference algorithms, and we propose two: a simple approach using interleaved sampling and a novel variational formulation that searches over a continuous space of parameterisations. We show that these approaches enable robust inference across a range of models, and can yield more efficient samplers than the best fixed parameterisation.
Epidemiology simulations have become a fundamental tool in the fight against the epidemics of various infectious diseases like AIDS and malaria. However, the complicated and stochastic nature of these simulators can mean their output is difficult to interpret, which reduces their usefulness to policymakers. In this paper, we introduce an approach that allows one to treat a large class of population-based epidemiology simulators as probabilistic generative models. This is achieved by hijacking the internal random number generator calls, through the use of a universal probabilistic programming system (PPS). In contrast to other methods, our approach can be easily retrofitted to simulators written in popular industrial programming frameworks. We demonstrate that our method can be used for interpretable introspection and inference, thus shedding light on black-box simulators. This reinstates much-needed trust between policymakers and evidence-based methods.
We consider probabilistic PCA and related factor models from a Bayesian perspective. These models are in general not identifiable as the likelihood has a rotational symmetry. This gives rise to complicated posterior distributions with continuous subspaces of equal density and thus hinders efficiency of inference as well as interpretation of obtained parameters. In particular, posterior averages over factor loadings become meaningless and only model predictions are unambiguous. Here, we propose a parameterization based on Householder transformations, which remove the rotational symmetry of the posterior. Furthermore, by relying on results from random matrix theory, we establish the parameter distribution which leaves the model unchanged compared to the original rotationally symmetric formulation. In particular, we avoid the need to compute the Jacobian determinant of the parameter transformation. This allows us to efficiently implement probabilistic PCA in a rotation invariant fashion in any state of the art toolbox. Here, we implemented our model in the probabilistic programming language Stan and illustrate it on several examples.
The need to condition distributional properties such as expectation, variance, and entropy arises in algorithmic fairness, model simplification, robustness and many other areas. At face value however, distributional properties are not random variables, and hence conditioning them is a semantic error and type error in probabilistic programming languages. On the other hand, distributional properties are contingent on other variables in the model, change in value when we observe more information, and hence in a precise sense are random variables too. In order to capture the uncertain over distributional properties, we introduce a probability construct -- the random conditional distribution -- and incorporate it into a probabilistic programming language Omega. A random conditional distribution is a higher-order random variable whose realizations are themselves conditional random variables. In Omega we extend distributional properties of random variables to random conditional distributions, such that for example while the expectation a real valued random variable is a real value, the expectation of a random conditional distribution is a distribution over expectations. As a consequence, it requires minimal syntax to encode inference problems over distributional properties, which so far have evaded treatment within probabilistic programming systems and probabilistic modeling in general. We demonstrate our approach case studies in algorithmic fairness and robustness.
Affective Computing is a rapidly growing field spurred by advancements in artificial intelligence, but often, held back by the inability to translate psychological theories of emotion into tractable computational models. To address this, we propose a probabilistic programming approach to affective computing, which models psychological-grounded theories as generative models of emotion, and implements them as stochastic, executable computer programs. We first review probabilistic approaches that integrate reasoning about emotions with reasoning about other latent mental states (e.g., beliefs, desires) in context. Recently-developed probabilistic programming languages offer several key desidarata over previous approaches, such as: (i) flexibility in representing emotions and emotional processes; (ii) modularity and compositionality; (iii) integration with deep learning libraries that facilitate efficient inference and learning from large, naturalistic data; and (iv) ease of adoption. Furthermore, using a probabilistic programming framework allows a standardized platform for theory-building and experimentation: Competing theories (e.g., of appraisal or other emotional processes) can be easily compared via modular substitution of code followed by model comparison. To jumpstart adoption, we illustrate our points with executable code that researchers can easily modify for their own models. We end with a discussion of applications and future directions of the probabilistic programming approach.
Weighted model integration (WMI) extends Weighted model counting (WMC) to the integration of functions over mixed discrete-continuous domains. It has shown tremendous promise for solving inference problems in graphical models and probabilistic programming. Yet, state-of-the-art tools for WMI are limited in terms of performance and ignore the independence structure that is crucial to improving efficiency. To address this limitation, we propose an efficient model integration algorithm for theories with tree primal graphs. We exploit the sparse graph structure by using search to performing integration. Our algorithm greatly improves the computational efficiency on such problems and exploits context-specific independence between variables. Experimental results show dramatic speedups compared to existing WMI solvers on problems with tree-shaped dependencies.
We develop a new Low-level, First-order Probabilistic Programming Language (LF-PPL) suited for models containing a mix of continuous, discrete, and/or piecewise-continuous variables. The key success of this language and its compilation scheme is in its ability to automatically distinguish parameters the density function is discontinuous with respect to, while further providing runtime checks for boundary crossings. This enables the introduction of new inference engines that are able to exploit gradient information, while remaining efficient for models which are not everywhere differentiable. We demonstrate this ability by incorporating a discontinuous Hamiltonian Monte Carlo (DHMC) inference engine that is able to deliver automated and efficient inference for non-differentiable models. Our system is backed up by a mathematical formalism that ensures that any model expressed in this language has a density with measure zero discontinuities to maintain the validity of the inference engine.
We present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. This method is efficient without restrictions on the probabilistic program; it is particularly practical for distributions which are not analytically tractable, including highly structured distributions that arise in probabilistic programs. We show how to automatically derive mean-field probabilistic programs and optimize them, and demonstrate that our perspective improves inference efficiency over other algorithms.
A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to plate diagrams for directed graphical models. To exploit efficient tensor algebra in graphs with plates of variables, we generalize undirected factor graphs to plated factor graphs and variable elimination to a tensor variable elimination algorithm that operates directly on plated factor graphs. Moreover, we generalize complexity bounds based on treewidth and characterize the class of plated factor graphs for which inference is tractable. As an application, we integrate tensor variable elimination into the Pyro probabilistic programming language to enable exact inference in discrete latent variable models with repeated structure. We validate our methods with experiments on both directed and undirected graphical models, including applications to polyphonic music modeling, animal movement modeling, and latent sentiment analysis.
Optimizing an expensive-to-query function is a common task in science and engineering, where it is beneficial to keep the number of queries to a minimum. A popular strategy is Bayesian optimization (BO), which leverages probabilistic models for this task. Most BO today uses Gaussian processes (GPs), or a few other surrogate models. However, there is a broad set of Bayesian modeling techniques that could be used to capture complex systems and reduce the number of queries in BO. Probabilistic programming languages (PPLs) are modern tools that allow for flexible model definition, prior specification, model composition, and automatic inference. In this paper, we develop ProBO, a BO procedure that uses only standard operations common to most PPLs. This allows a user to drop in a model built with an arbitrary PPL and use it directly in BO. We describe acquisition functions for ProBO, and strategies for efficiently optimizing these functions given complex models or costly inference procedures. Using existing PPLs, we implement new models to aid in a few challenging optimization settings, and demonstrate these on model hyperparameter and architecture search tasks.
Pyro is a probabilistic programming language built on Python as a platform for developing advanced probabilistic models in AI research. To scale to large datasets and high-dimensional models, Pyro uses stochastic variational inference algorithms and probability distributions built on top of PyTorch, a modern GPU-accelerated deep learning framework. To accommodate complex or model-specific algorithmic behavior, Pyro leverages Poutine, a library of composable building blocks for modifying the behavior of probabilistic programs.